Experimental methodology for benchmarking ICP-like algorithms

Leopoldo Armesto Luıs Montesano Javier Mınguez

Abstract— Scan matching techniques have been widely usedto compute the displacement of robots. This estimate is partof many algorithms addressing navigation and mapping, beingICP the most used to solve this problem. This paper addressesthe methodological aspects for evaluating ICP-like algorithms.In this sense, several tools are provided to select scenariosfor validating results and to validate point to facet distance,correspondence and pose estimation individually. In additionto this, the paper provides tools for analyzing robustness,precision, computational time and robustness sensibility toparameter variation. At hte end of the paper, we also presentsome map building results.

I. INTRODUCTION

Scan matching techniques are widely used to track therobot position using range data in many applications suchas navigation and mapping. The principle is to compute thesensor displacement between two consecutive configurationsby maximizing the overlap between the range measurementsobtained at each configuration. Although they are localin nature, in Robotics they have been widely used as animproved odometry in navigation systems [1] or to solve theinitial problem in SLAM [2], to aid loop-closing, etc.

The most popular scan matching methods usually followthe Iterative Closest Point (ICP) algorithm (principle bor-rowed from the computer vision community [3], where manygeometric ICP variants have been proposed to deal with theregistration problem in 3D, see [4] for a survey). The dif-ferent approaches modify the correspondences computationbetween meshes based on intersecting rays, projection ofpoints to the mesh, orthogonal vectors, compatibility tests oron metrics using color information. This information is alsoused to re-weigh the correspondences in the minimizationstep. In [5], authors propose a variation to ICP by usinga Z-buffer to find correspondences. The method does notnecessarily obtain the closest point but accelerates the com-putation time using the GPU (Graphic Processor Unit). Aclosed-form estimate for the ICP covariance was proposedin [6]. Recently, Generalized-ICP [7] has been extended thepoint to plane distance in [8]. By incorporating a probabilisticinterpretation, it uses planar approximations to implementa plane-to-plane minimization and to take advantage of thestructure of the environment.

For the scan matching problem, we can also find severalICP variants, e.g. [9], [10], [11], [12], [13] among others.

This work has been partially supported by the Vicerectorado de Investi-gacion, Desarrollo e Innovacion from Universidad Politecnica de Valencia

L. Armesto is with Control and Systems Engineering, UniversidadPolitecnica de Valencia, Valencia, Spain leoaran@isa.upv.es

J. Minguez and L. Montesano are with the I3A, Computer Sci-ence Department, Universidad de Zaragoza jminguez@unizar.es,montesano@unizar.es

Most of these ICP variants use the Euclidean distance tocompute correspondences. The limitation of this distanceto capture the sensor rotation was initially solved in [10]improving the performance of previous 2D methods. Thiscontribution has been recently extended to 3D in [14]obtaining better performance than ICP, specially in thepresence of large rotation errors. Other approaches includeIterative Dual Correspondence (IDC) [15], Hough Transform[16], [17], probabilistic approaches [18], [19], [20], NormalDistribution Transform [21], etc. The natural extension ofscan-matching and pair-registration is to consider a globalconsistent matching between partially overlapping point sets,known as N-Registration in the Vision community (see [22]for a comparison) and N-Scan Matching problem in Roboticscommunity [23].

Preliminary contributions to the scan matching problem,did not perform an exhaustive experimental validation. Inthose cases, authors claimed improvements with respect toICP, but experiments were focused to very few particu-lar cases, because the lack of a methodology to evaluateperformance of algorithms. It was generally accepted thatproviding simple examples or maps was enough proof fordemonstrating the performance of a method. During years,scan matching papers and more intensively SLAM papers,have included images with maps of labs, departments andmany places like post stamps you can collect but not evaluatequantitatively.

Nowadays, due to the high maturity achieved in SLAMand scan matching problems, the Robotic Community re-quires severe experimental validation on papers before be-ing accepted. In the last years, the growing interest ofbenchmarking tools has provide useful data repositories in2D [24] and in 3D [25]. The purpose of data repositoriesis to allow us to evaluate new algorithms with respectexisting ones under the same conditions and possibly withground-truth data. A clear example can be found in [11],where Censi appended his results to the ones previouslyobtained by Minguez in [10], without need to re-implementprevious existing techniques. However, data repositories arenot enough and new metrics for evaluating techniques arealso necessary in both SLAM and scan matching problemsas well as benchmarking tools to perform experimentation.A typical way to validate experimentally or in simulation isto use Monte Carlo runs. In this sense, in [10], a method forevaluating scan matching algorithms was initially introduced,where the key idea to their experimental validation is toinclude an statistical study of the robustness and accuracyby matching each scan by itself once rotated and translatedwith a random pose.

This paper addresses the problem of experimentation andevaluation of ICP-like scan matching algorithms. In thissense, the paper discusses tools that can be used for valida-tion and analysis of ICP-like algorithms, including selectionof appropriate scenarios, validation of core-functions (pointto facet distance), validation of correspondences and poseestimation methods, generation of robustness and precisiontables with different error levels, analysis of computationaltime and required number of iterations, generation of mapswith artificial odometry data to highlight particular charac-teristics and generation of parameter sensibility maps. Forthat purpose, the paper first describes a recent new metricapproach [14] as the extension of the MbICP [10] to 3D envi-ronments to be compared with well-known ICP method. It isnecessary to remark that, the main contribution of the paperis not the derivation of the new metric approach itself, butthe methodology employed to validate the results. In additionto this, the paper also describes in detail the implementationprocedure to achieve our experimental results.

II. ICP AND MBICP SUMMARY AND IMPLEMENTATION

ICP is a well-known technique used in the scan matchingcontext to provide a pair matching between two relativescans. The main steps of ICP-like algorithms are: 1) computethe correspondences (point to point and point to facet)between two scans and 2) estimate the displacement of thesensor.

The MbICP represents a new approach to implement suchas steps by taking into account the rotation of the sensor,by defining a new metric. In [14], the generalization to 3Dworkspaces of the metric introduced in [10] is presented.The new metric defines isodistance surfaces as ellipsoids,including the Euclidean metric by considering the parameterL = ∞, where L is represents a weighting factor betweentranslational and the rotational parts. The rationale is thehigher the L the higher influence has the translation part,thus, the closer to Euclidean metric approach. Figures from1(a) to 1(f) show different cases of the MbICP and ICPmetrics for point to point, point to segment and point tofacet distance computation.

The new metric affects on how distance at the correspon-dence step are computed in ICP-like algorithms but also inthe pose estimation step, since it is no longer a closed-formsolution but a linearised solution, see [14] for details.

Our implementation of ICP and MbICP includes thefollowing aspects:

Correspondence search: First, we construct facets fromraw data. In our case, we form two facets from the quad oftwo consecutive points within a scan and two consecutivescans, since our data input is in spherical coordinates (weare using a tilt rotating sensing system [26]). Implementthe core metric functionalities (either ICP and MbCIPmetrics) and perform the search efficiently. For that pur-pose, we have implemented an angular window filter anddistance threshold to constrain the search which implies areduction on computational cost.

(a) Point-to-point L =∞ (b) Point-to-point L = 2

(c) Point-to-segment L =∞ (d) Point-to-segment L = 2

(e) Point-to-facet L =∞ (f) Point-to-facet L = 3

Fig. 1. Isodistance curves of the the new metric, including the particularcase of the euclidean distance (L =∞).

Pose estimation: Implement pose estimation core func-tionalities (minimization), either using closed-form [27]or approximated [28] solutions. Also implement rigidtransformations of a scan with the estimated pose.Performance improvements: This covers from basic toadvance filters that aim to eliminate spurious data. In par-ticular, we are filtering out facet outliers with an adaptive-breakpoint detector [29] so we can detect openings such adoor. We are also rejecting points based on their distanceto the sensor frame, so if they are too far they might affectto accuracy, while if they are to close the robot and the3D rotating laser are measured. As advanced filters, wehave implemented the Trimmed ICP method [30] to filterout spurious data. Other possibilities are to use weightedcorrespondences and to perform a random selection ofpoints based on their orientation to reduce the amountof data [4]. As a very common convergence criteria weare using as stopping condition to reach a given numberof iterations and also existing if the position error androtational error are below a given threshold, but also weuse soft convergence criteria to ameliorate local minimaproblem (it exits when stopping conditions are obtainedseveral consecutive times) in addition to consider the errordecrement ratio [9]. Finally, we have implement parallelcomputation capabilities to run the algorithm on multi-coreprocessors [28] to reduce computational cost.

(a) Cube (b) Cube with correspondences

Fig. 2. This figure depicts the artificial cube generated to validatepreliminary aspects.

III. EXPERIMENTAL METHODOLOGY FORBENCHMARKING OF SCAN MATCHING ALGORITHMS

The proposed methodology for benchmarking scan match-ing algorithms consists of the following procedures:

Scenario Selection: Select appropriate scenarios to vali-date (off-line) the algorithm, either with artificial data andwith real data.Qualitative Validation: Perform qualitative validation testto verify core functionalities such as metrics, correspon-dences and pose estimation.Quantitative Validation: Based on the methodology pre-sented in [10] perform robustness, precision, computa-tional time and parameter sensibility analysis by perform-ing scan matching with the same scan with rotated andtranslated with random poses. In addition to this, performmapping of a cluttered scenario by integrating all pair scanmatching estimations.

A. Scenario Selection

In scan matching problems, it is crucial to select anappropriate scenario to validate the algorithm, either withartificial data and with real data. In particular, we have usedas artificial data a cube as shown in Fig. 2(a). It can be saidthat the cube is one of the most difficult cases to be solvedfor a scan matching algorithm because it has lots of singularconfigurations that may lead to a local minima. However,it covers the whole 3D space and contains few points andfacets, which simplifies the task of validation. In addition tothis, we use the dataset used in [26], which contains 72 3Dlaser scans recorded in a bakery with a tilt rotating in 2Dlaser scan. The experiment contains a single loop which hasshown to be enough to validate our method.

B. Qualitative Validation

At the very basic validation step, one should performqualitative validation tests to verify core functionalities of thealgorithm. We describe how to validate, qualitatively, metriccomputations, correspondences and pose estimations:

Metric: Validate core metric functionalities with a singlefacet by computing the closest point from a cloud of pointssurrounding the facet. Fig. 3 shows the behavior of thenew metric, where differences with respect to Euclideandistance can be appreciated, specially at the corners of thefacet.

Fig. 3. This figure depicts the metric validation with a single facet.

Fig. 4. Correspondences between two scans.

Correspondence: Using the cube as reference scan andgenerating artificial data as new scan (without noise),apply arbitrary random transformations to the new scanand find the correspondences between both scans. Fig. 2(b)show an example of correct correspondence with the newmetric, where the important key is that we are validatingcorrespondences at the full 3D space. Also, validate thecorrespondences with more complicated data such as full3D scan. Fig. III-B show an example of correspondenceswith the new metric for the dataset with real data, whereit can be appreciated that correspondences tend to linkpoints that are further, in terms of the Euclidean distance,than others, because of the intrinsic properties of the newmetric.Pose Estimation: Using the same scan and assumingknown correspondences, generate random transformationsand estimate the relative pose. When using a closed-form solutions like [27], both scans match in just onesingle iteration. When using an approximate solution,like the one proposed in [14], the procedure must beiterated several times until convergence. In addition tothis, we statistically analyze the robustness performanceof pose estimation methods to spurious associations. Byintroducing random errors from a uniform distribution intranslation and rotation, run a large number Monte Carlosimulations. Table I shows the pose results the estimationperformance using the pose estimation method proposedby Horn [27] and our proposed estimation method usingthe new metric which is a generalization of the estimationmethod proposed in [10] and used in the original MbICPfor the 2D case. With perfect correspondences and freeof noise, the performance of the ICP estimation methodis clearly higher than the MbICP one. This is expected

Spurious εt[mm] εθ[mrd]ICP MbICP ICP MbICP

0% 7.71e−09 2.13 1.03e−09 0.21710% 74.3 73.9 40 40.330% 42.9 41.5 24.6 25.850% 21.1 19 12.5 14.3

TABLE IESTIMATION PERFORMANCE FOR THE ICP AND MBICP ESTIMATORS.

TRANSLATION ERRORS εt[mm] AND ROTATION ERRORS εθ[mrd].

since the MbICP has to approximate while the ICP isa closed form solution. The comparison becomes moreinteresting in the presence of spurious correspondences.This is usually the case in the first iterations of any scanmatching process, since some points will not be associatedto the right part of the structure. In this case, the MbICPestimator shows slightly better accuracy for estimating thetranslational component than ICP, while the ICP estimatorseems to be more precise for estimating the rotationalcomponent.

C. Quantitative Validation

The goal is to obtain quantitative data to understand themore relevant properties of the scan matching techniques thatcan be evaluated. We are interested in robustness, that is theability to obtain valid estimations, but also accuracy as wellas computational time aspects and even more a parametersensibility study on robustness. Another type of quantitativestudy is to build maps to evaluate the performance with realdata by integrating all pair scan matching estimations withspurious data.

The detailed procedure is as follows:Scan vs. scan: Based on the methology presented in [10],where a scan is matched against itself after introducingrandom pose transformations we can provide the followinguseful metrics for evaluating scan matching algorithms:1) Robustness and accuracy tables: Prepare a set-upwhere each scan is matched against itself, but with randominitial locations. Define several levels of errors at the initialpositions, starting form small translations and rotations(Experiment 1) to larger ones (Experiment N ), with agiven increment on error bounds on each experiment.Then, run Monte Carlo simulation, one for each scan,each noise level and each random pose. Since we matcha scan against itself, the matching of both scans should inprinciple be perfect at convergence and we can calculatethe error made by each method against the ground truth(zero rotation and zero translation). For the analysis, weconsidered a successful run those solutions that convergedin less than a given number of iterations, whose error intranslation was lower than a pre-specified value and whoseerror in rotation was lower than a given threshold. Basedon this thresholds we compute percentages of true posi-tives (the solution converged below the threshold); falsepositives (the algorithm converged with errors above thethreshold); true negatives (the algorithm did not convergedand was still above threshold); and false negatives (thealgorithm did not converge but the solution was alreadybelow threshold). In our case, we have 50 random poses,

TABLE IIROBUSTNESS ANALYSIS OF SCAN MATCHERS.

Exp. ICP MbICPTP FP TN FN TP FP TN FN

#1 100 0 0 0 100 0 0 0#2 100 0 0 0 100 0 0 0#3 100 0 0 0 100 0 0 0#4 99.89 0 0.11 0 100 0 0 0#5 98.58 0.31 1.11 0 99.36 0.11 0.47 0.06#6 96.67 0.69 2.58 0.06 99 0.19 0.81 0#7 94.11 1.53 4.33 0.03 97.67 0.28 1.89 0.17#8 90.56 3.44 5.94 0.06 96.58 0.92 2.36 0.14

TABLE IIIPRECISION ANALYSIS OF SCAN MATCHERS.

Exp. ICP MbICPH M L H M L

#1 99.97 0.02778 0 100 0 0#2 99.94 0.05556 0 100 0 0#3 99.75 0.25 0 100 0 0#4 99.67 0.3337 0 100 0 0#5 99.32 0.6762 0 99.94 0.05591 0#6 99.34 0.6609 0 99.92 0.08418 0#7 98.88 1.122 0 99.94 0.05688 0#8 98.87 1.135 0 99.8 0.2013 0

8 experiments and 72 scans, which turns out to 28800

runs to obtain the tables. Table II shows the results thatwe have obtained for each method. In can be seen, that,when the error is small all the methods achieved 100%

of true positives. As the error increases from experiment#1 to #8, the percentage of true positives decreases forboth methods. In all the cases, the MbICP performedbetter than ICP since it has the highest percentage oftrue positives and the lowest number of false positives.For the analysis of the precision, we considered only thetrue positives cases and define the error bounds equallydistributed in three intervals corresponding to high (H),medium (M) and low (L) precision. Table III showsthe precision results for each method. In this case, theperformance of both methods is quite similar, althoughthe MbICP obtained slightly better results. It has to besaid that to obtain robustness and precision tables, wefirst run experimentation with 10 random poses per eachscan to pre-validate results. Once pre-validated, we havecompleted the experimentation with 50 random poses pereach scan.2) Computational time performance: One key aspectof every algorithm is to evaluate the computational time.Usually, more sophisticated methods require a more com-putational time. Other methods, focus on reducing thecomputational time while obtaining approximate solutions.This is always a trade-off between gained performance andcomputational time requirements. Figure 5(a) depicts themean number of iterations used by each method for eachexperiment. There are no significant differences betweenthe methods (smaller than five iterations in average).Regarding execution times, MbICP iterations is clearlymore expensive than ICP (see Figure 5(b)). Therefore,the constant overhead required by the MbICP algorithmis the price to pay for the improvement in robustness andprecision.3) Parameter sensibility:. A parameter sensibility map

(a) Iterations

(b) Computational Time

Fig. 5. Number of iterations and computational time required by the ICPand MbICP for the different levels of error.

obtained from a parameter sweep evaluating the robustnessperformance of each algorithm can be used to drawn somenew conclusions. In figures 6(a) and 6(b) the sensibilitymaps of ICP and MbICP for the experiment #8 is shown,where variations of angular window and distance thresholdparameters have generated different TP percentages inrobustness. It can be appreciated that, the MbICP showshigher robustness, as expected, and moreover, less sen-sibility to parameter variation, specially for the distancethreshold. The ICP clearly degradeates faster with lowerdistance threshold values and it has lower robustness val-ues. On the contrary, MbICP degradates with the narrowangular windows, because isodistance surfaces of the newmetric restricted to low rotations performs basically equalthan ICP and thus the robustness is degradated similarly.Mapping: Scan matching algorithms should perform suc-cessfully in map building by closing at least a loop,since the ability of closing multiple loops can be takenas a measure of the robustness and accuracy but withspurious data. Odometry data is frequently used to improvemapping results to ameliorate the difficulty of the problem.However, in our opinion, this can hide the benefits of aparticular technique, specially if your purpose is to findthe limits of your algorithms. For that reason, we proposeto introduce randomly bounded error on odometry data

(a) ICP

(b) MbICP

Fig. 6. Robustness sensibility map to parameter variation.

so that the algorithm can be tested to the limit. Based onthe ideas of multiple experiments with increasing errors oftables II and III, we have introduced errors in odometrydata according to the same conditions. Figures 8(a) to 8(f)show robot trajectories estimation and super-imposed laserscans at each position for a whole experiment (one loop inan old bakery), where in this case the matching has beenperformed between consecutive scans by introducing low,medium and large errors to odometry data. It can be ap-preciated from these figures, that the MbICP shows higherperformance than ICP with larger errors. Therefore, it canbe concluded that MbICP is more suitable for low qualityodometry data or in the absence of odometry sensing. Mappost-processing is also highly recommendable to improvethe quality of figures, where in our case, we have used anelevation map to show the map in an isometric view infigure 8. To obtain maps we have computed 216 differentmaps with different parameter values (including angularwindow angle, distance threshold and trimmed ICP ratio)and selected the “best” ones.

IV. CONCLUSIONS

This paper describes a methodology to experimentallyvalidate ICP-like algorithms. The methodology also includesa detailed description about implementation issues. In par-ticular, the methodology includes guidelines for selectingappropriate scenarios to validate algorithms with artificialand real data. In order to validate core metric-functions a

(a) ICP with low odometry errors. (b) MbICP with low odometry errors.

(c) ICP with medium odometry errors. (d) MbICP with medium odometry errors.

(e) ICP with large odometry errors. (f) MbICP with large odometry errors.

Fig. 8. 2D map views (XY plane) and elevation map of an old bakery obtained with different scan matching algorithms and odometry errors.

Fig. 7. 3D elevation map isometric view.

simple test for point to facet distance computation allow usto validate the new metric. Also guidelines for validatingcorrespondence search and pose estimation separately areprovided. The methodology becomes more sophisticated onthe proposed procedure for evalutation the robustness andprecision of ICP-like algorithm by means of Monte Carloruns. Computational time and required iterations are alsoconsidered using the same methodology. In addition tothis, we discuss the influence of parameters to presentedresults and in particular the sensibility of each algorithmto parameter variation. Using this methodology, we haveshown that the new metric is more robust, accurate andless sensible to parameter variations, but with an overheadon computational time. Finally, we have also analyzed howodometry data affects to map generation, showing intrinsicrobustness properties of each method by bring each casestudy to the limit.

ACKNOWLEDGEMENTS

Authors want to thank Pedro Pinies for the 3D datasetand the Research Institute of Design and Manufacturing forgranting us access to workstations to compute the results.

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