AUTOMATIC REGISTRATION OF CEREBRAL VASCULAR STRUCTURES

8/12/2019 AUTOMATIC REGISTRATION OF CEREBRAL VASCULAR STRUCTURES

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INTERNATIONAL JOURNAL OF DIGITAL INFORMATION AND WIRELESS COMMUNICATIONS (IJDIWC) 1(1): 1-13THE SOCIETY OF DIGITAL INFORMATION AND WIRELESS COMMUNICATIONS, 2011 (ISSN 2225-658X )

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Automatic Registration of Cerebral Vascular Structures

Marwa HERMASSI, Hejer JELASSI and Kamel HAMROUNIBP 37, Le Belvdre 1002 Tunis, Tunisia

[email protected], [email protected], [email protected]

ABSTRACT

In this paper we present a registrationmethod for cerebral vascular structures inthe 2D MRA images. The method is basedon bifurcation structures. The usualregistration methods, based on pointmatching, largely depend on the branchingangels of each bifurcation point. This maycause multiple feature correspondence dueto similar branching angels. Hence,

bifurcation structures offer betterregistration. Each bifurcation structure iscomposed of a master bifurcation point andits three connected neighbors. Thecharacteristic vector of each bifurcationstructure consists of the normalized

branching angle and length, and it isinvariant against translation, rotation,scaling, and even modest distortion. Thevalidation of the registration accuracy is

particularly important. Virtual and physicalimages may provide the gold standard forvalidation. Also, image databases may in thefuture provide a source for the objectivecomparison of different vascular registrationmethods.

KEYWORDS

Bifurcation structures, bifurcation points, branching angles, feature extraction, imageregistration, vascular structures.

1 INTRODUCTION

Image registration is the process ofestablishing pixel-to-pixelcorrespondence between two images ofthe same scene. Its quite difficult to

have an overview on the registrationmethods due to the important number of

publications concerning this subject suchas [1] and [2]. Some authors presentedexcellent overview of medical imagesregistration methods [3], [4] and [5].From these works, we can say that imageregistration is based on four elements:features, similarity criterion,transformation and finally, optimizationmethod. Many registration approachesare described in the literature. They can

be classified in three categories:Geometric approaches or feature-featureregistration methods, volumetricapproaches also known as image-imageapproaches and finally mixed methods.The first methods consist onautomatically or manually extractingfeatures from image. Features can be

significant regions, lines or points. Theyshould be distinct, spread all over theimage and efficiently detectable in bothimages. They are also expected to bestable in time to stay at fixed positionsduring the whole experiment [2]. Thesecond approaches optimize a similaritymeasure that directly compares voxelintensities between two images. Theseregistration methods are favored forregistering tissue images [6]. The mixed

methods are combinations between thetwo methods cited before. [7] developedan approach based on block matchingusing volumetric features combined to ageometric algorithm: the IterativeClosest Point algorithm (ICP). The ICPalgorithm uses the distance betweensurfaces and lines in images. Distance is


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a geometric similarity criterion, the sameas the Hausdorff distance or the distancemaps such as used in [8] and [9]. TheEuclidian distance is used to match

points features. On the other hand

volumetric criterion are based on pointsintensity such as the Lowest Square (LS)criterion used in monomodalregistration, correlation coefficient,correlation factor, Woods criterion [10]and the Mutual Information [11]. Thethird element, the transformation, can belinear such as affine, rigid and projectivetransformations. It can be non linearsuch as functions base, Radial BasisFunctions (RBF) and the Free Form

Deformations (FFD). The last step in theregistration process is the optimizationof the similarity criterion. It consists onmaximizing or minimizing the criterion.We can cite the Weighted Least Square[12], the one-plus-one revolutionaryoptimizer developed by Styner and al.[13] and used by Chillet and al. in [8].An overview of the optimizationmethods is presented on [14]. Thestructure of the cerebral vascularnetwork, shown in figure 1, presentsanatomical invariants which motivatesfor using robust features such as

bifurcation points as they are a stableindicator for blood flow.

Fig. 1. Vascular cerebral vessels.

Points matching techniques are basedon corresponding points on both images.These approaches are composed of twosteps: feature matching andtransformation estimation. The matching

process establishes the correspondence between two features groups. Once thematched pairs are efficient,transformation parameters can beidentified easily and precisely. The

branching angles of each bifurcation point are used to produce a probabilityfor every pair of points. As these angleshave a coarse precision which leads tosimilar bifurcation points, the matchingwont be unique and reliable to guideregistration. In this view Chen et al. [15]

proposed a new structural characteristicfor the feature-based retinal imagesregistration.

The proposed method consists on a

structure matching technique. Thisstructure, the bifurcation structure, iscomposed of a master bifurcation pointand its three connected neighbors. Thecharacteristic vector of each bifurcationstructure is composed the normalized

branching angles and lengths. The ideais to set a transformation obtained fromthe feature matching process and to

perform registration then. If doesntwork, another solution has to be tested tominimize the error. We propose to usethis technique to vascular structures in2D Magnetic Resonance angiographicimages.

2 PRETREATMENT STEPS:

2.1 Segmentation:

For the segmentation of the vascular

network, we use its connectivitycharacteristic. [16] proposes a technique based on the mathematical morphologywhich provides a robust transformation,the morphological construction. Itrequires two images: a mask image and amarker image and operates by iteratinguntil idem potency a geodesic dilatation


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of the marker image with respect to themask image. Applying a morphologicalalgorithm, named Toggle mapping, onthe original image followed by atransformation top hat which extract

clear details of the image provides themask image. This transformation isdefined by:

else f

f f f f if f

f TM f

sB

sB B B

1

11111

12

;

)(

(1)

Which 1 f and 2 f are respectively theoriginal image and the image improved, and are the morphological closing

and opening and B is the structuringelement.The size of the structuring element is

chosen in a way to improve first thevascular vessels borders in the originalimage, and then to extract all the detailswhich belong to the vascular network.First the clear details of the resultingimage of the toggle mapping areextracted by the process of top hat byopening. The resulting image isconsidered as the image mask. Thistransformation is defined by:

223 f f f B (2)

Second the extracted details maycontain other parasite or pathologicalobjects which are not connected to thevascular network. To eliminate theseobjects, we apply the suppremumopening with linear and oriented

structuring elements. The resultingimage will be considered as the markerimage. The equation of the suppremumopening is given by:

33sup4 max f f S f L L L (3)

Where 180..................0; L L ,are the structuring elements.

The morphological construction isfinally applied with the obtained maskand marker images according to the

equation:

414

445

33

3)(

f f with

f f R f

i f

i f

i f

i f

(4)

The result of image segmentation isshown on figure 2.

(a) (b)

(c) (d)

Fig. 2. Segmentation result. (a) and (c) Originalimage. (b) and (d)Segmented image.

2.2 Skeletonization:

The skeletonization step is crucial forthe registration. Indeed, without thisstep it becomes difficult


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to detect bifurcation points. It consistson reducing a form in a set of lines.Many skeletonization approaches existsuch as topological thinning, distancemaps extraction, analytical calculation

and the burning front simulation. Anoverview of the skeletonization methodsis presented in [17]. In this work, we optfor a topological thinningskeletonization. It consists on erodinglittle by little the objects border until theimage is centered and thin. Let X be anobject of the image and B the structuringelement. The skeleton is obtained byremoving from X the result of erosion ofX by B.

XB I = X \ ((((X B1) B2) B3) B4) (5)

The B i are obtained following a /4rotation of the structuring element. Theyare four in number shown in figure 3 (a).Figure 3 (b) shows different iterations ofskeletonization of a segmented image.

B B B B

Fig.3 (a). Different structured elements,following a /4 rotation.

Initial Image First iteration

Third iteration Fifth iteration

Eighth iterationAfter n iterations :

Skeleton

Fig.3 (b). Resulting skeleton after applying an iterativetopological thinning on the segmented image

3 BIFURCATION STRUCTURESEXTRACTION:

It is natural to explore and establishesa vascularization relation between twoangiographic images because thevascular vessels are robust and stablegeometric transformations and intensitychange. In this work we use the

bifurcation structure, shown on figure 4,

for the angiographic images registration.


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Fig. 4. The bifurcation structure is composed ofa master bifurcation point and its three connectedneighbors.

The structure is composed of a master bifurcation point and its three connectedneighbors. The master point has three

branches with lengths numbered 1, 2, 3

and angles numbered , , and , whereeach branch is connected to a bifurcation point. The characteristic vector of each bifurcation structure is:

333322221111 ,,,,,,,,,,,,,~ l l l x (6)

Where l i and i are respectively thelength and the angle normalized with:

360deg

)(3

1

reesinibranchtheof angle

ilengthesibranchtheof lengthl

i

ii

(7)

To extract the feature vectors of bifurcation structures, several steps must be applied to the reference image and theimage to register. We first identifyall bifurcation points, isolating thosewith three connected neighbors before

calculating the angles and distances ofthe structure.

In the angiographic images, bifurcations points are obvious visualcharacteristics and can be recognized bytheir T shape with three branches aroundas indicated in figure 5. Actually, in oneimage we can find bifurcation

points, trifurcation points and end pointsas shown in figure 5. The last two arecharacterized respectively

by 1 and 4 neighbors. A false bifurcation point, moreover, is too close to

another bifurcation point or with a short branch.

0 1 0

0 1 0

1 0 1

(a) (b) (c)

Fig. 5. Features characteristics of anangiographic image (a) Different characteristic

points of an angiographic image. A- Bifurcation point. B End point. C Trifurcation point. (b) Neighborhood of a bifurcation point. (c)Branching angles of a bifurcation point.

Let P be a point of the image. In a 3x3window, P has 8 neighbors Vi (i {1..8})which take 1 or 0 as value. Pix is thenumber of pixel corresponding to 1 inthe neighborhood of P is:

.)(8

1i

Vi P Pix (8)

Finally, the bifurcation points of theimage are defined by:

P TS _ BIFURCATION ={ THE POINTS P ( I , J ) AS P IX (P ( I , J ) ) 3;( I , J ) ( M , N ) WHERE M AND N ARE THE DIMENSIONS OF THE IMAGE } . (9)

To calculate the branching angles, weconsider a circle of radius R andcentered in P [18]. This circle intercepts

1

3

2

Branch 1

Branch 2Branch 3

l1

l2l3

11 33

3

2 2

2

1

A

CB


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the three branches in three points (I1, I2,I3) with coordinates respectively (x 1, y1),(x2, y2) and (x 3, y3). The angle of each

branch relative to the horizontal is given by:

.)(0

0

x x y y

arctg i

ii (10)

Where i is the angle of the ith branch

relative to the horizontal and (x 0, y0) arethe coordinates of the point P. The angelvector of the bifurcation point is written:

312312 _ Vector Angle (11)

Where 1, 2 et 3 correspond to theangles of each branch of the bifurcation

point relative to the horizontal. A secondsteps consists on selecting the best

bifurcation points, means those withonly three angles. We proceed as shownon algorithm 1. An example is shown infigure 6.

Algorithm 1: Selection of the best bifurcation points

Aim: Extraction of the angles vectorsand keeping only those with three anglesInitialization Pbs emptyFor each bifurcation point

Calculate the angles vector;[l, c] Size of the angles vector;

If c=3 Pbs [Pbs, bifurcation point];End if

End for

Fig. 6. Tracking of the bifurcation points. 1-Bifurcation point (three neighbors)Angles_vector = [135 90 135]. 2- Trifurcation

point (four neighbors).

After the localization of the bifurcation points, we start the trackingof the bifurcation structure. The aim isthe extraction of the characteristicvector. To proceed with the tracking, weexplore the neighborhood of each

bifurcation point. We followthe pixels equal to 1 in thisneighborhood until we find a bifurcation

point. Let P be the master bifurcation point, P 1, P2 and P 3 three bifurcation points, neighbors of P. In determiningwhether there is a connection

between P and his entourage, we followthe pixels equal to 1 in its vicinity. Thisinvolves taking each time the pixelapart and look in his neighborhood ifobjects exist and to identify as and whenthese objects are bifurcation points. We

proceed like presented in algorithm 1and shown in figure 7.

Algorithm 2: Search of the connectedneighbors

V PRepeatIn a 3x3 window of V search for Vi = 1

12


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If true then is Vi a bifurcation pointUntil Vi corresponds to a bifurcation

point.

1 0 1 0 0 0 0 1 0

0P

1 0 0 0 0 0

P

3 1

0 0 1 0 0 0 1 0 0

0 0 0 1 0 1 0 0 0

0 0 0 0 P 0 0 0 0

0 0 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0 0

0 0 0 1P

2 0 0 0 0

0 0 1 0 0 1 0 0 0(a) (b)

Fig. 7. Feature vector extraction. (a) Example ofsearch in the neighborhood of the master

bifurcation point. (b) Master bifurcation point, itsneighbors ad its angles and their corresponding

angles.

Each point of the structure is defined by its coordinates. So, let (x 0, y0), (x 1,y1), (x 2, y2) et (x 3, y 3) be the coordinatesrespectively of P, P 1, P2 et P 3. We have:

.)12(

)()(),(

)()(),(

)()(),(

203

20333

202

20222

201

20111

y y x x P P d l

y y x x P P d l

y y x x P P d l

.)13(

)()( _

)()(

)()(

03

03

01

0131

02

02

03

0323

01

01

02

0212

y y x x

arctg y y x x

arctg

y y x x

arctg y y x x

arctg

y y x x

arctg y y x x

arctg

Where l 1, l2 et l 3 are respectively the branches lengths that connect P to P 1, P 2 and P 3. 1 , 2 and 3 are the angles ofthe branches relative to the horizontaland , and are the angles betweenthe branches. Angles and distances haveto be normalized according to (7). An

example of the characteristic vector of a bifurcation structure is shown in figure8.

Fig. 8. Characteristic vector for this bifurcationstructure is : [37.4833, 173.0218, 105.4992,149.7120, 104.7886, 43.2781, 130.4748,110.7722, 80.8111, 168.4165, 32.2800, 56.5033,195.2551, 70.0168, 94.7279] Normalization

[0.3315, 0.4806, 0.2930, 0.4158, 0.2910,0.3828, 0.3624, 0.3077, 0.2244, 0.4678, 0.2855,0.1569, 0.5423, 0.1944, 0.2631]

4 FEATURE MATCHING :

The matching process seeks for a goodsimilarity criterion among all the pairs of

2

3 1

2 1

3

2

2

P 3

P 2

P 1

P

3

P

P3P2

P1


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structures. Let X and Y be the featuresgroups of two images containingrespectively a number M 1 and M 2 of

bifurcation structures. The similaritymeasure s i,j on each pair of bifurcation

structures is :

.),(, ji ji y xd s (14)

Where x i and y j are the characteristicvectors of the i th and the j th bifurcationstructures in both images. The term d(.)is the measure of the distance betweenthe characteristic vectors. Theconsidered distance here is the mean ofthe absolute value of the difference

between the feature vectors. Wecalculate the distance between thecharacteristic vector of the referenceimage and all the characteristic vectorsof the image to register and we onlykeep the minimum distance whichmeans two similar bifurcation structuresand good candidates for the matching

process. Figure 9 illustrates an exampleof matching process between two

bifurcation structures.

(a) (b)Characteristic vector 1:[0.3315, 0.4806,0.2930, 0.4158,0.2910, 0.3828,0.3624, 0.3077,0.2244, 0.4678,0.2855, 0.1569,0.5423, 0.1944,

Characteristic vector2 : [0.3434, 0.4825,0.2623, 0.4176,0.3199, 0.3749,0.3542, 0.3055,0.2355, 0.4589,0.2816, 0.1632,0.5286, 0.2069,

0.2631] 0.2644] s = 0.0101

Fig. 9. Bifurcation structures matching. (a)Structure of the reference image. (b) Structure ofthe image to register, result of the 15 rotation ofthe reference image. The distance between vector

1 and vector 2 is minimum compared with therest of the characteristic vectors of the image toregister. These two structures consist then goodcandidates for the matching process.

Unlike the three angles of the unique bifurcation point, the characteristicvector of the proposed bifurcationstructure contains classified elements,the length and the angle. This structurefacilitates the matching process byreducing the multiple correspondencesoccurrence as shown on figure 10.

Fig. 10. Matching process. (a) The bifurcation points matching may induce errors due tomultiple correspondences. (b) Bifurcationstructures matching.

5 REGISTRATION:TRASFORMATION MODELAND OPTIMIZATION:

Registration is the application of ageometric transformation based on the

bifurcation structures on the image toregister. We used the linear, affine and

projective transformations. We observedthat in some cases, the lineartransformation provides a better resultthan the affine transformation but wenote that in the general case, the affinetransformation is robust enough to


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provide a good result, in particular whenthe image go through distortions. Indeed,this transformation is sufficient to matchtwo images of the same scene takenfrom the same angle of view but with

different positions. The affinetransformation has generally four parameters, t x, ty, and s whichtransform a point with coordinates (x 1,y1) into a point with coordinates (x 2, y2)as follow:

.cossin

sincos

1

1

2

2

y

x s

t

t

y

x

y

x

(15)

The 2D affine transformation, ingeneral, may represent the spatialdistortions.

1

1

2221

1211

23

13

2

2

y

x

aa

aa

a

a

y

x

(16)

The purpose is to apply an optimalaffine transformation which parametersrealize the best registration. Therefinement of the registration and thetransformation estimation can besimultaneously reached by:

)),(),,((),( nmq pmn pq y x M y x M d e (17)

Here M(x p, yq) and M(x m, yn) arerespectively the parameters of theestimated transformation from pairs (x p,yq) and (x m, y n). d(.) is the difference. Ofcourse, successful candidates for theestimation are those with good similaritys. We retain finally the pairs of structuresthat generate transformation models

verifying a minimum error e. e is themean of the squared difference betweenmodels. This guarantees a moreefficient registration. Figure 11 shows anexample of estimating the parameters

of the affine transformation fromtwo structures pairs.

1st pair of structures Model 1 = [0.9, -0.3, 52.5, 0.2, 1, -102.6, 0, 0, 1]

2nd pair of structures Model 2 = [0.5, 0.4, -23.5, 1.6, -1, 104.6, 0, 0,1]

e = average (Model 2 Model 1) 2 = 0.0054(a)

3rd pair of structures

Model 3 = [0.9, -0.3, 52.5 0.2 1, -102.6, 0, 0, 1]


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4 th pair of structuresModel 4 = [-0.3, 0.7, 293.2, 0.5, 0, -21.5, 0, 0,1]

e= average (Model 4 Model 3) 2 = 7168.6 (b)

Fig. 11. Search of an optimal transformationmodel for the registration. (a) The error e has a

low value; structures are then kept for the finalregistration. (b) The error has an importantvalue; the 4th pair of structures is then rejectedand wont be used in th e final registration.

6 EXPERIMENTAL RESULTS:

We proceed to the structuresmatching using equations (6) and (14) tofind the initial correspondence. The

structures initially matched are used toestimate the transformation model andrefines the correspondence. Figures12(a) and 12(b) shows two angiographicimages. 12(b) has been rotated by 15.For this pair of images, 19 bifurcationstructures has been detected and give 17good matched pairs. The four bestmatched structures are shown in figures12(d) and 12(e). The aligned mosaicimages are presented in figure 12(c) and

12(f). Figure 13 presents the registrationresult for another pair of angiographicimages.

(a) (b)

(c) (f)

(d) (e)

Fig; 12. Registration result. (a) An angiographicimage. (b) A second angiographic image with a15 rotation compared to the first one. (c)Themosaic angiographic image. (d) Vascularnetwork and matched bifurcation structures of(a). (e) Vascular network and matched

bifurcation structures of (b). (f) Mosaic image ofthe vascular network.


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(a) (b) (c)

(d) (e) (f)

Fig. 13. Registration result for another pair ofimages. (a) An angiographic image. (b) A secondangiographic image with a 15rotation compared to the first one. (c)The mosaicangiographic image. (d) Vascular network andmatched bifurcation structures of (a). (e)Vascular network and matched bifurcationstructures of (b). (f) Mosaic image of thevascular network.

We observe that the limitation of themethod is that it requires a successfulvascular segmentation. Indeed, poorsegmentation can infer various artifactsthat are not related to the image and thusdistort the registration. The advantage ofthe proposed method is that it workseven if the image undergoes rotation,translation and resizing. We applied thismethod on images which undergoesrotation, translation or re-sizing. The

results are illustrated in Figure 14.

(a) (b) (c)First pair

(a) (d) (e)

Second pair

(a) (f) (g)Third pair

(a) (h) (i)Fourth pair

Fig. 14. Registration result on few different pairsof images. (a) Angiographic image. (b)Angiographic image after a 10 declination. (c)

Registration result of the first pairs. (d) ARMimage after sectioning. (e)Registration result forthe second pair. (f) ARM image after 90rotation. (g) Registration result for the third pair.(h) Angiographic image after 0,8 resizing,sectioning and 90 rotation. (i) Registrationresult of the fourth pair.

We find that the method works for


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images with leans, a sectioning and arotation of 90 . For these pairs ofimages, the bifurcation structures arealways 19 in number, with 17 good

branching structures matched and finally

4 structures selected to perform theregistration. But for the fourth pair ofimages, the registration does not work.For this pair, we detect 19 and 15

bifurcation structures that yield to 11matched pairs and finally 4 candidatestructures for the registration. We tried toimprove the registration by acting on thenumber of structures to match and bychanging the type of transformation. Weobtain 2 pairs of candidate structures for

the registration of which the result isshown in Figure 15.

(a) (b) (c)

Fig. 15. Registration improvement result. (a)Reference image. (b)Image to register (c) Mosaicimage.

7 CONCLUSION:

This paper presents a registrationmethod on the vascular structures in 2Dangiographic images. This methodinvolves the extraction of a bifurcationstructure consisting of master bifurcation

point and its three connected neighbors.Its feature vector is composed of the

branches lengths and branching angles

of the bifurcation structure. It isinvariant to rotation, translation, scalingand slight distortions. This method iseffective when the vascular tree isdetected on MRA image.

8 REFERENCES

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pages 1-36, October 1997.

4. Barillot C. Fusion de Donnes et Imagerie3D en Mdecine, Clearance report,Universit de Rennes 1, September 1999.

5. D Hill, P Batchelor, M Holden, D Hawkes,Medical Image Registration. Phys. Med.Biol.: 46, 2001

6. Passat N. Contribution la segmentationdes rseaux vasculaires crbraux obtenusen IRM. Intgration de connaissanceanatomique pour le guidage doutils demorphologie mathmatique, Thesis report,28 septembre 2005.

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Sciences thesis, Universit de Nice Sophia-Antipolis, February 2001.

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AUTOMATIC REGISTRATION OF CEREBRAL VASCULAR STRUCTURES

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