Eurographics Workshop on 3D Object Retrieval (2014) B. Bustos, H. Tabia, J.-P. Vandeborre, and R. Veltkamp (Editors) SHREC’14 Track: Shape Retrieval of Non-Rigid 3D Human Models D. Pickup 1∗ , X. Sun 1∗ , P. L. Rosin 1∗ , R. R. Martin 1∗ , Z. Cheng 2∗ , Z. Lian 3∗ , M. Aono 4 , A. Ben Hamza 9 , A. Bronstein 5 , M. Bronstein 14 , S. Bu 6 , U. Castellani 7 S. Cheng 6 , V. Garro 7 , A. Giachetti 7 , A. Godil 8 , J. Han 6 , H. Johan 10 , L. Lai, 13 B. Li 11 , C. Li 8 , H. Li, 13 , R. Litman 5 , X. Liu, 13 Z. Liu 6 , Y. Lu 11 , A. Tatsuma 4 , J. Ye 12 1 Cardiff University, UK 2 National University of Defense Technology, China 3 Peking University, China 4 Toyohashi University of Technology, Japan 5 Technion - Israel Institute of Technology, Israel 6 Northwestern Polytechnical University, China 7 University of Verona, Italy 8 National Institute of Standards and Technology, USA 9 Concordia University, Canada 10 Fraunhofer IDM@NTU, Singapore 11 Texas State University, San Marcos, USA 12 Penn State University, USA 13 Beijing Technology and Business University, China 14 University of Lugano, Switzerland ∗ Track organisers Abstract We have created a new benchmarking dataset for testing non-rigid 3D shape retrieval algorithms, one that is much more challenging than existing datasets. Our dataset features exclusively human models, in a variety of body shapes and poses. 3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. In this track nine groups have submitted the results of a total of 22 different methods which have been tested on our new dataset. 1. Introduction The ability to recognise a deformable object’s shape, regard- less of the pose of the object, is an important requirement for modern shape retrieval methods. Many state-of-the-art methods achieve extremely high accuracy when evaluated on the most recent benchmark [LGB ∗ 11]. It is therefore hard to distinguish between good methods, and there is little room to demonstrate improvement in approaches. There is thus a need for a more challenging benchmark for non-rigid 3D shape retrieval. Many novel apporaches have been published since the previous benchmark, and therefore a new compar- ison of state-of-the-art methods is also beneficial. We have created a new, more challenging, benchmarking dataset for testing non-rigid 3D shape retrieval algorithms. Our dataset features exclusively human models, in a vari- ety of body shapes and poses. 3D models of humans are commonly used within computer graphics and vision, there- fore the ability to distinguish between body shapes is an im- portant shape retrieval problem. The shape differences be- tween humans are much more subtle than the differences between the shape classes used in current benchmarks (e.g. ants and birds), yet humans are able to visually recognise specific individuals. Successfully performing shape retrieval on a dataset of human models is therefore a far more chal- lenging, but relevant task. We use our dataset to evaluate the retrieval performance of 22 different methods, submitted by nine different research groups. The track’s website is avail- able at [Tra]. c The Eurographics Association 2014. DOI: 10.2312/3dor.20141056
Transcript
Eurographics Workshop on 3D Object Retrieval (2014)B. Bustos, H. Tabia, J.-P. Vandeborre, and R. Veltkamp (Editors)
SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
D. Pickup1∗, X. Sun1∗, P. L. Rosin1∗, R. R. Martin1∗, Z. Cheng2∗, Z. Lian3∗, M. Aono4, A. Ben Hamza9, A. Bronstein5,
M. Bronstein14, S. Bu6, U. Castellani7 S. Cheng6, V. Garro7, A. Giachetti7, A. Godil8, J. Han6, H. Johan10,
L. Lai,13 B. Li11, C. Li8, H. Li,13, R. Litman5, X. Liu,13 Z. Liu6, Y. Lu11, A. Tatsuma4, J. Ye12
1Cardiff University, UK2National University of Defense Technology, China
3Peking University, China4Toyohashi University of Technology, Japan
5Technion - Israel Institute of Technology, Israel6Northwestern Polytechnical University, China
7University of Verona, Italy8National Institute of Standards and Technology, USA
11Texas State University, San Marcos, USA12Penn State University, USA
13Beijing Technology and Business University, China14University of Lugano, Switzerland
∗Track organisers
AbstractWe have created a new benchmarking dataset for testing non-rigid 3D shape retrieval algorithms, one that ismuch more challenging than existing datasets. Our dataset features exclusively human models, in a variety ofbody shapes and poses. 3D models of humans are commonly used within computer graphics and vision, and sothe ability to distinguish between body shapes is an important shape retrieval problem. In this track nine groupshave submitted the results of a total of 22 different methods which have been tested on our new dataset.
1. Introduction
The ability to recognise a deformable object’s shape, regard-less of the pose of the object, is an important requirementfor modern shape retrieval methods. Many state-of-the-artmethods achieve extremely high accuracy when evaluated onthe most recent benchmark [LGB∗11]. It is therefore hard todistinguish between good methods, and there is little roomto demonstrate improvement in approaches. There is thus aneed for a more challenging benchmark for non-rigid 3Dshape retrieval. Many novel apporaches have been publishedsince the previous benchmark, and therefore a new compar-ison of state-of-the-art methods is also beneficial.
We have created a new, more challenging, benchmarkingdataset for testing non-rigid 3D shape retrieval algorithms.
Our dataset features exclusively human models, in a vari-ety of body shapes and poses. 3D models of humans arecommonly used within computer graphics and vision, there-fore the ability to distinguish between body shapes is an im-portant shape retrieval problem. The shape differences be-tween humans are much more subtle than the differencesbetween the shape classes used in current benchmarks (e.g.ants and birds), yet humans are able to visually recognisespecific individuals. Successfully performing shape retrievalon a dataset of human models is therefore a far more chal-lenging, but relevant task. We use our dataset to evaluate theretrieval performance of 22 different methods, submitted bynine different research groups. The track’s website is avail-able at [Tra].
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
Figure 1: A selection of models included in our datasets.Above: Real dataset, below: Synthetic dataset.
2. Datasets
Our track uses two datasets, a Real dataset, obtained by scan-ning real human participants, and a Synthetic dataset, createdusing 3D modelling software. The latter may be useful fortesting algorithms intended to retrieve synthetic data, withwell sculpted local details, while the former may be moreuseful to test algorithms that are designed to work even inthe presence of noisy coarsely captured data lacking in localdetail.
2.1. Real Dataset
The Real dataset was built from point-clouds containedwithin the Civilian American and European Surface Anthro-pometry Resource (CAESAR) [cae]. This dataset comprises400 meshes, representing 40 human subjects (20 male, 20female) in 10 different poses. The point-cloud models weremanually selected from CAESAR to be models with signif-icant visual differences. We employed SCAPE (shape com-pletion and animation of people) [ASK∗05] to build articu-lated 3D meshes, by fitting a template mesh to each subject.Realistic deformed poses of each subject were built using adata-driven deformation technique [CLC∗13]. We remeshedthe models using freely available software [VC04, VCP08].The resulting models have approximately 15,000 vertices.
2.2. Synthetic Dataset
We also used the DAZ Studio [DAZ13] 3D mod-elling/animation software to create a dataset of synthetic hu-man models. The software includes a parametrized human
model, where parameters control body shape. We used thisto produce a dataset consisting of 15 different human mod-els (5 male, 5 female, 5 child), each with its own uniquebody shape. We generated 20 different poses for each mode,resulting in a dataset of 300 models. The same poses wereused for each body shape, and models are considered to be-long to the same class if they share the same body shape.All models were remeshed using the same method as forthe Real dataset. The resulting models have approximately60,000 vertices. A selection of both real and synthetic mod-els is shown in Figure 1.
3. Evaluation
We assessed two different retrieval tasks:
1. Returning a list of all models, ranked by shape similarityto a query model.
2. Returning a list of models that all share the same shapeas the query model.
For both tasks, every model in the database was used asa separate query model. In the first task, for each query weasked the participants to order all other models in the datasetin terms of similarity to the query model. In the second task,for each query the participants were asked to submit a listof arbitrary length of all models which they classify as ‘thesame shape’ as the query model. Both tasks were evaluatedseparately.
The evaluation procedure for Task 1 is identical to thatused in several previous SHREC tracks [LGB∗11]. We eval-uated the results using various statistical measures: preci-sion and recall, nearest neighbour (NN), first tier (1-T), sec-ond tier (2-T), e-measure (E-M), discounted cumulative gain(DCG), and precision and recall curves. Definitions of thesemeasures are given in [SMKF04]. The results for Task 2were evaluated using the F-Measure [BYRN11].
4. Methods
4.1. Simple shape measures, and Euclidean distancebased canonical forms D. Pickup, X. Sun,P. L. Rosin and R. R. Martin
This section presents two techniques, simple shape measuresbased on surface area, and skeleton driven canonical forms.
4.1.1. Simple shape measures
Two simple shape measures were tested separately on thedatasets. The first is the total surface area of the mesh. Thismeasure is not scale independent, and all human modelswere assumed to be properly scaled. In order to present ascale independent result, the second measure used is com-pactness. This is calculated as Volume2/SurfaceArea3. Bothmethods are trivial to implement, and are very efficient tocompute.
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
4.1.2. Skeleton driven canonical forms
A variant on the canonical forms presented by Elad and Kim-mel [EK03] is used to normalise the pose of all the modelsin the dataset, and then the rigid view-based method by Lianet al. [LGSX13] is used for retrieval. A canonical form isproduced by extracting a curve skeleton from a mesh, usingthe method by Au at al. [ATC∗08]. The SMACOF Multidi-mensional Scaling method used by [EK03] is then appliedto the skeleton, to put the skeleton into a canonical pose.The skeleton driven shape deformation method by Yan etal. [YHMY08] is then used to deform the mesh to the newpose defined by the canonical skeleton. This produces a sim-ilar canonical form to [EK03], but with the local featuresbetter preserved. The models in the Synthetic dataset are sim-plified to approximately 15000 vertices, and any holes arefilled, before computing the canonical form.
4.2. Hybrid shape descriptor and meta similaritygeneration for non-rigid 3D model retrieval, B. Li,Y. Lu, A. Godil and H. Johan
A hybrid shape descriptor [LGJ13] has been proposed tointegrate both geodesic distance-based global features andcurvature-based local features. An adaptive algorithm basedon Particle Swarm Optimization (PSO) is developed to adap-tively fuse different features to generate a meta similarity be-tween any two models. The approach can be generalized tosimilar approaches which integrate more or other features.It first extracts three component features of the hybrid shapedescriptor: curvature-based local feature, geodesic distance-based global feature, and Multidimensional scaling (MDS)based ZFDR [LJon] global feature. Based on the extractedfeatures, corresponding distance matrices are computed andthey are fused into a meta distance matrix based on PSO. Fi-nally, the distances are sorted to generate the retrieval lists.
Curvature-based local feature vector: VC. First, theCurvature Index feature of a vertex p is computed, which
characterizes local geometry: CI = 2π log(
√K2
1 +K22
2 ), whereK1 and K2 are the two principal curvatures in the x and ydirections respectively at p. Then the Curvature Index de-viation feature of the adjacent vertices of p is computed:
δCI =√
∑ni=1 (CIi−CI)
n , where CI1, CI2,. . .,CIn are the Cur-
vature Index values of the adjacent vertices of p and CI isthe mean Curvature Index of all the adjacent vertices. Next,to describe the local topological property, the Shape Indexfeature of p is computed: SI = 2
π arctan( K1+K2|K1−K2| ). After that,
a combined local shape descriptor is formed by concatenat-ing the above three local features: F = (CI,δCI,SI). Finally,based on the Bag-of-Words framework, the local feature vec-tor VC = (h1,h2, · · · ,hNC ) is generated, where the number ofcluster centres NC is set to 50.
Geodesic distance-based global feature vector: VG.First, to avoid the high computational cost involved in the
geodesic distance computation among many vertices, themodels are simplified to 1000 vertices. Next, the geodesicdistances among all the vertices of a simplified model aregenerated to form a geodesic distance matrix GDM. Finally,the GDM is decomposed based on Singular Value Decom-position and the first largest k eigenvalues are used as theglobal feature vector. In experiments, k is set to 50.
MDS-based ZFDR global feature vector: VZ . To lever-age pose and deformation variations of non-rigid models,Multidimensional scaling (MDS) techniques are utilized tomap the non-rigid models into a 3D canonical form. The pre-viously computed geodesic distances among the 1000 ver-tices of each simplified 3D model are used as the input ofMDS for the feature space transformation. Finally, the hy-brid global shape descriptor ZFDR [LJon] is used to charac-terize the features of the transformed 3D model in the newfeature space. There are four feature components in ZFDR:Zernike moments feature, Fourier descriptor feature, Depthinformation feature and Ray-based feature. This approachis named as MDS-ZFDR and Stress MDS is adopted in theexperiments. It was also found that for 3D human retrievalusing R feature only (that is MDS-R) can always achievebetter results than other combinations such as ZF, DR orZFDR. The reason should be related to the more salient fea-ture of the geometry-related ‘thickness’ variations in the hu-man models, such as fat versus slim bodies which are bet-ter characterized by the R feature, compared to other visual-related features like ZF and D.
Retrieval algorithm: (1) Computation of Curvature-based local feature vector VC based on the original modelsand local feature distance matrix MC generation; (2) Com-putation of Geodesic distance-based global feature vectorVG and global feature distance matrix MG. (3) MDS-basedZFDR global feature vector VZ and MDS-ZFDR global fea-ture distance matrix MZ computation; (4) PSO-based metadistance matrix generation and ranking. A meta distance ma-trix M = wCMC + wGMG + wZMZ is generated, where wC,wG and wZ fall in [0,1]. As a swarm intelligence optimiza-tion technique, PSO-based approach is robust and fast insolving problems that are non-linear and non-differentiable.It includes four steps: initialization, particles’ velocity andpositions update, search evaluation and result verification.The number of particles NP=10; the maximum number ofsearch iterations Nt=10; and First Tier is selected as the fit-ness value for search evaluation. Please note that the PSO-based weight assignment preprocessing step is only per-formed once for each of the test sets.
The ‘Hybrid_R’ runs only use ‘MDS-R’ features,compared to the original ‘Hybrid’ approach presentedin [LGJ13] which uses ‘MDS-ZFDR’. Besides comparingthe component features including ‘Curvature’, ‘Geodesic’distance and ‘MDS-ZFDR’ based features, the performanceof ‘MDS-R’ is compared with ‘MDS-ZFDR’.
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
4.3. Histograms of Area Projection Transform,A. Giachetti and V. Garro
Human characters are recognised with the Histograms ofArea Projection Transform (HAPT), general purpose shapedescriptors proposed in [GL12]. The method is based on aspatial map (Multiscale Area Projection Transform) that en-codes the likelihood of the points inside the shape of beingcentres of spherical symmetry. This map is obtained by com-puting for each radius of interest the value:
where S is the surface of interest, TR(S,�n) is the parallelsurface of S shifted along the normal vector (only in the in-ner direction) and kσ(�x) is a sphere of radius σ centred in thegeneric point �x where the map is computed. Values at dif-ferent radii are normalized in order to have a scale-invariantbehaviour, creating the Multiscale APT (MAPT):
MAPT(x,y,z,R,S) = α(R) APT(x,y,z,S,R,σ(R)) (2)
where α(R) = 1/4πR2 and σ(R) = c ·R (0 < c < 1).
A discretized MAPT is easily computed, for selected val-ues of R, on a voxelized grid including the surface mesh,with the procedure described in [GL12]. The map is com-puted in a grid of voxels with side s on a set of correspondingsampled radius values R1, ...,Rn . In the paper it is also shownthat histograms of MAPT computed inside the objects arevery good global shape descriptors, showing very good per-formances on the SHREC 2011 Non-Rigid Watertight con-test data [LGB∗11]. For that recognition task discrete MAPTmaps were quantized in 12 bins and histograms computed atthe different scales (radii) considered were concatenated cre-ating a unique descriptor. Voxel side and sampled radii werechosen differently for each model and proportional to thecubic root of the object volume, in order to have the samedescriptor for scaled versions of the same geometry. c wasalways taken equal to 0.5.
For the recognition of different human subjects, however,scale invariance is not wanted. For this reason a fixed voxelsize and a fixed set of radii are used.
The values for these parameters have been chosen differ-ently for the Real and the Synthetic datasets, using simpleheuristics. The algorithm was tested using three different pa-rameter configurations for each dataset (Real and Synthetic).The results were then compared, and the best configurationsfor each dataset were submitted to the track. The voxel sizewas taken similar to the size of the smaller details well de-fined in the meshes. For the Synthetic dataset, where fin-gers are visible and models are smaller, s = 4mm is usedand 11 increasing radii have been computed starting fromR1 = 8mm and iteratively adding a fixed step of 4mm for theremaining values {R2, . . . ,R11} . For the Real dataset, wheremodels are bigger and details are smoothed, s = 12mm isused applying 7 different radii starting from R1 = 24mmwith a constant radius increasing of 12mm.
The procedure for model comparison then simply consistsin concatenating the histograms computed at the differentscales and measuring distances between shapes by evaluat-ing the Jeffrey divergence of the corresponding concatenatedvectors.
In the tests this ‘general purpose’ shape comparison pro-cedure is applied without specific adaptations to the task.A possible way to specialize it for human body recognitionmay consist in learning discriminative sets of radii with afeature selection procedure or in recognizing and comparingspecific body regions.
The MAPT/histograms extraction (using the c++ imple-mentation available at http://www.andreagiachetti.it) for theReal dataset takes around 46 min, with a mean of 7 sec.for each model; the computation for the Synthetic datasetis much longer dealing with more detailed meshes: 2 hoursfor the entire dataset, 25 sec. for each shape. A single querytakes around 1.2 msec. using a Matlab implementation of theJeffrey divergence distance.
4.4. R-BiHDM, J. Ye
The R-BiHDM [YYY13] method is a spectral method usedfor general non-rigid shape retrival. Using modal analysis,the method projects Biharmonic distance [LRF10] map intoa low-frequency representation which operates on the modalspace spanned by the lowest eigenfunctions of shape Lapla-cian [RWP06, OBCS∗12], and then computes its spectrumas an isometric shape descriptor.
Let ψ0,ψ1, . . . ,ψm be the eigenfunctions of Laplacian Δcorresponding to its smallest eigenvalues 0 = λ0 < λ1 ≤. . . ≤ λm. Let d(x,y) be the Biharmonic distance betweentwo points on mesh, which is defined as
d(x,y)2 =m
∑i=1
1λ2
i
(ψi(x)−ψi(y))2 . (3)
The squared Biharmonic distance map D2 is a functionalmap defined by
D2[ f ](x) =∫
x∈Sd2(x,y) f (y)dy, (4)
where S is the differential manifold of shape. The reducedmatrix version of D2 is denoted by A = {ai, j}, where ai, j =⟨
ψi,D2ψ j
⟩S
=∫
S ψi(x)D2[ψ j](x)dx for 0 ≤ i, j ≤ m. Note
that tr(A) = 0 and all eigenvalues of A, denoted by µ0, . . . ,µm
are in a magnitude descending order, where µ0 > 0 andµi < 0 for i > 0. The shape descriptor is defined as a vec-tor [µ1, . . . ,µm]T (scale dependent) or [ µ1
µ0, . . . , µL
µ0]T (scale in-
dependent). For this shape contest, we choose L = 30 andm = 100. Finally, a normalized Euclidean distance is usedfor nearest neighbour queries. The descriptor is insensitiveto a number of perturbations, such as isometry, noise, andremeshing. It has superior discrimination capability regard-ing globally change of shape and is very efficient to com-
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
pute. It has been shown that scale independent descriptor (R-BiHDM) is more reliable for generic nonrigid shape tasks,while scale dependentdescriptor (R-BiHDM-s) is more suit-able for this human shape task.
4.5. HKS-TS and SIHKS-H, L. Lai, X. Lui and H. Li
The HKS-TS (heat kernel signature based on time serial) isan application of HKS [SOG09], which adds the statistics ofdynamic HKS on a shape according to an appropriate timeserial chosen using a subset of the Real data. The SIHKS-H(scale invariant heat kernel signature based on statistics his-togram) is an application of SI-HKS [BK10]. The SI-HKS iscalculated on the shape to form a histogram. Then the sim-ilarity between different shapes can be calculated accordingto the SIHKS-H. Different similarity will be found by usingdifferent methods. Finally, the ranking list can be producedaccording to the similarity. For Task 2 two methods are used,HKS-TS-HC and SIHKS-H-HC. They add a further process-ing step to the methods used for Task 1. HC means the hier-archical clustering algorithm. The hierarchical clustering al-gorithm is added for classification according to the similaritycalculating in Task 1. Intuitively, the algorithm is improvedto be fit for this task.
4.6. High-level Feature Learning for 3D Shapes, S. Bu,S. Chen, Z. Lui and J. Han
The proposed high-level feature learning method for 3Dshapes is carried out in the following three stages.
1. Low-level feature extraction: three representative in-trinsic features, scale-invariant heat kernel signature(SI-HKS) [BK10], shape diameter function (SDF)[GSCO07], and averaged geodesic distance (AGD)[HSKK01], are adopted as low-level descriptors.
2. Middle-level feature extraction: To tackle the spatial in-formation missing in the low-level features, a middle-level position-independent Bag-of-Features (BoF) is firstextracted from the above low-level 3D descriptors. In or-der to compensate the lack of structural relationship, theoriginal BoF is further extended into a geodesic-awareBoF (GA-BoF), which considers the geodesic distancebetween each pair of BoF on the 3D surface.
3. High-level feature learning: Finally, a deep learningbased approach is introduced to further learn high-levelfeatures from the GA-BoF, which is able to discover theintrinsic relationship among GA-BoF and provide highdiscriminative features for 3D shape retrieval.
4.6.1. Low-level 3D Shape Descriptors
In this research, the scale-invariant heat kernel signature,shape diameter function, and average geodesic distance areadopted as the low-level 3D shape descriptors which areused for generating middle-level features, since these threelocal descriptors are robust against non-rigid and complex
shape deformations. The first six frequency components ofthe SI-HKS, SDF and AGD descriptors are concatenated toform a low-level shape descriptor as
In this step, Bag-of-Features (BoFs) are computed torepresent the occurrence probability of geometric words,and Minkowski metric is adopted as feature weighting[CdAM12] for k-means to generate geometric words moreprecisely.
After the geometric words C = {c1,c2, ..,cK} of size K isobtained, the next step is to quantize the low-level descrip-tor space in order to obtain a compact representation. Foreach point x ∈ X with the descriptor F(x), feature distribu-tion φ(x) is defined as
φi(x) = c(x)exp
(−||F(x)− ci||22
kBoF σ2min
), (6)
where the constant c(x) is selected to satisfy ||φ(x)||1 = 1.
The geodesics on the mesh are used to measure the spa-tial relationship between each pair of BoFs on vertices, andintroduce the geodesics-aware Bag-of-Features (GA-BoF):
v(X) = N(X) ∑xi∈X
∑x j∈X
φ(xi)φ(x j)T exp
(−kgd
gd(xi,x j)σgd
),
(7)where N(X) is a normalization factor which makes fea-tures have a fixed maximum value of 1, σgd is the maximalgeodesic distance of any pair of vertices on the mesh, and kgddenotes the decay rate of distances, which is selected empir-ically. The resulting v is a K ×K matrix, which representsthe frequency of geometric words i and j appearing withina specified geodesic distance. This expression provides oc-currence probability of geometric words and relationship be-tween them.
4.6.3. Feature Learning via Deep Learning
In order to further deeply mine the relationship of featuresfrom intra-class shapes and inter-class shapes in a largedataset, deep learning is introduced into our framework,which will result in high-level features with strong gener-alization. Due to the fact that deep belief networks (DBN)[HOT06] has shown good performance and is a probabilisticapproach, DBN is adopted as the feature learning method toextract high-level features for the 3D shapes.
Stacking a number of the restricted Boltzmann machines(RBMs) and learning layer by layer from bottom to topgives rise to a DBN. It has been shown that the layer-by-layer greedy learning strategy [HOT06] is effective, andthe greedy procedure achieves approximate maximum like-lihood learning. In this method, the bottom layer RBM is
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
trained with the input data of GA-BoF, and the activationprobabilities of hidden units are treated as the input data fortraining the upper-layer RBM, and so on.
In the shape retrieval task, unlabelled 3D shape data areused to train the DBN layer-by-layer. After obtaining theoptimal parameters, the input GA-BoFs are processed layer-by-layer till the final layer which are used as the high-levelfeatures. In the retrieval, L2 distance of the features is usedto measure the similarity of two shapes X and Y as
ds(X,Y) = ||o(X)−o(Y)||2. (8)
4.7. Bag-of-Features approach with Augmented PointFeature Histograms, A. Tatsuma and M. Aono
The developed Augmented Point Feature His-tograms (APFH) expands Point Feature Histograms(PFH) [RMBB08] by adding the statistics of their geometricfeatures. PFH is known as a local feature vector for 3D pointclouds. PFH constructs a histogram of geometric featuresextracted from neighbouring oriented points. Improvingthe discriminant power of PFH by adding the mean andcovariance of its geometric features is investigated. BecauseAPFH is a local feature vector as well as PFH, it is invariantto the global deformation and articulation of the 3D model.
The overview of how the method defines the proposedAPFH is illustrated in Figure 2. With APFH, the first stepis to randomly generate oriented points on the triangle sur-face of a 3D model using Osada’s method [OFCD02]. Togenerate a random point p on an arbitrary triangle surfacecomposed of vertices va, vb, and vc, the following formulais employed:
p = (1−√r1)va +
√r1(1− r2)vb +
√r1r2vc. (9)
In the implementation, two random variables, r1 and r2 in theabove equation, are computed using the Niederreiter pseudo-random number generator [BFN94]. The oriented point isgenerated by inheriting the normal vector of the surface asan orientation of the point.
Next a PFH for each oriented point is constructed.The PFH finds the k-neighbourhood for each orientedpoint, and calculates a four-dimensional geometric featuref = [ f1, f2, f3, f4 ]T as proposed in [WHH03]. The four-dimensional geometric feature is defined as follows for everypair of points pa and pb in the k-neighbourhood, and for theirnormal vectors na and nb:
f1 = arctan(w ·nb,u ·na),
f2 = v ·nb,
f3 = u · pb −pa
d,
f4 = d,
where u = na, v = (pb − pa)× u/||(pb − pa)× u||, w =u × v, and d = ||pb − pa||. The PFH collects the four-dimensional geometric features in a 16-bin histogram fh. The
index of the histogram bin h is defined by the following for-mula:
h =4
∑i=1
s(t, fi) ·2i−1,
where s(t, f ) is a threshold function defined as 0 if f < t and1 otherwise. The threshold value of f1, f2, and f3 are set to0, and set the threshold value of f4 to the average value of f4in the k-neighbourhood.
Furthermore, the mean and covariance of the four-dimensional geometric features is calculated. Let fi be thefour-dimensional geometric feature of an oriented point inthe k-neighbourhood. The mean feature fm and covariancefeature fc in the k-neighbourhood are defined as follows:
fm =1k
k
∑i=1
fi,
fc = Upper
(1
k−1
k
∑i=1
(fi − fm)(fi − fm)T
),
where Upper(·) concatenates the upper triangular part of thematrix. Our APFH fAPFH is composed fh, fm , and fc.
Finally, APFH fAPFH is normalized with the power andthe L2 normalization [PSM10].
To compare 3D models, the set of APFH features of a 3Dmodel is integrated into a feature vector of the 3D model us-ing the Bag-of-Features (BoF) approach [BBGO11, SZ03].Moreover, the BoF is projected onto Jensen-Shannon kernelspace using the homogeneous kernel map method [VZ12].This approach is called BoF-APFH.
In addition, similarity between features is calculated us-ing the manifold ranking method with the unnormalizedgraph Laplacian [ZBS11]. This approach is called MR-BoF-APFH.
The parameters of each algorithm are fixed empirically.For the APFH, the number of points is set to 20000, andthe number of the neighbourhood to 55. For the BoF-APFHapproach, a codebook of 1200 centroids is generated usingK-means clustering, and used the SHREC’11 Non-rigid 3DWatertight dataset for training of the codebook.
4.8. BoF and SI-HKS, R. Litman, A. Bronstein,M. Bronstein and U. Castellani
All shapes were down-sampled to have 4,500 triangles. Foreach shape S in the data-set, an SI-HKS [BK10] descriptorxi was calculated in every point i ∈ S. Unsupervised dictio-nary learning was done over randomly selected descriptorsfrom all of the shapes using the SPAMS toolbox [MBPS09],with dictionary size of 32. The resulting 32 atom dictionaryD was, in essence, the bag-of-features of this method. Next,in every point descriptor xi was ‘replaced’ with a sparse codezi by solving pursuit problem
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
vb
va
vcp
npj
pi
fm
fc fjfi
fmfc
fh
fh
Figure 2: Overview of the Augmented Point Feature His-tograms (APFH).
minzi
12‖xi −Dzi‖2
2 +λ‖zi‖1. (10)
The resulting codes zi were subsequently pooled into a sin-gle histogram using mean pooling h = ∑i ziwi, with wi beingelement area of point i.
Lastly, the main contribution of this method: the initial Dhas undergone supervised training using about 30% of theshape-classes. Training was done using stochastic gradientdescent of the loss-function defined in [WS09].
Present are the performance of the supervised training(supDLtrain), and for reference, the performance of ini-tial unsupervised D (UnSup32). Additionally, a similar un-supervised method used in [BBGO11] is also presented(softVQ48). This method uses k-means clustering (with k =48) and soft vector-quantization, instead of dictionary learn-ing and pursuit, respectively.
4.9. Spectral Geometry, C. Li, A. Godil andA. Ben Hamza
The spectral geometry based framework in [Li13] is used forhuman body shape representation and retrieval. This frame-work is based on the eigendecomposition of the Laplace-Beltrami operator (LBO), which provides a rich set of eigen-bases that are invariant to isometric transformations. It con-sists of two main stages: (1) spectral graph wavelet sig-nature [LH13b] for descriptors extraction, and (2) intrin-sic spatial pyramid matching [LH13a] for shape compari-son. The cotangent weight scheme was used to discretizeLBO. The eigenvalues λi and associated eigenfunctions ϕϕϕican be computed by solving the generalized problem Cϕϕϕi =λiAϕϕϕi, i = 1,2, . . . ,m, where A is a positive-definite diag-onal area matrix and C is a sparse symmetric weight matrix.In the experiments m is set to 200.
Spectral graph wavelet signature: The first stage con-sists of the computation of a dense spectral descriptor h(x) ateach vertex of the triangle meshed shape X . In general, anyone of spectral descriptors with the eigenfunction-squaredform reviewed in [LH13c] can be used in the human bodyretrieval contests for isometric invariant representation. Inthis work the recently proposed spectral graph wavelet sig-nature (SGWS) is used as the local descriptor; it provides ageneral and flexible interpretation for the analysis and designof spectral descriptors Sx(t,x) = ∑m
i=1 g(t,λi)ϕ2i (x). In a bid
to capture the global and local geometry, a multi-resolutionshape descriptor was obtained by setting g(t,λi) as a cubicspline wavelet generating kernel and considering the scalingfunction. The resolution level is set as 2.
Intrinsic spatial pyramid matching: Given a vocab-ulary of representative local descriptors P = {pk, k =1,2, . . . ,K} learned by k-means, the dense descriptor S ={st , t = 1,2, . . . ,T} at each point of the shape is replacedby the Gaussian kernel based soft assignment Q = {qk, k =1,2, . . . ,K}.
Any function f on X can be written as the linear combi-nation of the eigenfunctions. Using the variational charac-terizations of the eigenvalues in terms of the Rayleigh-Ritzquotient, the second eigenvalue is given by
λ2 = inff⊥ϕϕϕ1
f ′C ff ′A f
(11)
The isocontours of the second eigenfunction (Figure 3)are used to cut the shape into R patches, thus the shape de-scription is the concatenation of R sub-histograms of Q alongeigenfunction value in the real line. To consider the two-signpossibilities in the concatenation, the histogram order is in-verted, and the scheme with the minimum cost is consid-ered as a better matching. The second eigenfunction is thesmoothest mapping from the manifold to the real line, re-sulting in this intrinsic partition quite stable. It provably ex-tends the property of popular SPM in image domain to cap-ture spatial information for meshed surfaces, so is referred asintrinsic spatial pyramid matching (ISPM) in [LH13a]. Thepartition number is set as 2 in this contest.
Finally, the result is ISPM induced histograms for shaperepresentation. The dissimilarity between two shapes iscomputed as the L1 distance.
Running time The method is implemented in MATLAB.The time consuming steps of the method are the computationof LBO and k-means dictionary learning. For a mesh with15,000 vertices, it takes 8 seconds to compute the LBO. Fora mesh with 60,000 vertices, it takes 37 seconds to computethe LBO. To learn a dictionary with 100 geometric words,it takes 45 minutes. Therefore, it averagely takes at most 24hours (less than one day) to run the program for each dataset.
D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian / SHREC’14 Track:Shape Retrieval of Non-Rigid 3D Human Models
Figure 3: The isocontours of the second eigenfunction.
5. Results
Here we evaluate the retrieval results of the methods de-scribed in Section 4, applied to the datasets described inSection 2. Table 1 shows the results of Task 1 evaluated us-ing the NN, 1-T, 2-T, E-M and DCG measures discussed inSection 3. All methods performed better on the Syntheticdataset, with most methods performing poorly on the Realdata. This shows that it is potentially easier to distinguishbetween synthetically generated objects, rather than objectscaptured from the ‘real world’, and that testing on syntheticdata is not a reliable way to predict performance on real data.The different classes in the Synthetic data may also be moreeasily distinguished because they have been manually de-signed to be different for this competition, whereas the mod-els in the Real dataset were generated from body scans ofhuman participants taken from an existing dataset, who mayor may not have had very different body shapes. There isin fact a much higher similarity between the classes in theReal dataset. Figure 4 shows the precision-recall curve forthe best performing methods submitted by each participant.
On the more challenging Real dataset, three methods, dueto Litman et al., Ye, and Giachetti and Garro, performed sig-nificantly better than the others. The best performing methodby Litman et al. was trained on a subset of the test set, andtherefore has an advantage over their other submissions, butthe unsupervised variants of their method still perform well.
The performance of different methods is far closer on theSynthetic dataset. The organisers (Pickup et al.) submittedtwo very simple methods, Surface Area and Compactness. Itis interesting to note that they perform better than many ofthe more sophisticated methods submitted, including theirown, and Surface Area is one of the top performing methodson the Synthetic dataset. These measures are obviously notnovel, but they highlight that sophistication does not alwayslead to better performance, and a simpler and computation-ally very efficient algorithm may suffice. Algorithms shouldconcentrate on what is truly invariant for each class.
Table 2 shows the results of Task 2 evaluated using theF-Measure. As for Task 1, the performance of all methods
Table 2: Retrieval results for Task 2. The 1st , 2nd and
3rd highest scores of each column are highlighted. ‡ signi-fies the method is aware of the class size, other annotationas for Table 1.
6. Conclusion
This paper compared non-rigid retrieval results obtained by22 different methods, submitted by nine research groups,on two new datasets of human body models. Thesedatasets are much more challenging than previous non-rigiddatasets [LGB∗11], as evidenced by lower success rates. Thedata obtained by scanning real human participants provedmore challenging than the synthetically generated data. Thisshows that there is a lot of room for future research to im-prove the analysis of ‘real’ data. If the performance of meth-ods is to be improved for real data, then more real datasetsare needed for testing purposes, as synthetic datasets do notadequately mimic the same challenge.
All methods submitted were designed for generic non-rigid shape retrieval. Our new dataset has created the poten-tial for new research into methods which specialise in shaperetrieval of humans.
Acknowledgements
This work was supported by EPSRC Research GrantEP/J02211X/1.
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