Research ArticleAssessment of Iterative Closest Point RegistrationAccuracy for Different Phantom Surfaces Captured byan Optical 3D Sensor in Radiotherapy

Gerald Krell1 Nazila Saeid Nezhad1 Mathias Walke2

Ayoub Al-Hamadi1 and Guumlnther Gademann2

1 Institute for Information Technology and Communication Engineering Otto-von-Guericke University MagdeburgUniversitatsplatz 2 39016 Magdeburg Germany2Clinic for Radiotherapy Otto-von-Guericke University Magdeburg Leipziger Straszlige 44 39120 Magdeburg Germany

Correspondence should be addressed to Gerald Krell krellovgude

Received 4 July 2016 Revised 30 September 2016 Accepted 25 October 2016 Published 9 January 2017

Academic Editor Ayman El-Baz

Copyright copy 2017 Gerald Krell et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An optical 3D sensor provides an additional tool for verification of correct patient settlement on a Tomotherapy treatmentmachineThe patientrsquos position in the actual treatment is comparedwith the intended position defined in treatment planning A commerciallyavailable optical 3D sensor measures parts of the body surface and estimates the deviation from the desired position withoutmarkers The registration precision of the in-built algorithm and of selected ICP (iterative closest point) algorithms is investigatedon surface data of specially designed phantoms captured by the optical 3D sensor for predefined shifts of the treatment table A rigidbody transform is compared with the actual displacement to check registration reliability for predefined limits The curvature typeof investigated phantom bodies has a strong influence on registration result which is more critical for surfaces of low curvatureWe investigated the registration accuracy of the optical 3D sensor for the chosen phantoms and compared the results with selectedunconstrained ICP algorithms Safe registration within the clinical limits is only possible for uniquely shaped surface regions buterror metrics based on surface normals improve translational registration Large registration errors clearly hint at setup deviationswhereas small values do not guarantee correct positioning

1 Introduction

Tomotherapy combines a CT scanner with a computer-cont-rolled radiation beam collimation system at the treatmentmachine [1] to precisely target tumors sparing healthy tissueThe system installed inMagdeburg hospital is a TomotherapyHD system which enables helical and fixed radiation in onesingle system A helical slit delivers radiation with most con-formal image guided radiotherapy (imrt) The x-ray sourcerotates in a helical path around the patient in order to acquirea 3D image The same x-ray source is used as treatmentbeam This source is rotating in a helical pattern around thepatient while the intensity of beam is modulated accordingto the tumor shape using ldquotungsten leavesrdquo These leavescreate thousands of beam elements called ldquobeamletsrdquo [2]

The radiation is delivered by a discrete-angle nonrotationalmethod sequentially moving the treatment table from thecenter of the system and for each angle of the gantry Opticalsensors provide an additional tool to verify the precisepositioning of the radiation target relative to the treatmentmachine The actual position in the treatment fraction iscompared with the desired position given by a previouslyrecorded reference surface The reliability of such ICP-basedalgorithms is investigated in this paper by comparing theresults of the implementation by the optical sensor withselected popular algorithms

2 Methods and Materials

21 Optical Sensors in Tomotherapy Nowadays image guidedmethods are increasingly used in radiotherapy [3ndash11] The

HindawiComputational and Mathematical Methods in MedicineVolume 2017 Article ID 2938504 13 pageshttpsdoiorg10115520172938504

2 Computational and Mathematical Methods in Medicine

target regions of irradiation and the intended dose distribu-tions are mostly defined on the basis of CT scans Then anirradiation plan is created which involves the placement ofthe patient with regard to the treatment machine and thecontrol of the irradiation beam The main aim is to hit thetumor with sufficient energy and to protect healthy tissue andorgans as much as possible against irradiation at the sametime Exact placement of the patient in the irradiation sessionis therefore very important In addition to correct positioningby integrated CT in the treatment machine optical sensorscan capture surface data

Optical surface sensors hence provide an additional toolfor contact-less verification of patient position and are nowgetting into clinical practice after a long-time developmentand use for scientific purposes

Our Tomotherapy HD accelerator unit (Accuray USA) iscombinedwith anAlignRT (VisionRTLtd LondonUK) sys-tem and consists of two pods laterally positioned correspond-ing to the virtual isocenter in front of the Tomotherapy boreThevirtual isocenter lies 700mmoutside in front of to the realradiation isocenter of the machine The distances of the twopods in respect to the virtual isocenter are about 20m Thetwopods are tightlymounted at upper ceiling of the treatmentroomThey are right and left of the Tomotherapy couch Eachof the two units each consists of two cameras (stereo) and aspeckle projector producing structured light (Figure 1(a)) togenerate a 3D model of the patientrsquos surface by close-rangephotogrammetry (triangulation) [12] The unit also includesa texture camera for visualization purposes which howeveris not used for alignment [3] The AlignRT parameters of theoptical system are estimated and verified by daily calibrationusing a calibration plate that is aligned with a virtual laserisocenter in front of the real isocenter Real-time capabilityof the AlignRT system relates to the ability of the sensor tocapture surface data fast enough to even follow typical humanmotion caused by respiration for example Although trackingof the surface is fast enough to meet these requirements thefirst registration takes longer and is therefore usually doneoffline

The units are installed at the ceiling in the treatment roomabove of the treatment table and in front of the irradiationgantry in such a way that they capture the body surface atthe target region (isocenter) diagonally downwards from twodirections in order to reduce occluded regions (Figure 1(b))The radiation gantry of the treatment machine is situatedon one point of a circle around the isocenter parallel to the119909119911-axes The 119909 119910 and 119911 position of the treatment tableat the radiation gantry can be shifted computer-controlledwith an accuracy of about 05mm Rotation of the treatmenttable is not possible although in real situations rotationaldisplacement of the patient must be expected

An optical sensor of the considered type estimates adistance map related to a measured surface by finding corre-spondences in images taken from two or more directions byphotogrammetricmethods [12 13] A typical scheme is first tocalculate a standard view of the recorded images by rectifyingthem on the basis of the camera parameters obtained bythe previous calibration Finding the correspondences in theimages gives the disparity maps which describe the parallax

caused by the distance between the cameras of one opticalsensor Together with camera calibration parameters thedepth map is then calculated from the disparity map whichcan be considered as a mesh of 3D points or as a point cloudBecause the depth values are calculated corresponding to thepixel grid neighborhood relations are directly given and amesh grid for instance consisting of triangles can be easilycalculatedThe surfaces of the two optical sensors of AlignRTare merged in one data file At the transition of the surfacedata of one sensor to the other some overlapping or gapsmay occur The software of the optical sensor handles theseproblems and produces a single more or less closed surfaceof triangles out of the data of the two sensors Details arenot given by the manufacturer Rigid registration parametersfor different snapshots of captured 3D surface data can becalculated by the propriety software

Optical sensors provide an additional modality to esti-mate the patient position on the basis of the outer bodyshape without increasing radiation load Here we considerthe application of the optical sensor without use of additionalmarkers The surface data captured is therefore a point cloudor amesh grid corresponding to pixels of the image sensor Insuch an unconstrained setting withoutmarkers we just knowthat a surface point estimated by the optical sensor belongs tosome corresponding point of the surface in the voxel imagecaptured for definition of the 3D planning volume But theexact position of this corresponding point on the surface inthis image which is usually a CT scan is not directly givenThis correspondence can only be estimated out of the formof the reference surface if it is successfully matched withthe surface to be tested In this way corresponding regionsare registered and transformation matrices are calculatedrepresenting a measure for the deviation between a referenceand a test surface

Two operation modes of the surface sensor are distin-guished in clinical practice the static setup verification ofpatient (single-frame surface acquisition) and the trackingof patient motion (continuous dynamic surface acquisitionmode) for example caused by respiration [3] In the lattercase the solid assumption is appropriate if the time step fromone surface capture to the next is small enough

For real patients the shapemay also have been changed inthe static setup phase introducing additional uncertainties inICP registration Respiratorymotion of a patient surface blursthe registration result which is an additional effect and shouldnot bemixedwith the uncertainty of ICP registrationMotionblur in the 3D measurement results may cause additionalproblems Our paper therefore considers the static case andshows that even with solid phantoms uncertainties remaindepending on the individual shape

22 Principles of ICP Algorithms Surface registration assu-mes that two or more surfaces can be matched by a geomet-rical transformation Resulting transformation parametersthen describe the deviation between the surfaces for a correctregistration In case of radiotherapy the optical sensor shouldensure that the patient is placed according to the irradiationplan The desired position is usually defined on basis of theCT data set If we want to compare a test surface measured

Computational and Mathematical Methods in Medicine 3

(a) One of two camera-projector units of AlignRT (opticalsensor) at the ceiling in treatment room It consists of astereo camera and a projector producing structured lightby laser speckle in a fixed arrangement

Left opticalsensor Right optical

sensor

Isocenter

y

z

x

120572roll

120572pitch

120572yaw

Treatment table

(b) Left and right optical sensors at the ceiling above of thetreatment table ldquolookrdquo diagonally downwards at the regionof irradiation (isocenter) Standing in front of the treatmentmachine the 119910-axis of the right-handed coordinate system pointsto the treatment machine 119909 to the right and 119911 to the top Theirradiation gantry hitting the same region is not depicted 120572roll120572pitch and 120572yaw describe the rotations around the 119909- 119910- and119911-axes respectively as shown The treatment table can only betranslationally shifted in 119909 119910 and 119911 direction

Figure 1 Optical sensor in radiotherapy

by optical sensors with the target position we would haveto extract the corresponding surface data out of the CT asa reference Tomotherapy gives us another option becausea CT is directly available at the treatment machine togetherwith the optical sensor we are able to bring the patient exactlyto the desired position by the CT modality The surface scanof the optical sensor at this position can be considered asa reference (target position) In later treatment sessions thememorized reference position can then be used to bring thepatient back to the desired position by the measured testsurface Also during the irradiation itself the correct positioncan be verified by the optical surface scan because in contrastto CT optical data are available during the whole treatment

221 Known Point-to-Point Correspondences The alignmentof surfaces is muchmore simple and unique in case of knowncorrespondences between reference and test surface Thisassumes that registered 119899 points of the reference surface 119901119894 =119901(119909119894 119910119894 119911119894) with index 119894 = 1 119899 and spatial coordinates119909119894 119910119894 119911119894 are ordered in pairs with 119899 points 119902119894 = 119902(119909119894 119910119894 119911119894) ofthe test surface

A linear transformation matrix 119877 and a translation offsetvector 119905 aligning reference and test surface are directlyestimated by minimization of the sum of the squared error

119864 (119877 119905) =119899

sum119894=1

1003817100381710038171003817119901119894 minus 119877119902119894 minus 11990510038171003817100381710038172 997888rarr Min (1)

which means that the (geometric) distance between thereference surface and the transformed test surface shouldbe as small as possible When the correct correspondencesare known a unique solution for 119877 and 119905 for given 119899 =119873 point pairs or a solution in the least square sense for119899 gt 119873 directly yields When limiting to an affine transform

the linear transform matrix with 1198732 parameters modifiesto a rotation matrix with 119873 rotation angles resulting in a2119873-dimensional optimization problem (together with the119873 translation parameters) Such a nonlinear equation cangenerally only be solved iteratively or with a linearizedapproximation assuming small angles

222 Unknown Point-to-Point Correspondences In generalwithout fiducial markers no direct correspondence betweenpoints of the surfaces is given and also the number of pointsto be registered may be different In this situation the trans-formation matrix cannot be determined immediately In ICPalgorithms the closest point in the reference is consideredas the corresponding point of the test surface iterativelyadapting the transformation matrix in each iterative stepSophisticated search strategies exist in order to avoid a com-plete search between the two surfaces The transformation ineach iterative step does not align the two surfaces perfectlybut brings them closer to each other in the converging case

Registration fails in the case of growing deviation betweenthe two surfaces in the iterative steps When convergingthe registration is terminated by a certain criterion suchas size or gradient of the deviation error that is a certainregistration error generally remains for real measurementdata ICP algorithms perform a local search on the errorsurface describing the deviation of the actual measurementfrom the target and estimate translation and rotationmatricesas registration parameter They converge well when a uniqueerrorminimum exists but problemsmay arise when trappingin side minima occurs In the latter case registration isinaccurate or fails completely

Reference [14] gives a good overview on ICP algorithmsfor technical applications with three synthetically generated

4 Computational and Mathematical Methods in Medicine

scenes providing test surfaces to evaluate the variants In thisway the correct transform is known exactly

ICP algorithms can be divided into different phasesAccording to [14] typical ICP algorithms perform the follow-ing steps

(1) Selection of the Source Points (Measurement) Differentcriteria for handling point clouds are considered Using thecomplete set of points to find the transformation parametersmight be slow therefore the data could be randomly or reg-ularly subsampled Another strategy is to extract significantpoints at edges or corners where the information is concen-trated This method of sampling requires preprocessing butit reduces the number of required points improving accuracyand efficiency of the algorithm

(2) Matching This step is the most costly step in ICPalgorithmThere are different methods such as building a kd-tree search to speed up finding corresponding closest pointsThe simplest idea is finding the closest point in the other pointcloud for each point The result of this method is generallystable but it computes slowly Another method to find thecorrespondence is ldquoshootingrdquo along the normal of each pointto the other point cloud The intersection of the normal andpoint cloud is considered as the corresponding point [14]There is a faster method to match the correspondence whichis projection based matching In this method the points lyingon the line of sight of one of the cameras are consideredcorrespondent In this case the result is good if two camerasare close enough [14]

(3) Weighting The matched point pairs can be weightedwith regard to certain additional criteria describing thesimilarity of the corresponding region such as color distancecurvature or direction of tangent normal [14] To this end theerror metric is multiplied by a weighting factor depending onthe specific criterion

(4) Rejection Rejection of certain point pairs can be imple-mented after each matching step in order to improve align-ment This can be done in the phase of search for the closestneighbor Several rejection methods have been proposed indifferent studies [14] rejection of those point pairs witha distance greater than a user specified limit rejection ofa certain portion of point pairs with largest distance andrejection of point pairs inconsistentwith neighbor pairs (rigidtransform)

(5) Error Metric andMinimizationThis step is the last step ofICP algorithm which measures the error between the pointclouds and tries to minimize the distance between two pointcloudsMostly either a ldquopoint-to-pointrdquo or a ldquopoint-to-planerdquoerror metric is applied In the first case if 119901119894 is a source pointand 119902119894 the corresponding point in the target point cloud and119872 is the transformation matrix then the sum of squareddistances has to be calculated and minimized [2]

119872min = argmin119872

119894

sum (119872 sdot 119901119894 minus 119902119894)2 (2)

Closed form solutions for this kind of error metric exist suchas singular value decomposition (SVD) dual quaternionsquaternions and orthonormalmatrices Accuracy and stabil-ity of these methods have been evaluated by [15]

In general point-to-plane error metric converges betterthan the point-to-point error metric [16] It minimizes thesum of squared distances between source points and thetangent plane at the target point which is orthogonal to theunit normal vector of that point Mathematically if 119901119894 is asource point and 119902119894 is the corresponding point in the targetpoint cloud and 119899119894 = 119899(119909119894 119910119894 119911119894) is the normal vector at 119902119894then the ICP algorithm estimates the rigid transformationmatrix by the minimizing function

119872normmin = argmin

119872

sum((119872 sdot 119901119894 minus 119902119894) sdot 119899)2 (3)

Because no closed form solutions for point-to-plane errormetric exist it is usually solved iteratively by nonlinearmethods such as Levenberg-Marquardt or it can be linearizedconsidering some approximation for rotation matrix 119877 suchas replacing sin 120579 by 120579 and cos 120579 by 1 The problem of thepoint-to-plane error metric is that it is sensitive to noise andthat it does not converge well if the distance between twopoint clouds is large [15 17]

The ICP algorithm can vary by changing the methods ineach step to improve the performance with regard to speedand stability depending on the amount of noise and outliersthe algorithm can deal with

23 Selected ICP Algorithms for Registration Four differ-ent under BSD license available ICP implementations inMatlab have been compared with the proprietary softwareof AlignRT for surface registration of phantoms We havechosen the same software platform because one criterionwas the option to compare the speeds We assumed that theimplementations belong to the most popular ones They allmeet the same general ideas of ICP registration and presentthe variety of unconstrained methods (without markers orusing colors) We found that the four chosen ICP algorithmsare well suited to be compared with the method appliedby AlignRT An interesting extension of work would beto include new approaches to point registration such asdescribed in [18]

(1) Wilmrsquos Algorithm [2 19] Point clouds are aligned byconsidering the complete points set The program finds thenearest neighbor by a kd-tree search which considerablyincreases the speed of matching Point-to-point or point-to-plane error metric can be selected by parameter settingAlignRT uses a similar point-to-plane metric as follows fromthe communication with the manufacturer

(2) Kroonrsquos [20] Modified This program uses a finite differ-ence model to align the point clouds The finite differencemethod also supports the transform types of resizing andshearing Several optimization functions are included forminimum searchWe added a global search approach by gen-erating different start points using a scatter-search methodto improve the results All starts points are evaluated and

Computational and Mathematical Methods in Medicine 5

the points which are unlikely to improve the minimum arerejected

(3) Renoaldrsquos [21] It is a simple ICP implementation whichuses all the data points It first finds the corresponding pointsby creating a Delaunay tessellation of points in a model tosearch for the closest pointThen it calculates the initial trans-formation matrix by singular value decomposition (SVD)and applies this to the target point cloudThe transformationmatrix is updated iteratively until no more correspondencescan be found

(4) Bergstromrsquos [22 23] It is similar to the Renoaldrsquos algorithmwith the main difference that after matching correspondingpoints the point pairs are weighted by the maximum pointdistance Levenberg-Marquardt algorithm is directly appliedto minimize the squared sum of the distances of closestpoints

Most of the implementations allow choosing amongmodes and modifying parametersThe best configuration forthis experimental setup has been investigated and shown inTable 3 The above given references give further details

24 Related Works Reference [4] compared suggested setupcorrection with a second and independently operatedmarker-based optical system with an anthropomorphic plas-tic phantom and healthy volunteers They found alignmentaccuracies of about 1mm for translation and 05∘ for rotationas an average Using markers is more invasive and time con-suming but in general safer than unconstrained registration

Extensive research has been done on the developmentof surface sensors The general ideas are shown in worksas [12 13] Reference [24] deals with the simulation ofphotogrammetric triangulation in order to develop the algo-rithms without need of acquisition of additional camera data

Reference [3] investigated the temporal stability of align-ment accuracy in the context of respiratory motion in anoperation mode where the sensor is triggered by the breath-ing phase A rigid flesh-colored mannequin torso phantomhas been used In this approach the optical sensor is com-bined with an infrared-based marker system for gating thebreathing state and a motorized mechanical stage Measuredsurface data has been compared with surface extracted fromCT as a reference High stability and errors in the submillime-ter range and less than 1∘ have been reported Additionallythe accuracy of recommended patient realignment has beenevaluated for 54 random shifts of the treatment table In ourinvestigations we focused our attention on the influence ofdifferent types of phantoms in order to learn how curvatureinfluences the registration reliability

Reference [14] gives helpful results how existing ICPalgorithms converge for synthesized surfaces Also differentsampling strategies for selection of registration points havebeen considered But for clinical practice it is important toverify these theoretical results with the real situation for dataof an existing optical sensor

Reference [7] evaluates a 3-Dimensional Surface ImagingSystem for Guidance in DIBH Therapy Setup data based on

captured 3D surfaces by the same surface imaging systemas we used was compared with setup data based on conebeam computed tomography (CBCT) and evaluated withregression based methods It was found that in the contextof breast cancer treatment 95 of the deviations less than04 cm detected by the optical sensor were less than 066 cmin the other mode of CBCT A comparison of megavoltageCBCT based registration and of AlignRT based registrationto its own particular reference is subjected to certain timeconstraints A CT scan itself as a possible reference and thelocal megavoltage CBCT scan on the Tomotherapy unit isusually a time-consuming procedure

Reference [6] reports on two commercial optical sensors(surface imaging systems) and compares them with theactual adjustments in patient positions made on the basis ofmegavoltage CT scans The deviations between the proposedcorrection of the optical sensor and the subjectively bestalignment of an expert have been statistically evaluatedTests have been performed on an Alderson phantom andon patients at headneck pelvic and chest regions It wasfound that the optical sensors can support patient positioningmainly at pelvic and chest regions because immobilization ofthe patient by special masks is not possible as in the case ofhead and neck region

Generally the AlignRT system is usable on nearly allpossible patient regions Some papers deal with clinicalapplications of optical sensors to different patient regionsBesides classical patient body region dependent applicationsthe frame- and mask-less cranial stereotactic radiosurgery isa new application field The comparison of breath inducedsurface movements with different registration modalitiesis subjected to different time constants of the acquisitiondevices The verification of DIBH (depth inspiration breath-hold) techniques with optical systems as theAlignRT systemis a new emerging procedure in the clinical practice

A feasibility study for the usability of the AlignRT systemto frame- and mask-less cranial stereotactic was presentedby [8] The presented technique shows the potential ofhead mold and surface monitoring to use in stereotactictreatments The accuracy of the surface imaging motiontracking system during the stereotactic treatment was ver-ified The results were additionally tested on the standardoptical guidance platform technique (kVCT by Varian)

Work [9] describes a clinical analysis of fifty patientswith the AlignRT system in comparison to megavoltageportal imaging Daily alignment with the 3D optical imagingsystem was found to be valuable for reducing setup errorsin comparison to skin markers Particularly the anterior-posterior alignment directions were with the optical systemnoticeably better

The possible synchronization of a classical CBCT systemwith the AlignRT has been shown by [10] An image guidedmethod for the synchronization of the X-ray projectionsis synchronized with optically sensed surface during usingCBCT without any further hardware requirements The pro-posedmethod can by generically applied to any configurationof the CBCT and optical imaging systems and also be used forextracranial tumor tracking

6 Computational and Mathematical Methods in Medicine

3 Generation of Test Surface Data

In order to generate surface data we focused our work onrigid phantoms because we are mostly interested in pureaccuracy of the sensor togetherwith the ICP algorithms in theideal caseThe investigated ICP algorithms do not treat shapevariations which is a motivation for using solid phantomsinstead of real cases The influence of motion of real humanbodies caused by respiration for instance is considered byother papers (eg [10 11])

31 Test Phantoms Because the contour characteristics of asurface is important for a safe registration specially designedphantoms of different surface types have been investigated Tothis end dedicated phantoms have been designed or selectedwith a size approximately covering the measurement volumeof the optical sensor of about 01m3 In this study fourdifferent phantoms have been measured by the optical sensorin order to generate point clouds for the evaluation of the ICPalgorithms

(i) Plane It is a simple plane horizontally placed on thetreatment tableThemain idea is to check the accuracy of theoptical sensor with regard to vertical shift of the treatmenttable (119911 direction)

(ii) 3plane It consists of two planes and an edge especiallybuilt to allow a unique matching with respect to all 119909-119910-119911space coordinates

(iii) BowlThebowl phantom ismore curved than a plane butambiguities with regard to rotations must be expected

(iv) Torso By the torso of amannequin a shape typical for thehuman body has been simulated The curvature of the torsophantom ismore ambiguous in the cranial-caudal (119910) than inthe dorsal-ventral transverse motion direction

The phantoms have been coated by white painting ortextile to produce a surface that can be well captured bythe cameras of the optical sensor when illuminated by thespeckle projector Measured point clouds of these phantomsare shown in Figure 2 As visible in Figure 2(c) the measuredsurfaces contained some points of the background (eg of thetreatment table) Such extra points obviously not originatingfrom the phantoms have been manually removed for the dataof all phantoms As an example Figures 2(c) and 2(d) showthe bowl surface before and after removing the extra pointsrespectively

32 Test Setup The above described ICP algorithms havebeen tested with surface data of the selected phantoms(Figure 2) moved to well-defined positions First the opti-cal sensor AlignRT has been calibrated according to theinstructions of the manufacturer Then the phantoms havebeen placed on the treatment table and a surface scan atthe origin has been captured This surface scan at central(zero) position of the treatment table served as a referenceto compare with surface scans at other positions To this

end the phantoms have been translationally shifted by thetreatment table in the directions 119889 = 119909 119910 119911 by distancesof 119904119889 = 05 10 plusmn100 200 (mm) For the plane translationwas only done in 119911 direction (119889 = 119911) because tests confirmthe obvious fact that a motion in 119909 or 119910 direction cannot bedetected if the plane phantom is placed in parallel to the 119909-119910-axes as we did

Figure 3 gives an example on how the operator sees thesituation on the monitoring screen of AlignRT It shows theestimated misalignment for translation and rotation in mmand ∘ respectively by numbers with one-digit accuracy afterthe comma and by bars At setup the therapists attempt tominimize the shifts (by minimizing the length of the bars)[11] The surface data is exported as object files and used forthe registration by the other ICP algorithms

After an initial phase real-time surface tracking is pos-sible with the AlignRT system AlignRT system deliverssufficiently fast displacement estimation for most medicalindications of about 10 frames per second Acceptable speedrelates mainly to the time needed for an initial alignmentwhich should not exceed about a second in order to beacceptable in clinical routine

Therefore two requirements result with regard to thespeed the alignment time should not be much longer than asecond because more cannot be accepted in clinical routine

In case of dynamic tracking the speed demands arise bythe typical patient motion to avoid subsampling on the onehand and to ensure that shape variations between two timesteps can be neglected for rigid registration In the ideal casethe registration should be faster than the surface sensor inorder to avoid reduction of frame rate

4 Results and Discussion

Rigid transform matrices (translation and rotation) for reg-istration of the reference with the tested position have beenestimated by the proposed ICP algorithms and with AlignRTThe investigated implementations specify the resulting coor-dinate transform for registration by different versions ofmatrices for homogenous coordinates For direct compar-ison these matrices have been transformed into a singlerepresentation for translation and rotation (see [12])

Translational shift values of registration 119889 in direction 119889yield directly from the offset part of the transform matricesTable 1 shows the results of registration together with theexpected translation values 119904119889 The translational registrationerror in direction 119889 is then given by 119890trans119889 = 119904119889 minus 119889

The total registered rotation is composed by a series ofthree rotations 119903 = roll pitch yaw around 119909- 119910- and 119911-axes respectively in the directions according to Figure 1(b)each quantified by the Euler angles 119903 = roll pitch yawThe rotatory registration error is 119890rot119903 = 119903minus120572119903 = 119903 for 120572119903 = 0because the measurement phantoms have not been rotated

We assumed a maximally allowed absolute registrationerror of 119890trans119889 max = 1mm for translation and of 119890rot119889 max = 05

∘

for rotation which are quite tough values in radiotherapy andmarked entries with |119890trans119889 | gt 119890

trans119889 max or |119890trans119889 | gt 119890

rot119889 max

boldface Other works set the allowable tolerance a bit higher

Computational and Mathematical Methods in Medicine 7

(a) Plane (b) 3plane (c) Bowl (before removingextra points)

(d) Bowl (after removingthe extra points)

(e) Torso

Figure 2 Surfaces of selected phantoms captured by the optical sensor AlginRT showing typical problems of real measurement data (a)measurement noise and systematic errors (c) extra points not belonging to the object of interest (b) and (e) seam from fusing the twosurfaces of left and right optical sensors

Figure 3 An example of the AlignRT monitoring screen seenduring measurement of the torso phantom and vertical shift ofthe treatment table 119904119889(119911) = 10mm The reference surface is shownin pink and the measured surface in green The suggested lineartranslations (vertical lateral and longitudinal) and rotations (yawpitch and roll) are shown by numbers and colored bars on the lefttogether with the RMS value (called magnitude MAG) The whitegraph is used to display a time series of the RMS values (not used inour experiment)

(eg [8] to 1mm1∘ and [11] to 3mm3∘) but working withrigid phantoms without motion motivates our stricter limits

Figure 4 shows as an example one of the best results ofaligned surfaces with the reference surface for a shift of 119904119889 =10mm in direction 119889 = 119911 using the Wilm approach Theresiduals have been estimated by triangulation of the surfacesand color-coded displaying the distances in 119911 direction Itbecomes clear that although the translational and rotationalparameters are within the limits this does not hold for allpoints of the surfacesThere are problems especially at slopingsurface parts at edges and at the stitching area of left andright optical sensors which explains the remaining deviationsafter applying the ICP algorithm

Table 2 summarizes Table 1 with regard to adhering thelimits 119890trans119889 max and 119890

rot119889 max As expected with the plane phan-

tom placed in parallel to the 119909119910 plane a safe registration isonly possible in 119911 direction and fails in 119909 and 119910 direction forall ICP algorithms For the other three phantoms 3planebowl and torso only the Wilm algorithm registers safely forthe translational parameters No algorithmhas problemswiththe rotatory parameters for any phantom except Wilm whichinterestingly fails for the torso phantom for pitch and yaw andAlignRT for yaw of the bowl phantom

Table 3 compares some important properties and resultsof the four tested algorithms that have been applied to fourdifferent test objects (phantoms) differently shifted relative toan original position The algorithms use different methodsto compute the rigid transformation matrix (translationand rotation) between two point clouds as described inSection 23 as the result of registration

Main operational principles of the algorithms are summa-rized their processing speed and accuracy give informationon their suitability for registration of our selected phantomsMain differences consist in the method for the closest pointsearch the weighting the error metric and the methodfor minimization Only Wilm uses kd-tree search whichis much more efficient than full search Only Bergstromapplies distance-based weighting None of the open sourcealgorithms includes rejection Among the open source algo-rithms only Wilm uses point-to-plane metric whereas allother apply a point-to-point criterion The AlignRT registra-tion results look similar to the Wilm implementation Thissupports the assumption that similar principles are used bythis proprietary program

The average processing time for each algorithm is alsoqualitatively given It varies between fastest processing(which was about a few seconds) and slowest processing(which was about 3 minutes) for the registration by theICP algorithm on a standard computer (Intel Core i7 64-bit Windows) in Matlab A more detailed evaluation ofprocessing speed is not given because we do not expect thatthe chosen algorithms are implemented in an optimal wayThis may be different for the commercial implementation ofAlignRT Renoald performed best with regard to processingspeedWilm and AlignRT show acceptable speed in the samerange Kroon is slow and Bergstrom is very slow in theinvestigated implementation and would not be acceptable inclinical routine

For offline verification speed plays a less important role aslong as the registration takes only seconds of time Thereforethose implementations indicated by + or ++ can be consid-ered acceptable in the intended application (see Section 32)In tracking applications when even the registration is doneonline the speed of the algorithms matters much more andthe patient alignment can be verified and corrected on the flybymoving the treatment table or adapting the irradiation But

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

Computational and Mathematical Methods in Medicine 3

(a) One of two camera-projector units of AlignRT (opticalsensor) at the ceiling in treatment room It consists of astereo camera and a projector producing structured lightby laser speckle in a fixed arrangement

Left opticalsensor Right optical

sensor

Isocenter

y

z

x

120572roll

120572pitch

120572yaw

Treatment table

(b) Left and right optical sensors at the ceiling above of thetreatment table ldquolookrdquo diagonally downwards at the regionof irradiation (isocenter) Standing in front of the treatmentmachine the 119910-axis of the right-handed coordinate system pointsto the treatment machine 119909 to the right and 119911 to the top Theirradiation gantry hitting the same region is not depicted 120572roll120572pitch and 120572yaw describe the rotations around the 119909- 119910- and119911-axes respectively as shown The treatment table can only betranslationally shifted in 119909 119910 and 119911 direction

Figure 1 Optical sensor in radiotherapy

by optical sensors with the target position we would haveto extract the corresponding surface data out of the CT asa reference Tomotherapy gives us another option becausea CT is directly available at the treatment machine togetherwith the optical sensor we are able to bring the patient exactlyto the desired position by the CT modality The surface scanof the optical sensor at this position can be considered asa reference (target position) In later treatment sessions thememorized reference position can then be used to bring thepatient back to the desired position by the measured testsurface Also during the irradiation itself the correct positioncan be verified by the optical surface scan because in contrastto CT optical data are available during the whole treatment

221 Known Point-to-Point Correspondences The alignmentof surfaces is muchmore simple and unique in case of knowncorrespondences between reference and test surface Thisassumes that registered 119899 points of the reference surface 119901119894 =119901(119909119894 119910119894 119911119894) with index 119894 = 1 119899 and spatial coordinates119909119894 119910119894 119911119894 are ordered in pairs with 119899 points 119902119894 = 119902(119909119894 119910119894 119911119894) ofthe test surface

A linear transformation matrix 119877 and a translation offsetvector 119905 aligning reference and test surface are directlyestimated by minimization of the sum of the squared error

119864 (119877 119905) =119899

sum119894=1

1003817100381710038171003817119901119894 minus 119877119902119894 minus 11990510038171003817100381710038172 997888rarr Min (1)

which means that the (geometric) distance between thereference surface and the transformed test surface shouldbe as small as possible When the correct correspondencesare known a unique solution for 119877 and 119905 for given 119899 =119873 point pairs or a solution in the least square sense for119899 gt 119873 directly yields When limiting to an affine transform

the linear transform matrix with 1198732 parameters modifiesto a rotation matrix with 119873 rotation angles resulting in a2119873-dimensional optimization problem (together with the119873 translation parameters) Such a nonlinear equation cangenerally only be solved iteratively or with a linearizedapproximation assuming small angles

222 Unknown Point-to-Point Correspondences In generalwithout fiducial markers no direct correspondence betweenpoints of the surfaces is given and also the number of pointsto be registered may be different In this situation the trans-formation matrix cannot be determined immediately In ICPalgorithms the closest point in the reference is consideredas the corresponding point of the test surface iterativelyadapting the transformation matrix in each iterative stepSophisticated search strategies exist in order to avoid a com-plete search between the two surfaces The transformation ineach iterative step does not align the two surfaces perfectlybut brings them closer to each other in the converging case

Registration fails in the case of growing deviation betweenthe two surfaces in the iterative steps When convergingthe registration is terminated by a certain criterion suchas size or gradient of the deviation error that is a certainregistration error generally remains for real measurementdata ICP algorithms perform a local search on the errorsurface describing the deviation of the actual measurementfrom the target and estimate translation and rotationmatricesas registration parameter They converge well when a uniqueerrorminimum exists but problemsmay arise when trappingin side minima occurs In the latter case registration isinaccurate or fails completely

Reference [14] gives a good overview on ICP algorithmsfor technical applications with three synthetically generated

4 Computational and Mathematical Methods in Medicine

scenes providing test surfaces to evaluate the variants In thisway the correct transform is known exactly

ICP algorithms can be divided into different phasesAccording to [14] typical ICP algorithms perform the follow-ing steps

(1) Selection of the Source Points (Measurement) Differentcriteria for handling point clouds are considered Using thecomplete set of points to find the transformation parametersmight be slow therefore the data could be randomly or reg-ularly subsampled Another strategy is to extract significantpoints at edges or corners where the information is concen-trated This method of sampling requires preprocessing butit reduces the number of required points improving accuracyand efficiency of the algorithm

(2) Matching This step is the most costly step in ICPalgorithmThere are different methods such as building a kd-tree search to speed up finding corresponding closest pointsThe simplest idea is finding the closest point in the other pointcloud for each point The result of this method is generallystable but it computes slowly Another method to find thecorrespondence is ldquoshootingrdquo along the normal of each pointto the other point cloud The intersection of the normal andpoint cloud is considered as the corresponding point [14]There is a faster method to match the correspondence whichis projection based matching In this method the points lyingon the line of sight of one of the cameras are consideredcorrespondent In this case the result is good if two camerasare close enough [14]

(3) Weighting The matched point pairs can be weightedwith regard to certain additional criteria describing thesimilarity of the corresponding region such as color distancecurvature or direction of tangent normal [14] To this end theerror metric is multiplied by a weighting factor depending onthe specific criterion

(4) Rejection Rejection of certain point pairs can be imple-mented after each matching step in order to improve align-ment This can be done in the phase of search for the closestneighbor Several rejection methods have been proposed indifferent studies [14] rejection of those point pairs witha distance greater than a user specified limit rejection ofa certain portion of point pairs with largest distance andrejection of point pairs inconsistentwith neighbor pairs (rigidtransform)

(5) Error Metric andMinimizationThis step is the last step ofICP algorithm which measures the error between the pointclouds and tries to minimize the distance between two pointcloudsMostly either a ldquopoint-to-pointrdquo or a ldquopoint-to-planerdquoerror metric is applied In the first case if 119901119894 is a source pointand 119902119894 the corresponding point in the target point cloud and119872 is the transformation matrix then the sum of squareddistances has to be calculated and minimized [2]

119872min = argmin119872

119894

sum (119872 sdot 119901119894 minus 119902119894)2 (2)

Closed form solutions for this kind of error metric exist suchas singular value decomposition (SVD) dual quaternionsquaternions and orthonormalmatrices Accuracy and stabil-ity of these methods have been evaluated by [15]

In general point-to-plane error metric converges betterthan the point-to-point error metric [16] It minimizes thesum of squared distances between source points and thetangent plane at the target point which is orthogonal to theunit normal vector of that point Mathematically if 119901119894 is asource point and 119902119894 is the corresponding point in the targetpoint cloud and 119899119894 = 119899(119909119894 119910119894 119911119894) is the normal vector at 119902119894then the ICP algorithm estimates the rigid transformationmatrix by the minimizing function

119872normmin = argmin

119872

sum((119872 sdot 119901119894 minus 119902119894) sdot 119899)2 (3)

Because no closed form solutions for point-to-plane errormetric exist it is usually solved iteratively by nonlinearmethods such as Levenberg-Marquardt or it can be linearizedconsidering some approximation for rotation matrix 119877 suchas replacing sin 120579 by 120579 and cos 120579 by 1 The problem of thepoint-to-plane error metric is that it is sensitive to noise andthat it does not converge well if the distance between twopoint clouds is large [15 17]

The ICP algorithm can vary by changing the methods ineach step to improve the performance with regard to speedand stability depending on the amount of noise and outliersthe algorithm can deal with

23 Selected ICP Algorithms for Registration Four differ-ent under BSD license available ICP implementations inMatlab have been compared with the proprietary softwareof AlignRT for surface registration of phantoms We havechosen the same software platform because one criterionwas the option to compare the speeds We assumed that theimplementations belong to the most popular ones They allmeet the same general ideas of ICP registration and presentthe variety of unconstrained methods (without markers orusing colors) We found that the four chosen ICP algorithmsare well suited to be compared with the method appliedby AlignRT An interesting extension of work would beto include new approaches to point registration such asdescribed in [18]

(1) Wilmrsquos Algorithm [2 19] Point clouds are aligned byconsidering the complete points set The program finds thenearest neighbor by a kd-tree search which considerablyincreases the speed of matching Point-to-point or point-to-plane error metric can be selected by parameter settingAlignRT uses a similar point-to-plane metric as follows fromthe communication with the manufacturer

(2) Kroonrsquos [20] Modified This program uses a finite differ-ence model to align the point clouds The finite differencemethod also supports the transform types of resizing andshearing Several optimization functions are included forminimum searchWe added a global search approach by gen-erating different start points using a scatter-search methodto improve the results All starts points are evaluated and

Computational and Mathematical Methods in Medicine 5

the points which are unlikely to improve the minimum arerejected

(3) Renoaldrsquos [21] It is a simple ICP implementation whichuses all the data points It first finds the corresponding pointsby creating a Delaunay tessellation of points in a model tosearch for the closest pointThen it calculates the initial trans-formation matrix by singular value decomposition (SVD)and applies this to the target point cloudThe transformationmatrix is updated iteratively until no more correspondencescan be found

(4) Bergstromrsquos [22 23] It is similar to the Renoaldrsquos algorithmwith the main difference that after matching correspondingpoints the point pairs are weighted by the maximum pointdistance Levenberg-Marquardt algorithm is directly appliedto minimize the squared sum of the distances of closestpoints

Most of the implementations allow choosing amongmodes and modifying parametersThe best configuration forthis experimental setup has been investigated and shown inTable 3 The above given references give further details

24 Related Works Reference [4] compared suggested setupcorrection with a second and independently operatedmarker-based optical system with an anthropomorphic plas-tic phantom and healthy volunteers They found alignmentaccuracies of about 1mm for translation and 05∘ for rotationas an average Using markers is more invasive and time con-suming but in general safer than unconstrained registration

Extensive research has been done on the developmentof surface sensors The general ideas are shown in worksas [12 13] Reference [24] deals with the simulation ofphotogrammetric triangulation in order to develop the algo-rithms without need of acquisition of additional camera data

Reference [3] investigated the temporal stability of align-ment accuracy in the context of respiratory motion in anoperation mode where the sensor is triggered by the breath-ing phase A rigid flesh-colored mannequin torso phantomhas been used In this approach the optical sensor is com-bined with an infrared-based marker system for gating thebreathing state and a motorized mechanical stage Measuredsurface data has been compared with surface extracted fromCT as a reference High stability and errors in the submillime-ter range and less than 1∘ have been reported Additionallythe accuracy of recommended patient realignment has beenevaluated for 54 random shifts of the treatment table In ourinvestigations we focused our attention on the influence ofdifferent types of phantoms in order to learn how curvatureinfluences the registration reliability

Reference [14] gives helpful results how existing ICPalgorithms converge for synthesized surfaces Also differentsampling strategies for selection of registration points havebeen considered But for clinical practice it is important toverify these theoretical results with the real situation for dataof an existing optical sensor

Reference [7] evaluates a 3-Dimensional Surface ImagingSystem for Guidance in DIBH Therapy Setup data based on

captured 3D surfaces by the same surface imaging systemas we used was compared with setup data based on conebeam computed tomography (CBCT) and evaluated withregression based methods It was found that in the contextof breast cancer treatment 95 of the deviations less than04 cm detected by the optical sensor were less than 066 cmin the other mode of CBCT A comparison of megavoltageCBCT based registration and of AlignRT based registrationto its own particular reference is subjected to certain timeconstraints A CT scan itself as a possible reference and thelocal megavoltage CBCT scan on the Tomotherapy unit isusually a time-consuming procedure

Reference [6] reports on two commercial optical sensors(surface imaging systems) and compares them with theactual adjustments in patient positions made on the basis ofmegavoltage CT scans The deviations between the proposedcorrection of the optical sensor and the subjectively bestalignment of an expert have been statistically evaluatedTests have been performed on an Alderson phantom andon patients at headneck pelvic and chest regions It wasfound that the optical sensors can support patient positioningmainly at pelvic and chest regions because immobilization ofthe patient by special masks is not possible as in the case ofhead and neck region

Generally the AlignRT system is usable on nearly allpossible patient regions Some papers deal with clinicalapplications of optical sensors to different patient regionsBesides classical patient body region dependent applicationsthe frame- and mask-less cranial stereotactic radiosurgery isa new application field The comparison of breath inducedsurface movements with different registration modalitiesis subjected to different time constants of the acquisitiondevices The verification of DIBH (depth inspiration breath-hold) techniques with optical systems as theAlignRT systemis a new emerging procedure in the clinical practice

A feasibility study for the usability of the AlignRT systemto frame- and mask-less cranial stereotactic was presentedby [8] The presented technique shows the potential ofhead mold and surface monitoring to use in stereotactictreatments The accuracy of the surface imaging motiontracking system during the stereotactic treatment was ver-ified The results were additionally tested on the standardoptical guidance platform technique (kVCT by Varian)

Work [9] describes a clinical analysis of fifty patientswith the AlignRT system in comparison to megavoltageportal imaging Daily alignment with the 3D optical imagingsystem was found to be valuable for reducing setup errorsin comparison to skin markers Particularly the anterior-posterior alignment directions were with the optical systemnoticeably better

The possible synchronization of a classical CBCT systemwith the AlignRT has been shown by [10] An image guidedmethod for the synchronization of the X-ray projectionsis synchronized with optically sensed surface during usingCBCT without any further hardware requirements The pro-posedmethod can by generically applied to any configurationof the CBCT and optical imaging systems and also be used forextracranial tumor tracking

6 Computational and Mathematical Methods in Medicine

3 Generation of Test Surface Data

In order to generate surface data we focused our work onrigid phantoms because we are mostly interested in pureaccuracy of the sensor togetherwith the ICP algorithms in theideal caseThe investigated ICP algorithms do not treat shapevariations which is a motivation for using solid phantomsinstead of real cases The influence of motion of real humanbodies caused by respiration for instance is considered byother papers (eg [10 11])

31 Test Phantoms Because the contour characteristics of asurface is important for a safe registration specially designedphantoms of different surface types have been investigated Tothis end dedicated phantoms have been designed or selectedwith a size approximately covering the measurement volumeof the optical sensor of about 01m3 In this study fourdifferent phantoms have been measured by the optical sensorin order to generate point clouds for the evaluation of the ICPalgorithms

(i) Plane It is a simple plane horizontally placed on thetreatment tableThemain idea is to check the accuracy of theoptical sensor with regard to vertical shift of the treatmenttable (119911 direction)

(ii) 3plane It consists of two planes and an edge especiallybuilt to allow a unique matching with respect to all 119909-119910-119911space coordinates

(iii) BowlThebowl phantom ismore curved than a plane butambiguities with regard to rotations must be expected

(iv) Torso By the torso of amannequin a shape typical for thehuman body has been simulated The curvature of the torsophantom ismore ambiguous in the cranial-caudal (119910) than inthe dorsal-ventral transverse motion direction

The phantoms have been coated by white painting ortextile to produce a surface that can be well captured bythe cameras of the optical sensor when illuminated by thespeckle projector Measured point clouds of these phantomsare shown in Figure 2 As visible in Figure 2(c) the measuredsurfaces contained some points of the background (eg of thetreatment table) Such extra points obviously not originatingfrom the phantoms have been manually removed for the dataof all phantoms As an example Figures 2(c) and 2(d) showthe bowl surface before and after removing the extra pointsrespectively

32 Test Setup The above described ICP algorithms havebeen tested with surface data of the selected phantoms(Figure 2) moved to well-defined positions First the opti-cal sensor AlignRT has been calibrated according to theinstructions of the manufacturer Then the phantoms havebeen placed on the treatment table and a surface scan atthe origin has been captured This surface scan at central(zero) position of the treatment table served as a referenceto compare with surface scans at other positions To this

end the phantoms have been translationally shifted by thetreatment table in the directions 119889 = 119909 119910 119911 by distancesof 119904119889 = 05 10 plusmn100 200 (mm) For the plane translationwas only done in 119911 direction (119889 = 119911) because tests confirmthe obvious fact that a motion in 119909 or 119910 direction cannot bedetected if the plane phantom is placed in parallel to the 119909-119910-axes as we did

Figure 3 gives an example on how the operator sees thesituation on the monitoring screen of AlignRT It shows theestimated misalignment for translation and rotation in mmand ∘ respectively by numbers with one-digit accuracy afterthe comma and by bars At setup the therapists attempt tominimize the shifts (by minimizing the length of the bars)[11] The surface data is exported as object files and used forthe registration by the other ICP algorithms

After an initial phase real-time surface tracking is pos-sible with the AlignRT system AlignRT system deliverssufficiently fast displacement estimation for most medicalindications of about 10 frames per second Acceptable speedrelates mainly to the time needed for an initial alignmentwhich should not exceed about a second in order to beacceptable in clinical routine

Therefore two requirements result with regard to thespeed the alignment time should not be much longer than asecond because more cannot be accepted in clinical routine

In case of dynamic tracking the speed demands arise bythe typical patient motion to avoid subsampling on the onehand and to ensure that shape variations between two timesteps can be neglected for rigid registration In the ideal casethe registration should be faster than the surface sensor inorder to avoid reduction of frame rate

4 Results and Discussion

Rigid transform matrices (translation and rotation) for reg-istration of the reference with the tested position have beenestimated by the proposed ICP algorithms and with AlignRTThe investigated implementations specify the resulting coor-dinate transform for registration by different versions ofmatrices for homogenous coordinates For direct compar-ison these matrices have been transformed into a singlerepresentation for translation and rotation (see [12])

Translational shift values of registration 119889 in direction 119889yield directly from the offset part of the transform matricesTable 1 shows the results of registration together with theexpected translation values 119904119889 The translational registrationerror in direction 119889 is then given by 119890trans119889 = 119904119889 minus 119889

The total registered rotation is composed by a series ofthree rotations 119903 = roll pitch yaw around 119909- 119910- and 119911-axes respectively in the directions according to Figure 1(b)each quantified by the Euler angles 119903 = roll pitch yawThe rotatory registration error is 119890rot119903 = 119903minus120572119903 = 119903 for 120572119903 = 0because the measurement phantoms have not been rotated

We assumed a maximally allowed absolute registrationerror of 119890trans119889 max = 1mm for translation and of 119890rot119889 max = 05

∘

for rotation which are quite tough values in radiotherapy andmarked entries with |119890trans119889 | gt 119890

trans119889 max or |119890trans119889 | gt 119890

rot119889 max

boldface Other works set the allowable tolerance a bit higher

Computational and Mathematical Methods in Medicine 7

(a) Plane (b) 3plane (c) Bowl (before removingextra points)

(d) Bowl (after removingthe extra points)

(e) Torso

Figure 2 Surfaces of selected phantoms captured by the optical sensor AlginRT showing typical problems of real measurement data (a)measurement noise and systematic errors (c) extra points not belonging to the object of interest (b) and (e) seam from fusing the twosurfaces of left and right optical sensors

Figure 3 An example of the AlignRT monitoring screen seenduring measurement of the torso phantom and vertical shift ofthe treatment table 119904119889(119911) = 10mm The reference surface is shownin pink and the measured surface in green The suggested lineartranslations (vertical lateral and longitudinal) and rotations (yawpitch and roll) are shown by numbers and colored bars on the lefttogether with the RMS value (called magnitude MAG) The whitegraph is used to display a time series of the RMS values (not used inour experiment)

(eg [8] to 1mm1∘ and [11] to 3mm3∘) but working withrigid phantoms without motion motivates our stricter limits

Figure 4 shows as an example one of the best results ofaligned surfaces with the reference surface for a shift of 119904119889 =10mm in direction 119889 = 119911 using the Wilm approach Theresiduals have been estimated by triangulation of the surfacesand color-coded displaying the distances in 119911 direction Itbecomes clear that although the translational and rotationalparameters are within the limits this does not hold for allpoints of the surfacesThere are problems especially at slopingsurface parts at edges and at the stitching area of left andright optical sensors which explains the remaining deviationsafter applying the ICP algorithm

Table 2 summarizes Table 1 with regard to adhering thelimits 119890trans119889 max and 119890

rot119889 max As expected with the plane phan-

tom placed in parallel to the 119909119910 plane a safe registration isonly possible in 119911 direction and fails in 119909 and 119910 direction forall ICP algorithms For the other three phantoms 3planebowl and torso only the Wilm algorithm registers safely forthe translational parameters No algorithmhas problemswiththe rotatory parameters for any phantom except Wilm whichinterestingly fails for the torso phantom for pitch and yaw andAlignRT for yaw of the bowl phantom

Table 3 compares some important properties and resultsof the four tested algorithms that have been applied to fourdifferent test objects (phantoms) differently shifted relative toan original position The algorithms use different methodsto compute the rigid transformation matrix (translationand rotation) between two point clouds as described inSection 23 as the result of registration

Main operational principles of the algorithms are summa-rized their processing speed and accuracy give informationon their suitability for registration of our selected phantomsMain differences consist in the method for the closest pointsearch the weighting the error metric and the methodfor minimization Only Wilm uses kd-tree search whichis much more efficient than full search Only Bergstromapplies distance-based weighting None of the open sourcealgorithms includes rejection Among the open source algo-rithms only Wilm uses point-to-plane metric whereas allother apply a point-to-point criterion The AlignRT registra-tion results look similar to the Wilm implementation Thissupports the assumption that similar principles are used bythis proprietary program

The average processing time for each algorithm is alsoqualitatively given It varies between fastest processing(which was about a few seconds) and slowest processing(which was about 3 minutes) for the registration by theICP algorithm on a standard computer (Intel Core i7 64-bit Windows) in Matlab A more detailed evaluation ofprocessing speed is not given because we do not expect thatthe chosen algorithms are implemented in an optimal wayThis may be different for the commercial implementation ofAlignRT Renoald performed best with regard to processingspeedWilm and AlignRT show acceptable speed in the samerange Kroon is slow and Bergstrom is very slow in theinvestigated implementation and would not be acceptable inclinical routine

For offline verification speed plays a less important role aslong as the registration takes only seconds of time Thereforethose implementations indicated by + or ++ can be consid-ered acceptable in the intended application (see Section 32)In tracking applications when even the registration is doneonline the speed of the algorithms matters much more andthe patient alignment can be verified and corrected on the flybymoving the treatment table or adapting the irradiation But

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

4 Computational and Mathematical Methods in Medicine

scenes providing test surfaces to evaluate the variants In thisway the correct transform is known exactly

ICP algorithms can be divided into different phasesAccording to [14] typical ICP algorithms perform the follow-ing steps

(1) Selection of the Source Points (Measurement) Differentcriteria for handling point clouds are considered Using thecomplete set of points to find the transformation parametersmight be slow therefore the data could be randomly or reg-ularly subsampled Another strategy is to extract significantpoints at edges or corners where the information is concen-trated This method of sampling requires preprocessing butit reduces the number of required points improving accuracyand efficiency of the algorithm

(2) Matching This step is the most costly step in ICPalgorithmThere are different methods such as building a kd-tree search to speed up finding corresponding closest pointsThe simplest idea is finding the closest point in the other pointcloud for each point The result of this method is generallystable but it computes slowly Another method to find thecorrespondence is ldquoshootingrdquo along the normal of each pointto the other point cloud The intersection of the normal andpoint cloud is considered as the corresponding point [14]There is a faster method to match the correspondence whichis projection based matching In this method the points lyingon the line of sight of one of the cameras are consideredcorrespondent In this case the result is good if two camerasare close enough [14]

(3) Weighting The matched point pairs can be weightedwith regard to certain additional criteria describing thesimilarity of the corresponding region such as color distancecurvature or direction of tangent normal [14] To this end theerror metric is multiplied by a weighting factor depending onthe specific criterion

(4) Rejection Rejection of certain point pairs can be imple-mented after each matching step in order to improve align-ment This can be done in the phase of search for the closestneighbor Several rejection methods have been proposed indifferent studies [14] rejection of those point pairs witha distance greater than a user specified limit rejection ofa certain portion of point pairs with largest distance andrejection of point pairs inconsistentwith neighbor pairs (rigidtransform)

(5) Error Metric andMinimizationThis step is the last step ofICP algorithm which measures the error between the pointclouds and tries to minimize the distance between two pointcloudsMostly either a ldquopoint-to-pointrdquo or a ldquopoint-to-planerdquoerror metric is applied In the first case if 119901119894 is a source pointand 119902119894 the corresponding point in the target point cloud and119872 is the transformation matrix then the sum of squareddistances has to be calculated and minimized [2]

119872min = argmin119872

119894

sum (119872 sdot 119901119894 minus 119902119894)2 (2)

Closed form solutions for this kind of error metric exist suchas singular value decomposition (SVD) dual quaternionsquaternions and orthonormalmatrices Accuracy and stabil-ity of these methods have been evaluated by [15]

In general point-to-plane error metric converges betterthan the point-to-point error metric [16] It minimizes thesum of squared distances between source points and thetangent plane at the target point which is orthogonal to theunit normal vector of that point Mathematically if 119901119894 is asource point and 119902119894 is the corresponding point in the targetpoint cloud and 119899119894 = 119899(119909119894 119910119894 119911119894) is the normal vector at 119902119894then the ICP algorithm estimates the rigid transformationmatrix by the minimizing function

119872normmin = argmin

119872

sum((119872 sdot 119901119894 minus 119902119894) sdot 119899)2 (3)

Because no closed form solutions for point-to-plane errormetric exist it is usually solved iteratively by nonlinearmethods such as Levenberg-Marquardt or it can be linearizedconsidering some approximation for rotation matrix 119877 suchas replacing sin 120579 by 120579 and cos 120579 by 1 The problem of thepoint-to-plane error metric is that it is sensitive to noise andthat it does not converge well if the distance between twopoint clouds is large [15 17]

The ICP algorithm can vary by changing the methods ineach step to improve the performance with regard to speedand stability depending on the amount of noise and outliersthe algorithm can deal with

23 Selected ICP Algorithms for Registration Four differ-ent under BSD license available ICP implementations inMatlab have been compared with the proprietary softwareof AlignRT for surface registration of phantoms We havechosen the same software platform because one criterionwas the option to compare the speeds We assumed that theimplementations belong to the most popular ones They allmeet the same general ideas of ICP registration and presentthe variety of unconstrained methods (without markers orusing colors) We found that the four chosen ICP algorithmsare well suited to be compared with the method appliedby AlignRT An interesting extension of work would beto include new approaches to point registration such asdescribed in [18]

(1) Wilmrsquos Algorithm [2 19] Point clouds are aligned byconsidering the complete points set The program finds thenearest neighbor by a kd-tree search which considerablyincreases the speed of matching Point-to-point or point-to-plane error metric can be selected by parameter settingAlignRT uses a similar point-to-plane metric as follows fromthe communication with the manufacturer

(2) Kroonrsquos [20] Modified This program uses a finite differ-ence model to align the point clouds The finite differencemethod also supports the transform types of resizing andshearing Several optimization functions are included forminimum searchWe added a global search approach by gen-erating different start points using a scatter-search methodto improve the results All starts points are evaluated and

Computational and Mathematical Methods in Medicine 5

the points which are unlikely to improve the minimum arerejected

(3) Renoaldrsquos [21] It is a simple ICP implementation whichuses all the data points It first finds the corresponding pointsby creating a Delaunay tessellation of points in a model tosearch for the closest pointThen it calculates the initial trans-formation matrix by singular value decomposition (SVD)and applies this to the target point cloudThe transformationmatrix is updated iteratively until no more correspondencescan be found

(4) Bergstromrsquos [22 23] It is similar to the Renoaldrsquos algorithmwith the main difference that after matching correspondingpoints the point pairs are weighted by the maximum pointdistance Levenberg-Marquardt algorithm is directly appliedto minimize the squared sum of the distances of closestpoints

Most of the implementations allow choosing amongmodes and modifying parametersThe best configuration forthis experimental setup has been investigated and shown inTable 3 The above given references give further details

24 Related Works Reference [4] compared suggested setupcorrection with a second and independently operatedmarker-based optical system with an anthropomorphic plas-tic phantom and healthy volunteers They found alignmentaccuracies of about 1mm for translation and 05∘ for rotationas an average Using markers is more invasive and time con-suming but in general safer than unconstrained registration

Extensive research has been done on the developmentof surface sensors The general ideas are shown in worksas [12 13] Reference [24] deals with the simulation ofphotogrammetric triangulation in order to develop the algo-rithms without need of acquisition of additional camera data

Reference [3] investigated the temporal stability of align-ment accuracy in the context of respiratory motion in anoperation mode where the sensor is triggered by the breath-ing phase A rigid flesh-colored mannequin torso phantomhas been used In this approach the optical sensor is com-bined with an infrared-based marker system for gating thebreathing state and a motorized mechanical stage Measuredsurface data has been compared with surface extracted fromCT as a reference High stability and errors in the submillime-ter range and less than 1∘ have been reported Additionallythe accuracy of recommended patient realignment has beenevaluated for 54 random shifts of the treatment table In ourinvestigations we focused our attention on the influence ofdifferent types of phantoms in order to learn how curvatureinfluences the registration reliability

Reference [14] gives helpful results how existing ICPalgorithms converge for synthesized surfaces Also differentsampling strategies for selection of registration points havebeen considered But for clinical practice it is important toverify these theoretical results with the real situation for dataof an existing optical sensor

Reference [7] evaluates a 3-Dimensional Surface ImagingSystem for Guidance in DIBH Therapy Setup data based on

captured 3D surfaces by the same surface imaging systemas we used was compared with setup data based on conebeam computed tomography (CBCT) and evaluated withregression based methods It was found that in the contextof breast cancer treatment 95 of the deviations less than04 cm detected by the optical sensor were less than 066 cmin the other mode of CBCT A comparison of megavoltageCBCT based registration and of AlignRT based registrationto its own particular reference is subjected to certain timeconstraints A CT scan itself as a possible reference and thelocal megavoltage CBCT scan on the Tomotherapy unit isusually a time-consuming procedure

Reference [6] reports on two commercial optical sensors(surface imaging systems) and compares them with theactual adjustments in patient positions made on the basis ofmegavoltage CT scans The deviations between the proposedcorrection of the optical sensor and the subjectively bestalignment of an expert have been statistically evaluatedTests have been performed on an Alderson phantom andon patients at headneck pelvic and chest regions It wasfound that the optical sensors can support patient positioningmainly at pelvic and chest regions because immobilization ofthe patient by special masks is not possible as in the case ofhead and neck region

Generally the AlignRT system is usable on nearly allpossible patient regions Some papers deal with clinicalapplications of optical sensors to different patient regionsBesides classical patient body region dependent applicationsthe frame- and mask-less cranial stereotactic radiosurgery isa new application field The comparison of breath inducedsurface movements with different registration modalitiesis subjected to different time constants of the acquisitiondevices The verification of DIBH (depth inspiration breath-hold) techniques with optical systems as theAlignRT systemis a new emerging procedure in the clinical practice

A feasibility study for the usability of the AlignRT systemto frame- and mask-less cranial stereotactic was presentedby [8] The presented technique shows the potential ofhead mold and surface monitoring to use in stereotactictreatments The accuracy of the surface imaging motiontracking system during the stereotactic treatment was ver-ified The results were additionally tested on the standardoptical guidance platform technique (kVCT by Varian)

Work [9] describes a clinical analysis of fifty patientswith the AlignRT system in comparison to megavoltageportal imaging Daily alignment with the 3D optical imagingsystem was found to be valuable for reducing setup errorsin comparison to skin markers Particularly the anterior-posterior alignment directions were with the optical systemnoticeably better

The possible synchronization of a classical CBCT systemwith the AlignRT has been shown by [10] An image guidedmethod for the synchronization of the X-ray projectionsis synchronized with optically sensed surface during usingCBCT without any further hardware requirements The pro-posedmethod can by generically applied to any configurationof the CBCT and optical imaging systems and also be used forextracranial tumor tracking

6 Computational and Mathematical Methods in Medicine

3 Generation of Test Surface Data

In order to generate surface data we focused our work onrigid phantoms because we are mostly interested in pureaccuracy of the sensor togetherwith the ICP algorithms in theideal caseThe investigated ICP algorithms do not treat shapevariations which is a motivation for using solid phantomsinstead of real cases The influence of motion of real humanbodies caused by respiration for instance is considered byother papers (eg [10 11])

31 Test Phantoms Because the contour characteristics of asurface is important for a safe registration specially designedphantoms of different surface types have been investigated Tothis end dedicated phantoms have been designed or selectedwith a size approximately covering the measurement volumeof the optical sensor of about 01m3 In this study fourdifferent phantoms have been measured by the optical sensorin order to generate point clouds for the evaluation of the ICPalgorithms

(i) Plane It is a simple plane horizontally placed on thetreatment tableThemain idea is to check the accuracy of theoptical sensor with regard to vertical shift of the treatmenttable (119911 direction)

(ii) 3plane It consists of two planes and an edge especiallybuilt to allow a unique matching with respect to all 119909-119910-119911space coordinates

(iii) BowlThebowl phantom ismore curved than a plane butambiguities with regard to rotations must be expected

(iv) Torso By the torso of amannequin a shape typical for thehuman body has been simulated The curvature of the torsophantom ismore ambiguous in the cranial-caudal (119910) than inthe dorsal-ventral transverse motion direction

The phantoms have been coated by white painting ortextile to produce a surface that can be well captured bythe cameras of the optical sensor when illuminated by thespeckle projector Measured point clouds of these phantomsare shown in Figure 2 As visible in Figure 2(c) the measuredsurfaces contained some points of the background (eg of thetreatment table) Such extra points obviously not originatingfrom the phantoms have been manually removed for the dataof all phantoms As an example Figures 2(c) and 2(d) showthe bowl surface before and after removing the extra pointsrespectively

32 Test Setup The above described ICP algorithms havebeen tested with surface data of the selected phantoms(Figure 2) moved to well-defined positions First the opti-cal sensor AlignRT has been calibrated according to theinstructions of the manufacturer Then the phantoms havebeen placed on the treatment table and a surface scan atthe origin has been captured This surface scan at central(zero) position of the treatment table served as a referenceto compare with surface scans at other positions To this

end the phantoms have been translationally shifted by thetreatment table in the directions 119889 = 119909 119910 119911 by distancesof 119904119889 = 05 10 plusmn100 200 (mm) For the plane translationwas only done in 119911 direction (119889 = 119911) because tests confirmthe obvious fact that a motion in 119909 or 119910 direction cannot bedetected if the plane phantom is placed in parallel to the 119909-119910-axes as we did

Figure 3 gives an example on how the operator sees thesituation on the monitoring screen of AlignRT It shows theestimated misalignment for translation and rotation in mmand ∘ respectively by numbers with one-digit accuracy afterthe comma and by bars At setup the therapists attempt tominimize the shifts (by minimizing the length of the bars)[11] The surface data is exported as object files and used forthe registration by the other ICP algorithms

After an initial phase real-time surface tracking is pos-sible with the AlignRT system AlignRT system deliverssufficiently fast displacement estimation for most medicalindications of about 10 frames per second Acceptable speedrelates mainly to the time needed for an initial alignmentwhich should not exceed about a second in order to beacceptable in clinical routine

Therefore two requirements result with regard to thespeed the alignment time should not be much longer than asecond because more cannot be accepted in clinical routine

In case of dynamic tracking the speed demands arise bythe typical patient motion to avoid subsampling on the onehand and to ensure that shape variations between two timesteps can be neglected for rigid registration In the ideal casethe registration should be faster than the surface sensor inorder to avoid reduction of frame rate

4 Results and Discussion

Rigid transform matrices (translation and rotation) for reg-istration of the reference with the tested position have beenestimated by the proposed ICP algorithms and with AlignRTThe investigated implementations specify the resulting coor-dinate transform for registration by different versions ofmatrices for homogenous coordinates For direct compar-ison these matrices have been transformed into a singlerepresentation for translation and rotation (see [12])

Translational shift values of registration 119889 in direction 119889yield directly from the offset part of the transform matricesTable 1 shows the results of registration together with theexpected translation values 119904119889 The translational registrationerror in direction 119889 is then given by 119890trans119889 = 119904119889 minus 119889

The total registered rotation is composed by a series ofthree rotations 119903 = roll pitch yaw around 119909- 119910- and 119911-axes respectively in the directions according to Figure 1(b)each quantified by the Euler angles 119903 = roll pitch yawThe rotatory registration error is 119890rot119903 = 119903minus120572119903 = 119903 for 120572119903 = 0because the measurement phantoms have not been rotated

We assumed a maximally allowed absolute registrationerror of 119890trans119889 max = 1mm for translation and of 119890rot119889 max = 05

∘

for rotation which are quite tough values in radiotherapy andmarked entries with |119890trans119889 | gt 119890

trans119889 max or |119890trans119889 | gt 119890

rot119889 max

boldface Other works set the allowable tolerance a bit higher

Computational and Mathematical Methods in Medicine 7

(a) Plane (b) 3plane (c) Bowl (before removingextra points)

(d) Bowl (after removingthe extra points)

(e) Torso

Figure 2 Surfaces of selected phantoms captured by the optical sensor AlginRT showing typical problems of real measurement data (a)measurement noise and systematic errors (c) extra points not belonging to the object of interest (b) and (e) seam from fusing the twosurfaces of left and right optical sensors

Figure 3 An example of the AlignRT monitoring screen seenduring measurement of the torso phantom and vertical shift ofthe treatment table 119904119889(119911) = 10mm The reference surface is shownin pink and the measured surface in green The suggested lineartranslations (vertical lateral and longitudinal) and rotations (yawpitch and roll) are shown by numbers and colored bars on the lefttogether with the RMS value (called magnitude MAG) The whitegraph is used to display a time series of the RMS values (not used inour experiment)

(eg [8] to 1mm1∘ and [11] to 3mm3∘) but working withrigid phantoms without motion motivates our stricter limits

Figure 4 shows as an example one of the best results ofaligned surfaces with the reference surface for a shift of 119904119889 =10mm in direction 119889 = 119911 using the Wilm approach Theresiduals have been estimated by triangulation of the surfacesand color-coded displaying the distances in 119911 direction Itbecomes clear that although the translational and rotationalparameters are within the limits this does not hold for allpoints of the surfacesThere are problems especially at slopingsurface parts at edges and at the stitching area of left andright optical sensors which explains the remaining deviationsafter applying the ICP algorithm

Table 2 summarizes Table 1 with regard to adhering thelimits 119890trans119889 max and 119890

rot119889 max As expected with the plane phan-

tom placed in parallel to the 119909119910 plane a safe registration isonly possible in 119911 direction and fails in 119909 and 119910 direction forall ICP algorithms For the other three phantoms 3planebowl and torso only the Wilm algorithm registers safely forthe translational parameters No algorithmhas problemswiththe rotatory parameters for any phantom except Wilm whichinterestingly fails for the torso phantom for pitch and yaw andAlignRT for yaw of the bowl phantom

Table 3 compares some important properties and resultsof the four tested algorithms that have been applied to fourdifferent test objects (phantoms) differently shifted relative toan original position The algorithms use different methodsto compute the rigid transformation matrix (translationand rotation) between two point clouds as described inSection 23 as the result of registration

Main operational principles of the algorithms are summa-rized their processing speed and accuracy give informationon their suitability for registration of our selected phantomsMain differences consist in the method for the closest pointsearch the weighting the error metric and the methodfor minimization Only Wilm uses kd-tree search whichis much more efficient than full search Only Bergstromapplies distance-based weighting None of the open sourcealgorithms includes rejection Among the open source algo-rithms only Wilm uses point-to-plane metric whereas allother apply a point-to-point criterion The AlignRT registra-tion results look similar to the Wilm implementation Thissupports the assumption that similar principles are used bythis proprietary program

The average processing time for each algorithm is alsoqualitatively given It varies between fastest processing(which was about a few seconds) and slowest processing(which was about 3 minutes) for the registration by theICP algorithm on a standard computer (Intel Core i7 64-bit Windows) in Matlab A more detailed evaluation ofprocessing speed is not given because we do not expect thatthe chosen algorithms are implemented in an optimal wayThis may be different for the commercial implementation ofAlignRT Renoald performed best with regard to processingspeedWilm and AlignRT show acceptable speed in the samerange Kroon is slow and Bergstrom is very slow in theinvestigated implementation and would not be acceptable inclinical routine

For offline verification speed plays a less important role aslong as the registration takes only seconds of time Thereforethose implementations indicated by + or ++ can be consid-ered acceptable in the intended application (see Section 32)In tracking applications when even the registration is doneonline the speed of the algorithms matters much more andthe patient alignment can be verified and corrected on the flybymoving the treatment table or adapting the irradiation But

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

Computational and Mathematical Methods in Medicine 5

the points which are unlikely to improve the minimum arerejected

(3) Renoaldrsquos [21] It is a simple ICP implementation whichuses all the data points It first finds the corresponding pointsby creating a Delaunay tessellation of points in a model tosearch for the closest pointThen it calculates the initial trans-formation matrix by singular value decomposition (SVD)and applies this to the target point cloudThe transformationmatrix is updated iteratively until no more correspondencescan be found

(4) Bergstromrsquos [22 23] It is similar to the Renoaldrsquos algorithmwith the main difference that after matching correspondingpoints the point pairs are weighted by the maximum pointdistance Levenberg-Marquardt algorithm is directly appliedto minimize the squared sum of the distances of closestpoints

Most of the implementations allow choosing amongmodes and modifying parametersThe best configuration forthis experimental setup has been investigated and shown inTable 3 The above given references give further details

24 Related Works Reference [4] compared suggested setupcorrection with a second and independently operatedmarker-based optical system with an anthropomorphic plas-tic phantom and healthy volunteers They found alignmentaccuracies of about 1mm for translation and 05∘ for rotationas an average Using markers is more invasive and time con-suming but in general safer than unconstrained registration

Extensive research has been done on the developmentof surface sensors The general ideas are shown in worksas [12 13] Reference [24] deals with the simulation ofphotogrammetric triangulation in order to develop the algo-rithms without need of acquisition of additional camera data

Reference [3] investigated the temporal stability of align-ment accuracy in the context of respiratory motion in anoperation mode where the sensor is triggered by the breath-ing phase A rigid flesh-colored mannequin torso phantomhas been used In this approach the optical sensor is com-bined with an infrared-based marker system for gating thebreathing state and a motorized mechanical stage Measuredsurface data has been compared with surface extracted fromCT as a reference High stability and errors in the submillime-ter range and less than 1∘ have been reported Additionallythe accuracy of recommended patient realignment has beenevaluated for 54 random shifts of the treatment table In ourinvestigations we focused our attention on the influence ofdifferent types of phantoms in order to learn how curvatureinfluences the registration reliability

Reference [14] gives helpful results how existing ICPalgorithms converge for synthesized surfaces Also differentsampling strategies for selection of registration points havebeen considered But for clinical practice it is important toverify these theoretical results with the real situation for dataof an existing optical sensor

Reference [7] evaluates a 3-Dimensional Surface ImagingSystem for Guidance in DIBH Therapy Setup data based on

captured 3D surfaces by the same surface imaging systemas we used was compared with setup data based on conebeam computed tomography (CBCT) and evaluated withregression based methods It was found that in the contextof breast cancer treatment 95 of the deviations less than04 cm detected by the optical sensor were less than 066 cmin the other mode of CBCT A comparison of megavoltageCBCT based registration and of AlignRT based registrationto its own particular reference is subjected to certain timeconstraints A CT scan itself as a possible reference and thelocal megavoltage CBCT scan on the Tomotherapy unit isusually a time-consuming procedure

Reference [6] reports on two commercial optical sensors(surface imaging systems) and compares them with theactual adjustments in patient positions made on the basis ofmegavoltage CT scans The deviations between the proposedcorrection of the optical sensor and the subjectively bestalignment of an expert have been statistically evaluatedTests have been performed on an Alderson phantom andon patients at headneck pelvic and chest regions It wasfound that the optical sensors can support patient positioningmainly at pelvic and chest regions because immobilization ofthe patient by special masks is not possible as in the case ofhead and neck region

Generally the AlignRT system is usable on nearly allpossible patient regions Some papers deal with clinicalapplications of optical sensors to different patient regionsBesides classical patient body region dependent applicationsthe frame- and mask-less cranial stereotactic radiosurgery isa new application field The comparison of breath inducedsurface movements with different registration modalitiesis subjected to different time constants of the acquisitiondevices The verification of DIBH (depth inspiration breath-hold) techniques with optical systems as theAlignRT systemis a new emerging procedure in the clinical practice

A feasibility study for the usability of the AlignRT systemto frame- and mask-less cranial stereotactic was presentedby [8] The presented technique shows the potential ofhead mold and surface monitoring to use in stereotactictreatments The accuracy of the surface imaging motiontracking system during the stereotactic treatment was ver-ified The results were additionally tested on the standardoptical guidance platform technique (kVCT by Varian)

Work [9] describes a clinical analysis of fifty patientswith the AlignRT system in comparison to megavoltageportal imaging Daily alignment with the 3D optical imagingsystem was found to be valuable for reducing setup errorsin comparison to skin markers Particularly the anterior-posterior alignment directions were with the optical systemnoticeably better

The possible synchronization of a classical CBCT systemwith the AlignRT has been shown by [10] An image guidedmethod for the synchronization of the X-ray projectionsis synchronized with optically sensed surface during usingCBCT without any further hardware requirements The pro-posedmethod can by generically applied to any configurationof the CBCT and optical imaging systems and also be used forextracranial tumor tracking

6 Computational and Mathematical Methods in Medicine

3 Generation of Test Surface Data

In order to generate surface data we focused our work onrigid phantoms because we are mostly interested in pureaccuracy of the sensor togetherwith the ICP algorithms in theideal caseThe investigated ICP algorithms do not treat shapevariations which is a motivation for using solid phantomsinstead of real cases The influence of motion of real humanbodies caused by respiration for instance is considered byother papers (eg [10 11])

31 Test Phantoms Because the contour characteristics of asurface is important for a safe registration specially designedphantoms of different surface types have been investigated Tothis end dedicated phantoms have been designed or selectedwith a size approximately covering the measurement volumeof the optical sensor of about 01m3 In this study fourdifferent phantoms have been measured by the optical sensorin order to generate point clouds for the evaluation of the ICPalgorithms

(i) Plane It is a simple plane horizontally placed on thetreatment tableThemain idea is to check the accuracy of theoptical sensor with regard to vertical shift of the treatmenttable (119911 direction)

(ii) 3plane It consists of two planes and an edge especiallybuilt to allow a unique matching with respect to all 119909-119910-119911space coordinates

(iii) BowlThebowl phantom ismore curved than a plane butambiguities with regard to rotations must be expected

(iv) Torso By the torso of amannequin a shape typical for thehuman body has been simulated The curvature of the torsophantom ismore ambiguous in the cranial-caudal (119910) than inthe dorsal-ventral transverse motion direction

The phantoms have been coated by white painting ortextile to produce a surface that can be well captured bythe cameras of the optical sensor when illuminated by thespeckle projector Measured point clouds of these phantomsare shown in Figure 2 As visible in Figure 2(c) the measuredsurfaces contained some points of the background (eg of thetreatment table) Such extra points obviously not originatingfrom the phantoms have been manually removed for the dataof all phantoms As an example Figures 2(c) and 2(d) showthe bowl surface before and after removing the extra pointsrespectively

32 Test Setup The above described ICP algorithms havebeen tested with surface data of the selected phantoms(Figure 2) moved to well-defined positions First the opti-cal sensor AlignRT has been calibrated according to theinstructions of the manufacturer Then the phantoms havebeen placed on the treatment table and a surface scan atthe origin has been captured This surface scan at central(zero) position of the treatment table served as a referenceto compare with surface scans at other positions To this

end the phantoms have been translationally shifted by thetreatment table in the directions 119889 = 119909 119910 119911 by distancesof 119904119889 = 05 10 plusmn100 200 (mm) For the plane translationwas only done in 119911 direction (119889 = 119911) because tests confirmthe obvious fact that a motion in 119909 or 119910 direction cannot bedetected if the plane phantom is placed in parallel to the 119909-119910-axes as we did

Figure 3 gives an example on how the operator sees thesituation on the monitoring screen of AlignRT It shows theestimated misalignment for translation and rotation in mmand ∘ respectively by numbers with one-digit accuracy afterthe comma and by bars At setup the therapists attempt tominimize the shifts (by minimizing the length of the bars)[11] The surface data is exported as object files and used forthe registration by the other ICP algorithms

After an initial phase real-time surface tracking is pos-sible with the AlignRT system AlignRT system deliverssufficiently fast displacement estimation for most medicalindications of about 10 frames per second Acceptable speedrelates mainly to the time needed for an initial alignmentwhich should not exceed about a second in order to beacceptable in clinical routine

Therefore two requirements result with regard to thespeed the alignment time should not be much longer than asecond because more cannot be accepted in clinical routine

In case of dynamic tracking the speed demands arise bythe typical patient motion to avoid subsampling on the onehand and to ensure that shape variations between two timesteps can be neglected for rigid registration In the ideal casethe registration should be faster than the surface sensor inorder to avoid reduction of frame rate

4 Results and Discussion

Rigid transform matrices (translation and rotation) for reg-istration of the reference with the tested position have beenestimated by the proposed ICP algorithms and with AlignRTThe investigated implementations specify the resulting coor-dinate transform for registration by different versions ofmatrices for homogenous coordinates For direct compar-ison these matrices have been transformed into a singlerepresentation for translation and rotation (see [12])

Translational shift values of registration 119889 in direction 119889yield directly from the offset part of the transform matricesTable 1 shows the results of registration together with theexpected translation values 119904119889 The translational registrationerror in direction 119889 is then given by 119890trans119889 = 119904119889 minus 119889

The total registered rotation is composed by a series ofthree rotations 119903 = roll pitch yaw around 119909- 119910- and 119911-axes respectively in the directions according to Figure 1(b)each quantified by the Euler angles 119903 = roll pitch yawThe rotatory registration error is 119890rot119903 = 119903minus120572119903 = 119903 for 120572119903 = 0because the measurement phantoms have not been rotated

We assumed a maximally allowed absolute registrationerror of 119890trans119889 max = 1mm for translation and of 119890rot119889 max = 05

∘

for rotation which are quite tough values in radiotherapy andmarked entries with |119890trans119889 | gt 119890

trans119889 max or |119890trans119889 | gt 119890

rot119889 max

boldface Other works set the allowable tolerance a bit higher

Computational and Mathematical Methods in Medicine 7

(a) Plane (b) 3plane (c) Bowl (before removingextra points)

(d) Bowl (after removingthe extra points)

(e) Torso

Figure 2 Surfaces of selected phantoms captured by the optical sensor AlginRT showing typical problems of real measurement data (a)measurement noise and systematic errors (c) extra points not belonging to the object of interest (b) and (e) seam from fusing the twosurfaces of left and right optical sensors

Figure 3 An example of the AlignRT monitoring screen seenduring measurement of the torso phantom and vertical shift ofthe treatment table 119904119889(119911) = 10mm The reference surface is shownin pink and the measured surface in green The suggested lineartranslations (vertical lateral and longitudinal) and rotations (yawpitch and roll) are shown by numbers and colored bars on the lefttogether with the RMS value (called magnitude MAG) The whitegraph is used to display a time series of the RMS values (not used inour experiment)

(eg [8] to 1mm1∘ and [11] to 3mm3∘) but working withrigid phantoms without motion motivates our stricter limits

Figure 4 shows as an example one of the best results ofaligned surfaces with the reference surface for a shift of 119904119889 =10mm in direction 119889 = 119911 using the Wilm approach Theresiduals have been estimated by triangulation of the surfacesand color-coded displaying the distances in 119911 direction Itbecomes clear that although the translational and rotationalparameters are within the limits this does not hold for allpoints of the surfacesThere are problems especially at slopingsurface parts at edges and at the stitching area of left andright optical sensors which explains the remaining deviationsafter applying the ICP algorithm

Table 2 summarizes Table 1 with regard to adhering thelimits 119890trans119889 max and 119890

rot119889 max As expected with the plane phan-

tom placed in parallel to the 119909119910 plane a safe registration isonly possible in 119911 direction and fails in 119909 and 119910 direction forall ICP algorithms For the other three phantoms 3planebowl and torso only the Wilm algorithm registers safely forthe translational parameters No algorithmhas problemswiththe rotatory parameters for any phantom except Wilm whichinterestingly fails for the torso phantom for pitch and yaw andAlignRT for yaw of the bowl phantom

Table 3 compares some important properties and resultsof the four tested algorithms that have been applied to fourdifferent test objects (phantoms) differently shifted relative toan original position The algorithms use different methodsto compute the rigid transformation matrix (translationand rotation) between two point clouds as described inSection 23 as the result of registration

Main operational principles of the algorithms are summa-rized their processing speed and accuracy give informationon their suitability for registration of our selected phantomsMain differences consist in the method for the closest pointsearch the weighting the error metric and the methodfor minimization Only Wilm uses kd-tree search whichis much more efficient than full search Only Bergstromapplies distance-based weighting None of the open sourcealgorithms includes rejection Among the open source algo-rithms only Wilm uses point-to-plane metric whereas allother apply a point-to-point criterion The AlignRT registra-tion results look similar to the Wilm implementation Thissupports the assumption that similar principles are used bythis proprietary program

The average processing time for each algorithm is alsoqualitatively given It varies between fastest processing(which was about a few seconds) and slowest processing(which was about 3 minutes) for the registration by theICP algorithm on a standard computer (Intel Core i7 64-bit Windows) in Matlab A more detailed evaluation ofprocessing speed is not given because we do not expect thatthe chosen algorithms are implemented in an optimal wayThis may be different for the commercial implementation ofAlignRT Renoald performed best with regard to processingspeedWilm and AlignRT show acceptable speed in the samerange Kroon is slow and Bergstrom is very slow in theinvestigated implementation and would not be acceptable inclinical routine

For offline verification speed plays a less important role aslong as the registration takes only seconds of time Thereforethose implementations indicated by + or ++ can be consid-ered acceptable in the intended application (see Section 32)In tracking applications when even the registration is doneonline the speed of the algorithms matters much more andthe patient alignment can be verified and corrected on the flybymoving the treatment table or adapting the irradiation But

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

6 Computational and Mathematical Methods in Medicine

3 Generation of Test Surface Data

In order to generate surface data we focused our work onrigid phantoms because we are mostly interested in pureaccuracy of the sensor togetherwith the ICP algorithms in theideal caseThe investigated ICP algorithms do not treat shapevariations which is a motivation for using solid phantomsinstead of real cases The influence of motion of real humanbodies caused by respiration for instance is considered byother papers (eg [10 11])

31 Test Phantoms Because the contour characteristics of asurface is important for a safe registration specially designedphantoms of different surface types have been investigated Tothis end dedicated phantoms have been designed or selectedwith a size approximately covering the measurement volumeof the optical sensor of about 01m3 In this study fourdifferent phantoms have been measured by the optical sensorin order to generate point clouds for the evaluation of the ICPalgorithms

(i) Plane It is a simple plane horizontally placed on thetreatment tableThemain idea is to check the accuracy of theoptical sensor with regard to vertical shift of the treatmenttable (119911 direction)

(ii) 3plane It consists of two planes and an edge especiallybuilt to allow a unique matching with respect to all 119909-119910-119911space coordinates

(iii) BowlThebowl phantom ismore curved than a plane butambiguities with regard to rotations must be expected

(iv) Torso By the torso of amannequin a shape typical for thehuman body has been simulated The curvature of the torsophantom ismore ambiguous in the cranial-caudal (119910) than inthe dorsal-ventral transverse motion direction

The phantoms have been coated by white painting ortextile to produce a surface that can be well captured bythe cameras of the optical sensor when illuminated by thespeckle projector Measured point clouds of these phantomsare shown in Figure 2 As visible in Figure 2(c) the measuredsurfaces contained some points of the background (eg of thetreatment table) Such extra points obviously not originatingfrom the phantoms have been manually removed for the dataof all phantoms As an example Figures 2(c) and 2(d) showthe bowl surface before and after removing the extra pointsrespectively

32 Test Setup The above described ICP algorithms havebeen tested with surface data of the selected phantoms(Figure 2) moved to well-defined positions First the opti-cal sensor AlignRT has been calibrated according to theinstructions of the manufacturer Then the phantoms havebeen placed on the treatment table and a surface scan atthe origin has been captured This surface scan at central(zero) position of the treatment table served as a referenceto compare with surface scans at other positions To this

end the phantoms have been translationally shifted by thetreatment table in the directions 119889 = 119909 119910 119911 by distancesof 119904119889 = 05 10 plusmn100 200 (mm) For the plane translationwas only done in 119911 direction (119889 = 119911) because tests confirmthe obvious fact that a motion in 119909 or 119910 direction cannot bedetected if the plane phantom is placed in parallel to the 119909-119910-axes as we did

Figure 3 gives an example on how the operator sees thesituation on the monitoring screen of AlignRT It shows theestimated misalignment for translation and rotation in mmand ∘ respectively by numbers with one-digit accuracy afterthe comma and by bars At setup the therapists attempt tominimize the shifts (by minimizing the length of the bars)[11] The surface data is exported as object files and used forthe registration by the other ICP algorithms

After an initial phase real-time surface tracking is pos-sible with the AlignRT system AlignRT system deliverssufficiently fast displacement estimation for most medicalindications of about 10 frames per second Acceptable speedrelates mainly to the time needed for an initial alignmentwhich should not exceed about a second in order to beacceptable in clinical routine

Therefore two requirements result with regard to thespeed the alignment time should not be much longer than asecond because more cannot be accepted in clinical routine

In case of dynamic tracking the speed demands arise bythe typical patient motion to avoid subsampling on the onehand and to ensure that shape variations between two timesteps can be neglected for rigid registration In the ideal casethe registration should be faster than the surface sensor inorder to avoid reduction of frame rate

4 Results and Discussion

Rigid transform matrices (translation and rotation) for reg-istration of the reference with the tested position have beenestimated by the proposed ICP algorithms and with AlignRTThe investigated implementations specify the resulting coor-dinate transform for registration by different versions ofmatrices for homogenous coordinates For direct compar-ison these matrices have been transformed into a singlerepresentation for translation and rotation (see [12])

Translational shift values of registration 119889 in direction 119889yield directly from the offset part of the transform matricesTable 1 shows the results of registration together with theexpected translation values 119904119889 The translational registrationerror in direction 119889 is then given by 119890trans119889 = 119904119889 minus 119889

The total registered rotation is composed by a series ofthree rotations 119903 = roll pitch yaw around 119909- 119910- and 119911-axes respectively in the directions according to Figure 1(b)each quantified by the Euler angles 119903 = roll pitch yawThe rotatory registration error is 119890rot119903 = 119903minus120572119903 = 119903 for 120572119903 = 0because the measurement phantoms have not been rotated

We assumed a maximally allowed absolute registrationerror of 119890trans119889 max = 1mm for translation and of 119890rot119889 max = 05

∘

for rotation which are quite tough values in radiotherapy andmarked entries with |119890trans119889 | gt 119890

trans119889 max or |119890trans119889 | gt 119890

rot119889 max

boldface Other works set the allowable tolerance a bit higher

Computational and Mathematical Methods in Medicine 7

(a) Plane (b) 3plane (c) Bowl (before removingextra points)

(d) Bowl (after removingthe extra points)

(e) Torso

Figure 2 Surfaces of selected phantoms captured by the optical sensor AlginRT showing typical problems of real measurement data (a)measurement noise and systematic errors (c) extra points not belonging to the object of interest (b) and (e) seam from fusing the twosurfaces of left and right optical sensors

Figure 3 An example of the AlignRT monitoring screen seenduring measurement of the torso phantom and vertical shift ofthe treatment table 119904119889(119911) = 10mm The reference surface is shownin pink and the measured surface in green The suggested lineartranslations (vertical lateral and longitudinal) and rotations (yawpitch and roll) are shown by numbers and colored bars on the lefttogether with the RMS value (called magnitude MAG) The whitegraph is used to display a time series of the RMS values (not used inour experiment)

(eg [8] to 1mm1∘ and [11] to 3mm3∘) but working withrigid phantoms without motion motivates our stricter limits

Figure 4 shows as an example one of the best results ofaligned surfaces with the reference surface for a shift of 119904119889 =10mm in direction 119889 = 119911 using the Wilm approach Theresiduals have been estimated by triangulation of the surfacesand color-coded displaying the distances in 119911 direction Itbecomes clear that although the translational and rotationalparameters are within the limits this does not hold for allpoints of the surfacesThere are problems especially at slopingsurface parts at edges and at the stitching area of left andright optical sensors which explains the remaining deviationsafter applying the ICP algorithm

Table 2 summarizes Table 1 with regard to adhering thelimits 119890trans119889 max and 119890

rot119889 max As expected with the plane phan-

tom placed in parallel to the 119909119910 plane a safe registration isonly possible in 119911 direction and fails in 119909 and 119910 direction forall ICP algorithms For the other three phantoms 3planebowl and torso only the Wilm algorithm registers safely forthe translational parameters No algorithmhas problemswiththe rotatory parameters for any phantom except Wilm whichinterestingly fails for the torso phantom for pitch and yaw andAlignRT for yaw of the bowl phantom

Table 3 compares some important properties and resultsof the four tested algorithms that have been applied to fourdifferent test objects (phantoms) differently shifted relative toan original position The algorithms use different methodsto compute the rigid transformation matrix (translationand rotation) between two point clouds as described inSection 23 as the result of registration

Main operational principles of the algorithms are summa-rized their processing speed and accuracy give informationon their suitability for registration of our selected phantomsMain differences consist in the method for the closest pointsearch the weighting the error metric and the methodfor minimization Only Wilm uses kd-tree search whichis much more efficient than full search Only Bergstromapplies distance-based weighting None of the open sourcealgorithms includes rejection Among the open source algo-rithms only Wilm uses point-to-plane metric whereas allother apply a point-to-point criterion The AlignRT registra-tion results look similar to the Wilm implementation Thissupports the assumption that similar principles are used bythis proprietary program

The average processing time for each algorithm is alsoqualitatively given It varies between fastest processing(which was about a few seconds) and slowest processing(which was about 3 minutes) for the registration by theICP algorithm on a standard computer (Intel Core i7 64-bit Windows) in Matlab A more detailed evaluation ofprocessing speed is not given because we do not expect thatthe chosen algorithms are implemented in an optimal wayThis may be different for the commercial implementation ofAlignRT Renoald performed best with regard to processingspeedWilm and AlignRT show acceptable speed in the samerange Kroon is slow and Bergstrom is very slow in theinvestigated implementation and would not be acceptable inclinical routine

For offline verification speed plays a less important role aslong as the registration takes only seconds of time Thereforethose implementations indicated by + or ++ can be consid-ered acceptable in the intended application (see Section 32)In tracking applications when even the registration is doneonline the speed of the algorithms matters much more andthe patient alignment can be verified and corrected on the flybymoving the treatment table or adapting the irradiation But

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

Computational and Mathematical Methods in Medicine 7

(a) Plane (b) 3plane (c) Bowl (before removingextra points)

(d) Bowl (after removingthe extra points)

(e) Torso

Figure 2 Surfaces of selected phantoms captured by the optical sensor AlginRT showing typical problems of real measurement data (a)measurement noise and systematic errors (c) extra points not belonging to the object of interest (b) and (e) seam from fusing the twosurfaces of left and right optical sensors

Figure 3 An example of the AlignRT monitoring screen seenduring measurement of the torso phantom and vertical shift ofthe treatment table 119904119889(119911) = 10mm The reference surface is shownin pink and the measured surface in green The suggested lineartranslations (vertical lateral and longitudinal) and rotations (yawpitch and roll) are shown by numbers and colored bars on the lefttogether with the RMS value (called magnitude MAG) The whitegraph is used to display a time series of the RMS values (not used inour experiment)

(eg [8] to 1mm1∘ and [11] to 3mm3∘) but working withrigid phantoms without motion motivates our stricter limits

Figure 4 shows as an example one of the best results ofaligned surfaces with the reference surface for a shift of 119904119889 =10mm in direction 119889 = 119911 using the Wilm approach Theresiduals have been estimated by triangulation of the surfacesand color-coded displaying the distances in 119911 direction Itbecomes clear that although the translational and rotationalparameters are within the limits this does not hold for allpoints of the surfacesThere are problems especially at slopingsurface parts at edges and at the stitching area of left andright optical sensors which explains the remaining deviationsafter applying the ICP algorithm

Table 2 summarizes Table 1 with regard to adhering thelimits 119890trans119889 max and 119890

rot119889 max As expected with the plane phan-

tom placed in parallel to the 119909119910 plane a safe registration isonly possible in 119911 direction and fails in 119909 and 119910 direction forall ICP algorithms For the other three phantoms 3planebowl and torso only the Wilm algorithm registers safely forthe translational parameters No algorithmhas problemswiththe rotatory parameters for any phantom except Wilm whichinterestingly fails for the torso phantom for pitch and yaw andAlignRT for yaw of the bowl phantom

Table 3 compares some important properties and resultsof the four tested algorithms that have been applied to fourdifferent test objects (phantoms) differently shifted relative toan original position The algorithms use different methodsto compute the rigid transformation matrix (translationand rotation) between two point clouds as described inSection 23 as the result of registration

Main operational principles of the algorithms are summa-rized their processing speed and accuracy give informationon their suitability for registration of our selected phantomsMain differences consist in the method for the closest pointsearch the weighting the error metric and the methodfor minimization Only Wilm uses kd-tree search whichis much more efficient than full search Only Bergstromapplies distance-based weighting None of the open sourcealgorithms includes rejection Among the open source algo-rithms only Wilm uses point-to-plane metric whereas allother apply a point-to-point criterion The AlignRT registra-tion results look similar to the Wilm implementation Thissupports the assumption that similar principles are used bythis proprietary program

The average processing time for each algorithm is alsoqualitatively given It varies between fastest processing(which was about a few seconds) and slowest processing(which was about 3 minutes) for the registration by theICP algorithm on a standard computer (Intel Core i7 64-bit Windows) in Matlab A more detailed evaluation ofprocessing speed is not given because we do not expect thatthe chosen algorithms are implemented in an optimal wayThis may be different for the commercial implementation ofAlignRT Renoald performed best with regard to processingspeedWilm and AlignRT show acceptable speed in the samerange Kroon is slow and Bergstrom is very slow in theinvestigated implementation and would not be acceptable inclinical routine

For offline verification speed plays a less important role aslong as the registration takes only seconds of time Thereforethose implementations indicated by + or ++ can be consid-ered acceptable in the intended application (see Section 32)In tracking applications when even the registration is doneonline the speed of the algorithms matters much more andthe patient alignment can be verified and corrected on the flybymoving the treatment table or adapting the irradiation But

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

8 Computational and Mathematical Methods in Medicine

Table 1 Registered translations 119909 119910 and 119911 and rotations roll pitch and yaw from the investigated sample implementations of the ICPalgorithm for the tested phantoms plane 3plane bowl and torso and treatment table shifts 119904119889 in different directions 119889 = 119909 119910 119911 Translationswith an absolute translational registration error |119890trans119889 | gt 119890

trans119889 max = 1mmand rotations with an absolute registration error 119890rot119903 gt 119890

rot119889 max = 05

∘

are marked boldface

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yawWilm algorithm

Plane

05 119911 04282 00087 05482 minus00001 minus00012 0000010 119911 14503 04656 10627 00000 minus00123 00000100 119911 04760 08346 100927 00002 minus00022 minus00005200 119911 00827 11255 200975 minus00001 00213 minus00007

3plane

05 119911 minus00100 01440 05325 minus00000 00001 minus0000310 119911 minus00395 01362 10882 00001 00004 00001100 119911 minus01475 01217 100550 00003 00001 minus00003200 119911 minus00665 minus00903 209796 00005 00012 minus00006100 119910 minus01237 99743 00157 00001 00004 00001minus100 119910 minus01991 minus96955 01602 00002 minus00001 00004100 119909 98886 03100 01109 00013 minus00004 00001

Bowl

05 119911 00749 00702 04491 minus00006 00013 minus0000010 119911 00596 01477 09348 minus00010 minus00018 minus00011100 119911 minus00084 00054 101927 00061 00121 00004200 119911 03618 00843 200056 00005 00382 minus00001100 119910 minus01668 99264 01325 00035 minus00678 minus00033minus100 119910 00885 minus97892 minus03034 00004 00246 minus00006100 119909 99217 minus00522 00799 minus00014 minus00400 minus00024minus100 119909 minus98553 01800 minus00533 minus00005 00854 minus00005

Torso

05 119911 minus00239 minus00895 05171 00033 15783 minus1578510 119911 minus00986 minus01490 10508 00022 16005 minus16007100 119911 00303 01723 99136 00090 11490 minus11480200 119911 00995 01012 198599 00017 08377 minus08362100 119910 01819 99194 minus01830 00009 09571 09572minus100 119910 minus01553 minus95344 00316 00020 minus14725 14724100 119909 101230 minus00174 minus00374 00047 15300 minus15299minus100 119909 minus98724 minus00488 minus00401 00034 minus16261 16263

Kroon algorithm

Plane

05 119911 minus04031 minus01523 05499 minus00001 minus00001 minus000010 119911 minus09254 minus02737 10675 00002 00005 minus00001100 119911 13403 12951 100872 00002 minus00015 minus00004200 119911 minus37160 07362 200891 minus00001 00007 minus00008

3plane

05 119911 00023 minus01280 03746 minus00005 00000 0000010 119911 minus00470 minus02840 08252 minus00001 00003 00001100 119911 minus15692 minus58559 73710 minus00125 minus00045 minus00043200 119911 10803 minus49535 181806 10803 00014 minus00021100 119910 00793 65978 minus13214 minus00066 minus00004 minus00003minus100 119910 minus01597 minus66084 minus13826 00062 00004 00006100 119909 07600 minus00439 00272 00002 00008 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00572 minus00864 05162 00015 00002 minus00004100 119911 minus14703 minus02302 89576 00087 00022 minus00420200 119911 minus12950 minus01217 190383 000206 00035 minus00554100 119910 minus02905 88071 00682 00369 minus00581 minus00027minus100 119910 02614 minus86043 03671 minus00368 00533 00006100 119909 94381 minus04111 00864 00023 00202 minus00048minus100 119909 minus91155 05139 01217 00004 minus00187 00473

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

Computational and Mathematical Methods in Medicine 9

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Torso

05 119911 03474 14598 01776 minus00003 00003 minus0012810 119911 03474 15383 00214 minus00012 00013 minus00214100 119911 00014 02854 104856 00004 00018 minus00006200 119911 02456 08967 208858 00016 00010 minus00012100 119910 01391 08154 05305 00032 minus00002 minus00007minus100 119910 00276 minus07041 minus03240 minus00025 00002 minus00003100 119909 107852 06038 00172 00002 00026 minus00353minus100 119909 minus106538 minus15451 02848 00005 minus00080 00327

Renoald algorithm

Plane

05 119911 minus03951 minus01486 05499 minus00001 minus00001 minus0000010 119911 minus08802 minus02661 10675 00000 00006 minus00001100 119911 12549 11879 100882 00002 minus00010 minus00005200 119911 minus20547 minus04494 200903 minus00001 minus00040 minus00006

3plane

05 119911 00041 minus01311 03722 minus00005 00000 0000010 119911 minus00469 minus02864 08242 minus00006 00003 00001100 119911 minus00744 minus45305 82095 minus00099 minus00003 minus00039200 119911 09315 minus67487 168058 minus00134 00058 00033100 119910 01794 40410 minus11857 minus00124 minus00004 minus00002minus100 119910 minus02608 minus54906 13925 00088 00009 00005100 119909 07315 minus00448 00321 00002 00009 minus00018

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00571 minus00831 05143 00015 00003 minus00004100 119911 minus12139 minus01348 88075 00069 00014 minus00393200 119911 minus15751 minus01130 187352 00056 00045 minus00556100 119910 minus04060 75070 minus00636 00356 minus00402 minus00014minus100 119910 03518 minus85498 02583 minus00358 00521 00009100 119909 88252 minus02963 minus01059 minus00000 00147 minus00470minus100 119909 minus89940 04230 01382 00007 minus00171 00477

Torso

05 119911 02920 04220 07578 00005 00012 minus0032110 119911 02378 04817 10779 00003 00009 minus00315100 119911 minus00037 02426 104506 00001 00018 minus00006200 119911 03008 minus01655 187455 minus00011 00022 minus00001100 119910 01177 07804 04367 00028 minus00002 minus00004minus100 119910 00045 minus06522 minus02843 minus00022 00001 minus00001100 119909 104139 04050 00860 00004 00015 minus00327minus100 119909 minus104768 minus06117 01427 minus00003 minus00019 00334

Bergstrom algorithm

Plane

05 119911 00818 minus00440 02600 00009 00004 minus0000310 119911 minus09302 minus02768 10675 00000 00005 minus00001100 119911 minus48742 minus03023 100866 00002 00013 minus00008200 119911 minus37203 07381 200894 minus00000 00001 minus00008

3plane

05 119911 00023 minus012880 03746 minus00005 00003 0000010 119911 minus00470 minus02840 minus08252 minus00060 00003 00001100 119911 minus89059 41357 116053 00083 minus00080 minus00024200 119911 10816 minus49472 181816 minus00095 00014 minus00021100 119910 minus21412 137773 16485 00079 00060 00009minus100 119910 minus01596 minus66095 13820 00062 00004 00006100 119909 84082 28181 12289 00064 minus00053 minus00034

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

10 Computational and Mathematical Methods in Medicine

Table 1 Continued

PhantomShift Registration

Translationmm Rotation∘

119904119889mm 119889 119909 119910 119911 roll pitch yaw

Bowl

05 119911 00818 minus00440 02600 00009 00004 minus0000410 119911 00527 minus00803 05211 00016 00003 minus00004100 119911 minus01868 minus00644 102913 minus00002 minus01752 00064200 119911 06199 minus00374 202321 00092 minus01716 00172100 119910 00319 100246 minus04303 00058 minus01689 00073minus100 119910 04347 minus94345 09152 minus00312 minus01553 00238100 119909 99406 minus21170 06590 00190 00004 00001minus100 119909 minus103737 minus16094 03040 00133 00020 minus00003

Torso

05 119911 03383 minus25946 08076 00004 00001 minus0012810 119911 01906 minus26231 09682 minus00000 00000 minus00121100 119911 00014 02854 104856 00040 00018 minus00006200 119911 minus04539 minus03521 194238 00008 00023 00150100 119910 05342 89866 03959 00007 minus00020 minus00169minus100 119910 minus01569 minus86553 12477 minus00070 00020 00012100 119909 104504 minus25372 04949 00003 00003 minus00131minus100 119909 minus102027 25363 03930 minus00003 minus00002 00120

AlignRT algorithm

Plane

05 119911 01 03 00 00 00 0010 119911 02 01 05 00 00 01100 119911 03 00 101 00 00 01200 119911 02 12 201 00 00 02

3plane

05 119911 00 01 05 00 00 0010 119911 01 01 11 00 00 00100 119911 00 02 102 00 00 00200 119911 00 01 201 00 00 01100 119910 02 102 02 00 00 00minus100 119910 01 minus98 01 00 00 00100 119909 98 02 01 00 00 00

Bowl

05 119911 01 01 05 00 00 0010 119911 01 02 11 00 00 00100 119911 01 02 100 01 00 12200 119911 03 03 199 01 00 16100 119910 02 103 02 00 01 16minus100 119910 07 minus98 02 01 01 27100 119909 101 02 02 00 01 01minus100 119909 minus100 05 02 00 00 17

Torso

05 119911 01 00 06 00 00 0010 119911 01 00 11 00 00 00100 119911 01 00 99 01 00 01200 119911 02 01 198 00 01 01100 119910 02 101 02 00 00 00minus100 119910 02 minus98 01 01 00 00100 119909 100 02 01 00 00 00minus100 119909 minus99 01 00 00 00 00

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

Computational and Mathematical Methods in Medicine 11

(a) Plane all residuals are below119890trans119889 max

(b) 3plane problems atedges and tilted planes

(c) Bowl problems at slopingsurface parts

(d) Torso holes at stitching area of the twosensors

Figure 4 Residuals of surface pairs shifted by 119904119889 = 10mm in direction 119889 = 119911 of the studied phantoms captured by the optical sensor AlginRTand aligned by the Wilm approach

Table 2 Summary of registration success and fail for translations (119909 119910 119911) and rotation (rot) + denotes success when the specifiedmisalignment threshold is deceeded and otherwise minus labels the failing when the threshold is exceeded

AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Motion 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot 119909 119910 119911 rot

Phantom

Plane minus minus + + minus minus + + minus minus + + minus minus + + + minus + +3plane + + + + minus minus minus + minus minus minus + minus minus minus + + + + +Bowl + + + + minus minus minus + minus minus minus + + minus + + + + + minusTorso + + + minus + minus + + + minus + + + minus + + + + + +

+ |119890trans119889 | lt 119890trans119889 max or |119890

rot119903 | lt 119890

rot119889 max minus |119890

trans119889 | ge 119890

trans119889 max or |119890

rot119903 | ge 119890

rot119889 max

Table 3 Overall assessment of the tested ICP algorithms

Property AlgorithmWilm Kroon Renoald Bergstrom AlignRT

Closest point search kd-tree Full Full Full mdash119886

Weighting None None None Distance-based mdash119886

Rejection None None None None mdash119886

Error metric Point-to-plane Point-to-point Point-to-point Point-to-point Point-to-plane

Minimization Linearization ofrotation matrix Global search SVD Levenberg-Marquardt mdash119886

Speed119887 + minus ++ minusminus +Max |119890rot119903 | lt10mm gt10mm gt10mm gt10mm lt10mmMax |119890trans119889 | gt05∘ lt05∘ lt05∘ lt05∘ gt05∘119886

Unknown119887++ very fast + fast minus slow minusminus very slow

in this case the algorithm needs much less iterations becausethe position differences from time step to time step are muchsmaller compared to the first alignment in the static case

In Table 3 an overall assessment of the expected reg-istration error between expected shift and the translationcalculated by the ICP algorithms is given Translation in 119909and 119910 direction was omitted for the plane phantom becauseno registration was possible due to the missing structurein viewing field and therefore only the translation in the 119911direction is specified

One observation from the experiments is that the distanceof shift does not affect the registration accuracy much Also

the required time for convergence is not really affected obvi-ously because the algorithms adapt their step size accordingto the gradient

Much more important are the structure and curvature ofthe surfaces to be aligned With an ambiguous surface theerror surface has flat areas where ICP algorithms are likelyto stick in a local minimum Registration fails in this case toalign the surfaces [25]

Wilmrsquos implementation shows the best results amongthe studied ICP algorithms for translational registrationThe reason for that is obviously the use of the point-to-plane error metric which is the main difference to the

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

12 Computational and Mathematical Methods in Medicine

other algorithms all failing with the above specified accuracydemands Interestingly Wilm fails with rotatory registrationfor the torso phantom Possibly the normal parameter of thepoint-to-plane error metric has disadvantages in this caseSimilar happens for the AlignRT implementation but for thebowl phantom

5 Conclusion

In the paper different unconstrained ICP algorithms havebeen compared for real (noisy) data produced by an opticalsensor as part of a Tomotherapy HD system Registration hasto deal with mainly two difficulties the deficiencies of thesensor (noise) and the ambiguities resulting from the shapeof the measured object Reference [3] found accuracies betterthan 1mm and 05∘ for the used mannequin torso phantomwith the proprietary registration software of the AlignRTsystemWe could show that such accuracies are only possiblefor well curved surfaces whereas gross errors may occur forregistration of other not uniquely shaped surfaces and are notmuch effected by the chosen ICP registration algorithm

The results show that obviously standard ICP algorithmsonly considering point cloud or surface data are too unre-liable to serve as single verification tool of correct patientsettlement Of course large correction values calculated byICP registration give a clear hint that positioning is incorrectwhereas the opposite case does not hold as small value is noguarantee for correct alignment Depending on the curvatureof the actually captured surface parts small ICP registrationcorrection values are estimated even with wrong positioningbecause the ICP algorithm sticks in local minima Theregistration information in parallel to the main orientationof the surface is only helpful in the case of unique surfacestructure A safe registration useful for setup correctionmostly yields perpendicular to the main orientation of thesurface Therefore the result of ICP registration can onlysupport the expertise of the clinical personnel as an additionaltool for the positioning of the patient with regard to thetreatment machine

To improve the probability of reaching a correct devi-ation minimum without fiducial markers other variants ofICP algorithm including additional criteria such as colorsnormals and curvatures [25]may be appliedThehardware ofthe optical sensor supports this because an additional camerafor capturing texture data is included in each measurementunit But according to [3] although calibrated together withthe stereo cameras it can be only used for virtually projectingtexture data on the captured surfaces but not to supportregistration Particularly uncertainties of the registration in119909-119910 direction could be reduced by this information

Ongoing work is done on the estimation of confidencevalues of registration Depending on curvatures character-istics of the treated regions an estimation of the reliabilityof a registration could be given Also alternative registra-tion approaches to surface registration such as probabilisticmethods [18] seem promising to improve the results andworthy of further investigation

Competing Interests

The authors declare no conflict of interests

Authorsrsquo Contributions

Gerald Krell Nazila Nezhad and Mathias Walke carriedout the experiments measured and collected the data andanalyzed the results and wrote the manuscript Ayoub Al-Hamadi and Gunther Gademann contributed to the exper-iments design and to the interpretation of results

References

[1] J Van Dyk T Kron G Bauman and J J Battista ldquoTomother-apy a lsquorevolutionrsquo in radiation therapyrdquo Physics in Canada vol58 no 2 pp 79ndash86 2002

[2] H M Kjer and J Wilm Evaluation of surface registrationalgorithms for PET motion correction [PhD thesis] TechnicalUniversity of Denmark DTUDK-2800 Kgs Lyngby Denmark2010

[3] C Bert K G Metheany K Doppke and G T Y Chen ldquoAphantom evaluation of a stereo-vision surface imaging systemfor radiotherapy patient setuprdquo Medical Physics vol 32 no 9pp 2753ndash2762 2005

[4] P J Schoffel W Harms G Sroka-Perez W Schlegel and C PKarger ldquoAccuracy of a commercial optical 3D surface imagingsystem for realignment of patients for radiotherapy of thethoraxrdquo Physics in Medicine and Biology vol 52 no 13 pp3949ndash3963 2007

[5] G Godin M Rioux and R Baribeau ldquoThree-dimensionalregistration using range and intensity informationrdquo in Proceed-ings of the Processing and Analysis of 3D Data vol 2350 ofProceedings of SPIE pp 279ndash290 Boston Mass USA October1994

[6] M Wiencierz K Kruppa and L Ludemann ldquoClinical valida-tion of two surface imaging systems for patient positioning inpercutaneous radiotherapyrdquo httpsarxivorgabs160203749

[7] TAlderliesten J-J SonkeA Betgen et al ldquoAccuracy evaluationof a 3-dimensional surface imaging system for guidance indeep-inspiration breath-hold radiation therapyrdquo InternationalJournal of Radiation Oncology Biology Physics vol 85 no 2pp 536ndash542 2013

[8] L I Cervino T Pawlicki J D Lawson and S B Jiang ldquoFrame-less andmask-less cranial stereotactic radiosurgery a feasibilitystudyrdquo Physics in Medicine and Biology vol 55 no 7 pp 1863ndash1873 2010

[9] A P Shah T Dvorak M S Curry D J Buchholz and S LMeeks ldquoClinical evaluation of interfractional variations forwhole breast radiotherapy using 3-dimensional surfacerdquo Prac-tical Radiation Oncology vol 3 no 1 pp 16ndash25 2013

[10] A Fassi J Schaerer M Riboldi D Sarrut and G Baroni ldquoAnimage-basedmethod to synchronize cone-beamCT and opticalsurface trackingrdquo Journal of Applied Clinical Medical Physicsvol 16 no 2 2015

[11] D B Wiant S Wentworth J M Maurer C L VanderstraetenJ A Terrell and B J Sintay ldquoSurface imaging-based analysis ofintrafraction motion for breast radiotherapy patientsrdquo Journalof Applied Clinical Medical Physics vol 15 no 6 article 49572014

[12] T Luhmann ldquoClose range photogrammetry for industrialapplicationsrdquo ISPRS Journal of Photogrammetry and RemoteSensing vol 65 no 6 pp 558ndash569 2010

[13] R Y Tsai ldquoA versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV

Computational and Mathematical Methods in Medicine 13

cameras and lensesrdquo in Radiometry L B Wolff S A Shaferand G Healey Eds pp 221ndash244 Jones and Bartlett Burling-ton Mass USA 1992 httpdlacmorgcitationcfmid=136913136938

[14] S Rusinkiewicz and M Levoy ldquoEfficient variants of the ICPalgorithmrdquo in Proceedings of the 3rd International Conferenceon 3-D Digital Imaging and Modeling (3DIM rsquo01) pp 145ndash152Quebec City Canada June 2001

[15] DW Eggert A Lorusso and R B Fisher ldquoEstimating 3-D rigidbody transformations a comparison of four major algorithmsrdquoMachine Vision and Applications vol 9 no 5-6 pp 272ndash2901997

[16] K-L Low Linear Least-Squares Optimization for Point-to-Plane ICP Surface Registration Chapel Hill University of NorthCarolina Chapel Hill NC USA 2004

[17] N J Mitra N Gelfand H Pottmann and L Guibas ldquoRegis-tration of point cloud data from a geometric optimizationperspectiverdquo in Proceedings of the 2nd Symposium on GeometryProcessing (SGP rsquo04) pp 22ndash31 Nice France July 2004

[18] A Myronenko and X Song ldquoPoint set registration coherentpoint driftrdquo IEEE Transactions on Pattern Analysis andMachineIntelligence vol 32 no 12 pp 2262ndash2275 2010

[19] Iterative Closest PointmdashFile ExchangemdashMATLAB Centralhttpwwwmathworkscommatlabcentralfileexchange27804-iterative-closest-point

[20] Finite Iterative Closest PointmdashFile ExchangemdashMATLAB Cen-tral httpwwwmathworkscommatlabcentralfileexchange24301-finite-iterative-closest-point

[21] The Simple GUI program for point clouds RegistrationmdashFileExchangemdashMATLAB Central httpwwwmathworkscommatlabcentralfileexchange35019-the-simple-gui-program-for-point-clouds-registration

[22] P Bergstrom and O Edlund ldquoRobust registration of pointsets using iteratively reweighted least squaresrdquo ComputationalOptimization and Applications vol 58 no 3 pp 543ndash561 2014

[23] Iterative Closest Point MethodmdashFile ExchangemdashMATLABCentral httpwwwmathworkscommatlabcentralfileexcha-nge12627-iterative-closest-point-method

[24] S von Enzberg E Lilienblum and B Michaelis ldquoA physicalsimulation approach for active photogrammetric 3D measure-ment systemsrdquo in Proceedings of the IEEE Instrumentation andMeasurement Technology Conference (I2MTC rsquo11) pp 1ndash5 May2011

[25] DMunch B Combes and S Prima ldquoAmodified ICP algorithmfor normal-guided surface registrationrdquo in Proceedings of theProgress in Biomedical Optics and Imaging vol 7623 of Proceed-ings of SPIE San Diego Calif USA February 2010

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