A Performance Evaluation of Surface Normals-based Descriptors for Recognition of Objects Using CAD-Models

A Performance Evaluation of Surface Normals-based Descriptors forRecognition of Objects Using CAD-Models

C. M. Mateo1, P. Gil2 and F. Torres21University Institute for Computing Research, University of Alicante, San Vicente del Raspeig, Spain

2Department of Physics, Systems Engineering and Signal Theory, University of Alicante, San Vicente del Raspeig, Spain{cm.mateo, pablo.gil, fernando.torres}@ua.es

Keywords: 3D Object Recognition, 3D Surface Descriptors, Surface Normal, Geometric Modelling.

Abstract: This paper describes a study and analysis of surface normal-base descriptors for 3D object recognition. Specif-ically, we evaluate the behaviour of descriptors in the recognition process using virtual models of objects cre-ated from CAD software. Later, we test them in real scenes using synthetic objects created with a 3D printerfrom the virtual models. In both cases, the same virtual models are used on the matching process to findsimilarity. The difference between both experiments is in the type of views used in the tests. Our analysisevaluates three subjects: the effectiveness of 3D descriptors depending on the viewpoint of camera, the ge-ometry complexity of the model and the runtime used to do the recognition process and the success rate torecognize a view of object among the models saved in the database.

1 INTRODUCTION

The 3D object recognition process has had importantadvances in the last years. In recent works, many ap-proaches use range sensors to obtain depth of objectspresent in a scene. The depth information has per-mitted to change the techniques and algorithms forextracting features from image. In addition, this onehas been used to design and create new descriptors foridentification objects from scene captured by rangesensors (Rusu, 2009) and (Lai, 2013). LIDARSs,Time of Flight cameras (ToF) or RGBD sensors, suchas Kinect or Asus Xtion PRO Live, provide depth andallow us to recover the 3D structure of scene froma single image. The choice of the kind of sensoris depending on the context and lighting conditions(indoors, outdoors) and type of specific application(guided/navigation of robots or vehicles, people de-tection, human-machine interaction, object recogni-tion and reconstruction, etc.). Furthermore, the recog-nition methodology applied to retrieve the 3D objectshape is different depends on whether the object isrigid or non-rigid. A variety of methods for detec-tion of rigid and non-rigid objects were presented in(Wohlkinger et al., 2012) and (Lian et al., 2013), re-spectively.

In this work, rigid object recognition is done. Butrigid object recognition can be based on visual fea-tures information such as bounding, skeleton, silhou-

ette, colour, texture, moments, etc. or geometric fea-tures such as vectors normal, voxels, etc. obtainedfrom depth information captured from a range sen-sor. Examples of descriptors for rigid objects basedon geometric features, are: PFH (Point Feature His-togram) and FPFH (Fast Point Feature Histogram)(Rusu, 2009); VFH (Viewpoint Feature Histogram)(Rusu et al., 2010); CVFH (Clustered Viewpoint Fea-ture Histogram) (Aldoma et al., 2011); and SHOT(Signature of Histograms of Otientations) (Tombariet al., 2010). All of them describe the geometry ofan object using normal vectors to its surface which isrepresented by a point clouds. Other descriptors suchas ESF (Ensemble of shape Functions) (Wohlkingerand Vincze, 2011a) and SVDS (shape Distributionon Voxel Surfaces) (Wohlkinger and Vincze, 2011b);GRSD (Global Radius based Surface Descriptors)(Marton et al., 2011) are based on voxels to representthe object surface. SGURF (Semi-Global Unique Ref-erence Frames) and OUR-CVFH (Oriented, Uniqueand Repeatable CVFH) (Aldoma et al., 2012b) arealso other noteworthy descriptors because they havethe advantage to the ambiguity over the camera rollangle. SGURF is computed from a single viewpointof the object surface and OUR-CVFH is based on amix between SGURF and CVFH. CVFH is brieflydiscussed below.

In this paper, 3D rigid object recognition based onobject category recognition is done. Also, we have

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introduced some novelty into the performance shownin (Wohlkinger et al., 2012) and (Alexandre, 2012).We have created views from a virtual camera whichcaptures information of virtual models with differentviewpoints. Afterwards, we have created the 3D rigidobjects from CAD models using 3D printer to testif the behavioural changes of the descriptors are sig-nificant. Thereby, the errors in the recognition pro-cess can be better controlled. Thus, both descriptors,model and object, are computed from known perfectgeometrical figures. Therefore, the recognition errorsonly depend on the geometry of the isolated objectin the scene and the precision of descriptor for mod-elling and identifying these objects. It is importantemphasize that evaluated descriptors cannot be usedif the scene was not previously segmented and the ob-jects are localized therein.

The rest of this paper is structured as follows. 3Ddescriptors based on geometric information are com-mented in Section 2. In Section 3, we present the sim-ilarity measures proposed for associating objects tomodels. Experimental results of the descriptors eval-uation is shown in Section 4 and 5. Finally, section 6,contains the conclusions.

2 3D DESCRIPTORS

In this paper, we work with isolated rigid objects withuncluttered backgrounds in indoor scenes. Hence, ourappearance model is based on a set of different featuredescriptors. In particular, five descriptors are used inthe experimentation. For each descriptor type, we usethe same training framework. That is the same ob-jects as dataset or test data. The training framework isdetailed later (Section 4). The descriptors are alwayscomputed over a mesh consists of a point cloud. Thedescriptors only include geometric information basedon the surface shape but they do not include colour orother type of visual features information. The idea isto evaluate 3D objects recognition methods based on3D descriptors without using additional appearanceinformation such as colour and texture from scene im-age, information position/orientation from geoloca-tion and odometry techniques obtained. The absenceof colour and texture provides generality for workingwith unknown objects and simplifies the runtime inthe recognition task. Frequently, in the industrial en-vironments are used objects and pieces without thiskind of information. Those are made of metal or plas-tic material with homogeneous colour and they canonly be differenced by means of geometry and sur-face features.

The five feature descriptors based on surface nor-

mal vectors: PFH, FPFH, SHOT, VFH and CVFH,were chosen because they retrieve enough geometri-cal information of shape. This information will giveus the ability to make further analysis in industrialpieces. In the literature, descriptors are grouped aslocal and global recognition pipeline. The main dif-ference among these groups is the size of signatureand the number of signatures to describe the surface.In the first, descriptor is represented by a signature foreach point of surface, but, in the second, it saves allviewpoint information using one signature for wholesurface. A brief description:

PFH, It is a set of signatures from several localneighbourhoods. For each point is computed a 3-tuple, 〈 α, φ, θ 〉 of angles which represent therelation among normals in their neighbourhood,according to Darboux frame. Then in order to,compute each final signature, the method adds therelations among all points within neighbourhoodin the surface. Therefore the complexity compu-tational isO

(

nk2)

. The signature dimensionalityis 125.

FPFH, This is based on the same idea thatPFH, ituses a Darboux frame to make relations amongpair of points within a neighbourhood with ra-dio r for computing each local surface signature.This descriptor generates a linear complexity inthe number of neighbours,O(nk). This approxi-mation changes the relations among a point and itsneighbours located with a distance smaller thanr,adding a specific weight according to the distancebetween point and every neighbour. The signaturedimensionality is 33.

SHOT, In this descriptor a partitioned spherical gridis used as local reference frame. For each volumeof the partitioned grid, a signature of the amountof cosθi between the normal at each point of sur-face and the normal at the query feature point iscomputed. A normalization of descriptor is re-quired to provide it robustness towards point den-sity variations. The signature dimensionality is352.

VFH, It is based on FPFH. Each signature consists ofa histogram with two components; one has the an-gles〈α,φ,θ〉 which is calculated as the angular re-lation between a point’s normal and the normal ofthe point cloud’s centroid, and other represent theangles between the vector determined by the sur-face centroid and viewpoint. This descriptor hascomplexity ofO(n). The signature dimensionalityis 308.

CVFH, This descriptor is an extension toVFH. Thebasic idea is to identify an object from splitting it

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(a) Cone (b) Cube (c) Cylinder (d) Prism (e) Sphere

Figure 1: Primive shapes of the models.

in a set of smooth and continuous regions or clus-ters. The edges, ridges and other discontinuities inthe surface are not considered because these partsare more affected by the noise. Thereby, for eachof these clusters is computed itsVFH descrip-tor. CVFH describes a surface as a histogram inwhich each histogram item represents the centroidto surface and the average of the normals amongall points of surface. Again, the dimensionality is308.

Other descriptors such as Radius-based (RSD andGRSD) or voxels-based (SVDS andESF) are not stud-ied here. This decision was taken because the re-sults shown in (Aldoma et al., 2012a) and (Alexandre,2012) that Normal-based descriptors are best withhousehold object as proving the accumulated recog-nition rate, ROC curve for recognition and Recall-vs-(1-Precision).

3 SIMILARITY MEASURES

Similarity measures are used to associate the CAD-model and the object view. The similarity measuresare defined like distance metrics. Four type of dis-tance metrics,ds = {dL1,dL2,dχ2,dH} are used tocompare the CAD-model,C j, which represents a ob-ject category with the object view in the scene. Thedefinitions for the four distances are:

dL1 (p,q) =n

∑i=1

pi − qi (1)

dL2 (p,q) =

√

n

∑i=1

(pi − qi)2 (2)

dχ2 (p,q) =n

∑i=1

(pi − qi)2

pi + qi(3)

dH (p,q) =1√2

√

n

∑i=1

(√

pi −√

qi)2 (4)

wheredL1 defines the Manhattan distance,dL2 isEuclidean distance,dχ2 defines Chi-squared distanceanddH is Hellinger distance. Andn is point dimen-sions, beingp andq two arbitrary points.

Each CAD-model,C j is defined by a set of viewsC j =

{

c j1,c j2 . . . ,c jr}

wherer is the number of view-points from where the CAD-model is observed witha virtual camera. Furthermore, each view is repre-sented by a set of descriptors defined as following,

c jl ={

m jl1 ,m

jl2 ,m

jl3 ,m

jl4 ,m

jl5

}

wherel represents the

view identifier andj the object class defined in theCAD-model. This set represents a hybrid descrip-tor composed of five components. A component foreach type of descriptor:PFH, FPHF, SHOT, VFHandCVFH. Similarly, for each object,Oi is definedby a set of viewsOi = {oi1,oi2, . . . ,oin} wheren is thenumber of viewpoints from where the object in sceneis captured using a virtual or real camera. As well,each view is represented by a set of descriptors de-fined as following,oik =

{

vik1 ,v

ik2 ,v

ik3 ,v

ik4 ,v

ik5

}

wherekrepresents the view identifier, andi is the object iden-tifier.

Then, the difference between each component ofthe CAD-model descriptor and object descriptor, iscalculated according to equations (1), (2), (3) and (4).

The similarity,dc, between object category,C j inthe database and the object in scene, is computed byusing the minimum distance for each type of descrip-tor, following equation (5). The comparison is donefor all models saved in the database.

dc (Oi,C j) = minoik∈Oi ∧ c jl∈C j

{

d(

oik,c jl

)}

(5)

d(

oik,c jl

)

=

√

ds (oik,c jl)2+ ds (c jl ,oik)

2 (6)

wheres represents the kind of distance defined inequation (1), (2), (3) and (4).

4 EXPERIMENTS

Test data were created to analyse the 3D descriptorsbehaviour. They were created like a dataset of the 5basic shapes which are used like models of objects.They are a sphere, cube, cone, cylinder and triangu-lar prism (Figure 1). These models represent differ-ent surfaces without colour, texture or another charac-teristic different to geometry. Each CAD-model was

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(a) Tesselated-sphere and arbitrary viewpoints

(b) Top, side and another.

Figure 2: (a) Camera poses to obtain views. (b) Virtual andreal objects views from three arbitrary poses, respectively.

created as a point cloud from CAD software. EachCAD-model represents an object category in order torecognize. They are represented by a point cloud withvariable number of points, with regards to the viewand the kind of shape.

The correspondence process between model andobject must be consistent. For this reason, in thispaper, we have evaluated this process using CAD-models. In addition, we did not use keypoints com-puted from the surface and so the noise due to in-accuracy in its location is almost eliminated. There-fore, factors like the repeatable of keypoints with re-spect to viewpoint variations cannot be produced. Wehave used all points in the surface to analyse andevaluate the descriptors behaviour, thoroughly. If wehad only evaluated the descriptors with a number ofpoints chosen from surface, i.e. keypoints, the anal-ysis had been limited to effectiveness of those. Thekeypoints must be chosen to avoid redundant or sparseinformation (keypoints close or too far themselves,respectively). Generally, the descriptors based onkeypoints are efficient but they are little descriptiveand they are not robust to noise. Other descriptors,such as local/regional or global descriptors are moresuitable to noise. Moreover, they are useful to han-dle partial/complete surface information and so theyare more descriptive on objects with poor geometricstructure. Therefore, they are more suitable to cate-gorize objects in a recognition process, as can be seenhere.

In the experiments, geometric transformations areapplied to the point cloud of CAD-models shown inFigure 1. Geometric transformations simulate view-point of the objects in scene of real world. Geometrictransformations applied were rotations, translationsand scale changes from different camera poses (Fig-ure 2). The recognition process consists of a match-ing process among CAD models and objects in or-

der to associate and identify the object category. Theobject category is given by the object greatest simi-larity between the object and the geometric shape ofa model (Figure 3, Figure 4 and Figure 5), applyingEquation 5.

In order to evaluate the behaviour descriptors andfind which works best in recognition process, we haveplanned two type of experiments. Firstly, virtual ob-jects are created from CAD-models selecting views tobuild the test database (Figure 3). Thus, at least, weguarantee that all views created for the test databaseare equals to one view of a CAD-model. Secondly,virtual objects are created from CAD-models apply-ing one or more transformation on those (Figure 4).These transformations are chosen to provide differentviews to any view used within a model so we ensurea total difference between test database and models.In this case, we have worked with 42 and 38 differentviews of the test and model database, respectively.

Figure 3 shows a comparison in which the match-ing process is done combining all descriptors withall distances for virtual object views without trans-formations. This comparison allows us to determinethe capacity of similarity measures for classificationof object views in categories according to a CAD-model. The obtained results report better recognitionwhen the matching process is done usingL1 distancesand the worst results are generated byL2 distance, inboth case is independent from the used 3D descrip-tor. In addition,L2 distance causes confusion in therecognition as distance matrices ofPFH, FPFH andSHOT demonstrate.χ2 andH provide similar resultsalthoughH is slightly better.

Figure 4 shows an interesting additional experi-ment. It consists in reporting recognition results withregard to the transformation level. The difficulty inthe matching process is increased due to the loss ofsimilarity among the virtual object views with trans-formation and the models. In this case, both distancematrices,VFH andSHOT, report about a growth ofconfusion level in the recognition regardless of dis-tance metric. Furthermore, bothPFH andFPFH arenot practically changed their behaviour. Summariz-ing, CVFH is the most stable descriptor although thechosen distance metric is different or the object viewsare not exactly equal to any model views.

Finally, we have tried out the behaviour of the twobest descriptors using the two best similarity mea-sures when the recognition process is realized fromreal physical objects. In this case, the views for thetest database are obtained by means of acquisitionprocess from Kinect. In this last experiment, CAD-models are used to create 5 real physical objects us-ing a 3D printer. They were created using PLA (PLA:

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(a) PFH (L2) (b) PFH (χ2) (c) PFH (H) (d) PFH (L1)

(e) FPFH (L2) (f) FPFH (χ2) (g) FPFH (H) (h) FPFH (L1)

(i) SHOT (L2) (j) SHOT (χ2) (k) SHOT (H) (l) SHOT (L1)

(m) VFH (L2) (n) VFH (χ2) (o) VFH (H) (p) VFH (L1)

(q) CVFH (L2) (r) CVFH (χ2) (s) CVFH (H) (t) CVFH (L1)

Figure 3: Distance matrix when model set is compared with itself (Model vs Model).

PolyLactic Acid or PolyLActide) filament of 3mm di-ameter. The print allowed us a precisely controllingof the size, exact shape and the building material thatobjects would have in the scene. This is done be-cause we would not have an appropriated error han-dling, if household objects similar to (Rusu, 2009) or(Alexandre, 2012) had been used in our experiments.Perhaps, in those cases, the errors in the recognitionprocess were influenced by the properties of buildingmaterial, the capture and digitalized process when theshapes are not exactly like the CAD-model, etc. For

this reason, we have built our own objects for the testdatabase. After we have captured from Kinect thesereal physical objects using different pose cameras inthe scene. In particular, the test data set has a total of32 camera views for each object. These viewpointsrepresent rotations and translations. The object hasbeen rotated from 4 different angles (0,

π6 ,

π3 ,

π2)rad in

two different axis (in relation of the main axis andminor axis of the object). In addition, the object hasbeen translated to 4 different positions which repre-sent (origin, near, left and right). This way the scale

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(a) PFH (χ2) (b) PFH (L1)

(c) FPFH (χ2) (d) FPFH (L1)

(e) SHOT (χ2) (f) SHOT (L1)

(g) VFH (χ2) (h) VFH (L1)

(i) CVFH (χ2) (j) CVFH (L1)

Figure 4: Distance matrix when model set is compared withtest set (Model vs Test).

changes have also been considered. The result can beseen in Figure 5 which shows the matching processbetween all objects and all CAD-models.

As the above Figures 4 clearly shown,CVFH isthe most effective to recognize virtual objects. There-fore, it turns out a good choice to apply it to recog-nize real physical objects using similar views to thosewere registered for the virtual objects as is shown inFigure 5. A comparison of Figures 4(i)- 4(j) and Fig-ures 5(c)- 5(d) demonstrate that the presence of varia-tions, such as present noise, lacking of points to definethe surface when the view is captured from camera orloosing of smoothing surface due to noise points inthe acquisition process, have worsened the matching

(a) VFH (χ2) (b) VFH (L1)

(c) CVFH (χ2) (d) CVFH (L1)

Figure 5: Distance matrix for matching process amongmodels and real scenes.

process. Consequently, the distance between a viewand false model are closer to zero. This fact is clearlyobserved between cylinder and cone.

5 ANALYSIS AND EVALUATIONOF TIME AND ACCURACY

The recognition process behaviour have been evalu-ated with regards to the relation between runtime andaccuracy. A complete set of experiments were de-signed. Summarizing, the recognition process con-sisted of three steps: a) Building database: Calcula-tion of descriptors for each view in each model savedin the database. b) Calculation of descriptors for realand virtual (test) views. c) Matching between testviews by means of computing difference among allmodels views saved in the database and arbitrary testview.

The runtime of steps a) and b) on the recogni-tion process is changing and it depends on amount ofpoints in the view, the number of views per model, thenumber of models and the descriptor characteristics.Thus, we have to measure the runtime cost depend-ing on detail level of its representation in each pointcloud. Figure 6 shows the runtime for each descrip-tor depending on the shape. Each graph representsthe runtime of all descriptors for each shape (for eachshape were used 162 views with different amount ofpoints). On the one hand, as observed, the runtimedependency with shape complexity is least-significantthan computational complexity of feature descriptor.It is because all shapes keep the following relation:PFH >> FPFH >> SHOT >> CVFH >> VFH.Although, the shape complexity affects to stability oflocal feature descriptors runtime (Figure 6(f)).VFH

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300 400 500 600 700 800 900 1000 110010

0

101

102

103

104

Number of points

Des

crip

tor

runt

ime

(mse

c.)

pfhfpfhshotvfhcvfh

(a) Cone

300 400 500 600 700 800 900 1000 110010

0

101

102

103

104

Number of points

Des

crip

tor

runt

ime

(mse

c.)

pfhfpfhshotvfhcvfh

(b) Cube

300 400 500 600 700 800 900 1000 110010

0

101

102

103

104

Number of points

Des

crip

tor

runt

ime

(mse

c.)

pfhfpfhshotvfhcvfh

(c) Cylinder

300 400 500 600 700 800 900 1000 110010

0

101

102

103

104

Number of points

Des

crip

tor

runt

ime

(mse

c.)

pfhfpfhshotvfhcvfh

(d) Prism

300 400 500 600 700 800 900 1000 110010

0

101

102

103

104

Number of points

Des

crip

tor

runt

ime

(mse

c.)

pfhfpfhshotvfhcvfh

(e) Sphere

���� ���� ������ � ���� ����

��� ������ ������ ������� ����� �����

���� �������� ��������� �������� ��������� �������

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���� �������� ��������� �������� ��������� ���������

(f) Mean and standard errors

Figure 6: Descriptor runtime depending on the shape.

Cone Cube Cylinder Prism Sphere10

0

101

102

103

104

105

106

Mat

chin

g ru

ntim

e(m

sec.

)

shotpfhfpfhcvfhvfh

(a) Euclidean

Cone Cube Cylinder Prism Sphere10

0

101

102

103

104

105

106

Mat

chin

g ru

ntim

e(m

sec.

)

shotpfhfpfhcvfhvfh

(b) Chi-squared

Cone Cube Cylinder Prism Sphere10

0

101

102

103

104

105

106

107

Mat

chin

g ru

ntim

e(m

sec.

)

shotpfhfpfhcvfhvfh

(c) Hellinger

Cone Cube Cylinder Prism Sphere10

0

101

102

103

104

105

106

107

Mat

chin

g ru

ntim

e(m

sec.

)

shotpfhfpfhcvfhvfh

(d) Manhattan

Figure 7: Matching runtime for each descriptor dependingon the shape.

andCVFH are the fastest in this comparison.On the other hand, a study of the balance be-

tween runtime and accuracy is realized in step c).Firstly, Figure 7 shows the mean runtime in match-ing process between a test view and models database.Again, the set of global descriptors (VFH andCVFH)is faster than others (103 times), independently for thehigh dimensionality of its signatures. Secondly, Fig-ure 8 shows the difference between accuracy whenthe matching process is made using models such astest views and when it is made using test views. Inaddition, accuracy is less using local descriptors thanglobal descriptors. AlthoughCVFH has the best ac-curacy rate, another important issue is the metric se-

shot pfh fpfh cvfh vfh0

20

40

60

80

100

Acc

urac

y (%

)

Model vs ModelModel vs Test

(a) Euclidean

shot pfh fpfh cvfh vfh0

20

40

60

80

100

Acc

urac

y (%

)

Model vs ModelModel vs Test

(b) Chi-squared

shot pfh fpfh cvfh vfh0

20

40

60

80

100

Acc

urac

y (%

)

Model vs ModelModel vs Test

(c) Hellinger

shot pfh fpfh cvfh vfh0

20

40

60

80

100

Acc

urac

y (%

)

Model vs ModelModel vs Test

(d) Manhattan

Figure 8: Accuracy rates for descriptors depending on met-ric used in matching process.

lection. In terms of runtime, this selection is not out-standing (Figure 7), but it is important in terms ofaccuracy (Figure 8). In the experiments, model vsmodel represented in Figure 3, a 20% increase of ac-curacy rate is obtained. WhenL1 is used as observedin Figure 8(a) - 8(d). Nevertheless, the best result isobtained usingχ2 in th experiment, model vs test rep-resented in Figure 4. In this case, a 5% increase ofaccuracy is achieved.

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6 CONCLUSIONS

This paper discusses the effectiveness of using 3D de-scriptors based on normals to surfaces in order to rec-ognize geometric objects. 3D descriptors were usedfor real physical and virtual objects recognition bymeans of matching with virtual geometric models. Atotal of 6028 tests have been done. Where 3800 tests(4 different distances, 5 descriptors, 5 shapes and 38views per shape) are from the model-vs-model ex-periment, 2100 tests (2 different distances, 5 descrip-tors, 5 shapes and 42 views per shape) are from themodel-vs-test experiment and 128 tests (2 differentdistances, 2 descriptors, one shape and 32 views) arefrom the model-vs-real-physical-object experiment.SHOT andFPFH are run in CPU-based parallel im-plementation. The computer specification is IntelCore i7-4770k processor, equipped with 16GB of sys-tem memory and GPU is Nvidia GeForce 770GTX.The effectiveness of recognition process is evaluatedby measuring the runtime and the precision to achievesuccess rate of the recognition process. Those are de-pending on the type of descriptor, resolution of thepoint cloud which represents each object, and thelevel of accuracy required for the recognition.

ACKNOWLEDGEMENTS

The research leading to these result has receivedfunding from the Spanish Government and EuropeanFEDER funds (DPI2012-32390) and the Valencia Re-gional Government (PROMETEO/2013/085).

REFERENCES

Aldoma, A., Marton, Z.-C., Tombari, F., Wohlkinger, W.,Potthast, C., Zeisl, B., Rusu, R. B., Gedikli, S., andVincze, M. (2012a). Tutorial: Point cloud library:Three-dimensional object recognition and 6 dof poseestimation. In IEEE Robot. Automat. Mag., vol-ume 19, pages 80–91.

Aldoma, A., Tombari, F., Rusu, R. B., and Vincze,M. (2012b). Our-cvfh - oriented, unique and re-peatable clustered viewpoint feature histogram forobject recognition and 6dof pose estimation. InDAGM/OAGM Symposium, pages 113–122.

Aldoma, A., Vincze, M., Blodow, N., Gossow, D., Gedikli,S., Rusu, R. B., and Bradski, G. R. (2011). Cad-modelrecognition and 6dof pose estimation using 3d cues.In IEEE International Conference on Computer VisionWorkshops, ICCV 2011 Workshops, Barcelona, Spain,November 6-13, 2011, pages 585–592.

Alexandre, L. A. (2012). 3D descriptors for object and cate-gory recognition: a comparative evaluation. InWork-

shop on Color-Depth Camera Fusion in Robotics atthe IEEE/RSJ International Conference on IntelligentRobots and Systems (IROS), Vilamoura, Portugal.

Lai, K. (2013). Object Recognition and Semantic SceneLabeling for RGB-D Data. PhD thesis, University ofWashington, Washington, USA.

Lian, Z., Godil, A., Bustos, B., Daoudi, M., Hermans, J.,Kawamura, S., Kurita, Y., Lavoue, G., Van Nguyen,H., Ohbuchi, R., Ohkita, Y., Ohishi, Y., Porikli, F.,Reuter, M., Sipiran, I., Smeets, D., Suetens, P., Tabia,H., and Vandermeulen, D. (2013). A comparisonof methods for non-rigid 3d shape retrieval.PatternRecogn., 46(1):449–461.

Marton, Z.-C., Pangercic, D., Blodow, N., and Beetz, M.(2011). Combined 2d-3d categorization and clas-sification for multimodal perception systems.I. J.Robotic Res., 30(11):1378–1402.

Rusu, R. B. (2009).Semantic 3D object maps for every-day manipulation in human living environments. PhDthesis, Technical University Munich.

Rusu, R. B., Bradski, G. R., Thibaux, R., and Hsu, J. (2010).Fast 3d recognition and pose using the viewpoint fea-ture histogram. InIROS, pages 2155–2162. IEEE.

Tombari, F., Salti, S., and Stefano, L. D. (2010). Uniquesignatures of histograms for local surface descrip-tion. In Proceedings of the 11th European Conferenceon Computer Vision Conference on Computer Vision:Part III, ECCV’10, pages 356–369, Berlin, Heidel-berg. Springer-Verlag.

Wohlkinger, W., Aldoma, A., Rusu, R. B., and Vincze, M.(2012). 3dnet: Large-scale object class recognitionfrom cad models. InICRA, pages 5384–5391. IEEE.

Wohlkinger, W. and Vincze, M. (2011a). Ensemble ofshape functions for 3d object classification. InRO-BIO, pages 2987–2992. IEEE.

Wohlkinger, W. and Vincze, M. (2011b). Shape distri-butions on voxel surfaces for 3d object classificationfrom depth images. InICSIPA, pages 115–120. IEEE.

A�Performance�Evaluation�of�Surface�Normals-based�Descriptors�for�Recognition�of�Objects�Using�CAD-Models

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