Shape Outlier Detection Using Pose Preserving Dynamic Shape Models

Transcription

1 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models Chan-Su Lee Ahmed Elgammal Department of Computer Siene, Rutgers University, Pisataway, NJ 8854 USA Abstrat In this paper, we introdue a framework for shape outlier, like arrying objet, detetion in different people from different views using pose preserving dynami shape models. We model dynami human shape deformations in different people using kinematis manifold embedding and deomposition of nonlinear mapping using kernel map and multilinear analysis. The generative model supports pose-preserving shape reonstrution in different people, views and body poses. Iterative estimation of shape style and view with pose preserving generative model allows estimation of outlier in addition to aurate body pose. The model is also used for hole filling in the bakground-subtrated silhouettes using mask generated from the best fitting shape model. Experimental results show aurate estimation of arrying objets with hole filling in disrete and ontinuous view variations. 1. Introdution The shape deformation in human motion ontains rih information suh as body pose, person identity, and even emotional states of the person. It implies that human shape deformations vary in different body poses, shape styles, and emotional states. Different observation onditions like view and bakground ause further variations in the observed image or extrated shapes. The shape deformation of human motion like gait auses variations of topology and nonlinear deformations in observed shape sequenes. When we have a good generative shape deformation models aording to state parameters like body pose, shape style and view, we an solve many problems in human motion analysis, traking and reognition. This paper presents a dynami shape model of human mo- Appearing in Proeedings of the Workshop on Mahine Learning Algorithms for Surveillane and Event Detetion at the 3rd ICML, 6. Copyright 6 by the author(s)/owner(s). tion with deomposition of body pose, shape style and view. To model nonlinear shape deformations by multiple fators, we propose kinematis manifold embedding and kernel mapping in addition to multilinear analysis of olleted nonlinear mappings. The kinematis manifold embedding, whih represents body onfiguration in low dimensional spae based on motion aptured data and invariant to different people and view, is used to model dynamis of shape deformation aording to intrinsi body onfiguration. The entire intrinsi onfiguration an have one-toone orrespondene with kinematis manifold (Se..1). Using this kinematis manifold embedding, individual differenes of shape deformations an be solely ontained in nonlinear mappings. By utilizing multilinear analysis for these mappings, we an ahieve deompositions of shape styles and views in addition to the body poses (Se..). Iterative estimation of body pose, shape style and view parameters of given the deomposable generative model provides pose preserving, style preserving reonstrution of shape in different view human motion (Se..3). The proposed pose preserving, dynami shape models are used to detet shape outlier, like arrying objets, from sequenes of silhouette images. The detetion of arrying objets is one of the key element in visual surveillane systems (Haritaoglu et al., 1999). In gait hallenge problem, the performane of gait reognition derease dramatially for probe set with briefase (Sarkar et al., 5). Our pose-preserving dynami shape model detets arrying objets as outliers. By removing outliers from extrated shape, we an estimate body pose and other fators aurately in spite of variations of shapes due to arrying objets (Se. 3.3). Hole filling based on signed distane representation of shape (Se. 3.1) also helps orreting shapes from inaurate bakground subtration (Se. 3.). Iterative proedure of hole filling and outlier detetion using pose preserving shape reonstrution ahieves gradual hole filling and advane in preision of arrying objets detetion (Se. 3.4). Experimental results using CMU Mobo gait database (Gross & Shi, 1) and our own data set from multiple views show aurate estimation of arrying objet with orretion of silhouettes from multiple people and multiple view silhouettes with holes (Se. 4).

2 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models 1.1. Related Work There have been a lot of work on ontour traking from luttered environment suh as ative shape models (ASM) (Cootes et al., 1995), ative ontours (Isard & Blake, 1998), and exemplar-based traking (Toyama & Blake, 1). Spatiotemporal models are also used for ontour traking (Baumberg & Hogg, 1996). However, there are few works to model shape variations in different people and views as a generative model with apturing nonlinear shape deformations. The framework to separate the motion from the style in a generative fashion was introdued in our previous work (Elgammal & Lee, 4b), where the motion is represented in a low dimensional nonlinear manifold. Nonlinear manifold learning tehnique an be used to find intrinsi body onfiguration spae (Wang et al., 3; Elgammal & Lee, 4b). However, disovered manifolds are twisted differently aording to person styles, views, and other fators like lothes in image sequenes (Elgammal & Lee, 4a). We propose kinematis manifold embedding as an alternative uniform representation of intrinsi body onfiguration (Se..1). Shape models are used for segmentation and traking of medial image using level sets (Tsai et al., 3; Paragios, 3; Leventon et al., ). The shape priors also used as onstraints in geodesi ative ontours (Rousson & Paragios, ). These shape priors an be used for posepreserving shape estimation. However, this model does not ontain dynami harateristis of shape deformations in human motion. This paper presents the generative dynami shape model in multiple view and people using kinematis manifold embedding. In spite of the importane of arrying objets or outliners detetion in visual surveillane system, there has been few works foused on arrying objets detetion due to diffiulties in modeling variations of shape due to arrying objets. Deteting arrying objet has been designed to work under a visual surveillane system (Haritaoglu et al., 1999). By analyzing symmetry in silhouette model, they deteted arrying objet by aperiodi outlier regions. The system is very sensitive to noise of foreground objet detetion, size of arrying objet, and the axis of symmetry whih is used to ompute asymmetri of shape (BenAbdelkader & Davis, ). Amplitude of the shape feature and the loation of deteted objets are onstrained to improve auray of arrying objet detetion (BenAbdelkader & Davis, ). Deteting outlier aurately and removing noise and filling hole in extrated silhouette still remains unresolved. This paper proposes gradual detetion of outlier, and orretion of noise silhouette by hole filling and shape outlier removal using pose-preserving dynami shape model.. Pose Preserving Dynami Shape Models We an think of the shape of a dynami objet as instanes driven from a generative model. Let y t R d be the shape of the objet at time instane t represented as a point in a d-dimensional spae. This instane of the shape is driven from a model in the form y t = γ(b t ;s,v), (1) where the γ( ) is a nonlinear mapping funtion that maps from a representation of the body pose b t into the observation spae given a mapping parameter s, v that haraterizes the person shape and view variations in a way independent of the onfiguration. Given this generative model, we an fully desribe observation instane y t by state parameters b t, s, and v. For the generative model, we need low dimensional representation of body pose b t invariant to the view and shape style. We need universal representation for body onfiguration invariant to the variation of observation in different people and in different view. Kinematis manifold embedding is used for intrinsi manifold representation of body onfiguration b t..1. Kinematis Manifold Embedding We find low dimensional representation of kinematis manifold by applying nonlinear dimensionality redution tehniques for motion aptured data. We first onvert joint angles of motion apture data into joint loations in 3 dimensional spaes. We align global transformation in advane in order to model motion only due to body onfiguration hange. Loally linear embedding (LLE) (Roweis & Saul, ) is applied to find low dimensional intrinsi representation from the high dimensional data (olletion of joint loation). The disovered manifold is onedimensional twisted irular manifold in three-dimensional spaes Figure 1. Kinematis manifold embedding and its mean manifold: two different views in 3D spae The manifold is represented using a one-dimensional parameter by spline fitting. In order to find intrinsi manifold representation using nonlinear dimensionality redution, dense sampling from the manifold points is required. We use multiple yles to find kinematis intrinsi mani-

3 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models fold representation by LLE. For one-dimensional representation of the multiple yles, we use mean-manifold representation in the parameterizations. The mean manifold an be found by averaging multiple yles after deteting yles by measuring geodesi distane along the manifold. The mean-manifold is parameterized by spline fitting by a one-dimensional parameter β t R and a spline fitting funtion g : R R 3 that satisfies b t = g(β t ), whih is used to map from the parameter spae into the three dimensional embedding spae. Fig. 1 shows kinematis manifold from motion apture data with three walking yles and their mean manifold representation... Deomposing and Modeling Shape Style Spae Individual variations of the shape deformation an be disovered in the nonlinear mapping spae between the kinematis manifold embedding and the observation in different people. If we have pose-aligned shape for all the people, then it beomes relatively easy to find shape variations aording to the shape style. Similarly, as we have ommon representation of the body pose, all the differenes of the shape deformation an be ontained in the mapping between the embedding points and observation sequenes. We employ nonlinear mapping based on empirial kernel map (Shlkopf & Smola, ) to apture nonlinear deformation in differene body pose. There are three steps to model individual shape deformations using nonlinear mapping. We fous on gait, walking sequene. But it an be appliable to other yli motion analysis in different people. First, for a given shape deformation sequene, we detet gait yles and embed olleted shape deformation data to the intrinsi manifold. In our ase, kinematis manifold is used for gait embedding in eah deteted yle. As the kinematis manifold omes from onstant speed walking motion aptured data, we an embed the shape sequene in equally spaed points along the manifold. Seond, we learn nonlinear mapping between the kinematis embedding spae and shape sequenes. Aording to the representer theorem (Kimeldorf & Wahba, 1971), we an find a mapping that minimizes the regularized risk in the following form for given patterns x i and target values y i = f (x i ): f (x) = m i=1 α i k(x i,x). () The solutions lie on the linear span of kernels entered on data points. The theorem shows that any nonlinear mapping is equivalent to a linear projetion from a kernel map spae. In our ase, this kernel map allows modeling of motion sequene with different number of frames as a ommon linear projetion from the kernel map spae. The mapping oeffiients of the linear projetion an be obtained by solving the linear system [y sv 1 ysv N sv ] = C sv [ψ(x sv 1 ) ψ(xsv N sv )]. (3) Given motion sequene with N s shape styles and N v view, we obtain N s N v number of mapping oeffiients. Third, multi-linear tensor analysis an be used to deompose the gait motion mapping into orthogonal fators. Tensor deomposition an be ahieved by higher-order singular value deomposition (HOSVD) (Lathauwer et al., )(Vasilesu & Terzopoulos, 3), whih is a generalization of SVD. All the oeffiient vetors an be arranged in an order-three gait motion oeffiient tensor C with a dimension of N s N v N, where N is the dimension of mapping oeffiient. The oeffiient tensor an be deomposed as C = A 1 S V 3 F where S is the olletion of the orthogonal basis for the shape style subspae. V represents the orthogonal basis of the view spae and F represents the basis of the mapping oeffiient spae. A is a ore tensor whih governs the interations among different mode bases. The overall generative model an be expressed as y t = A s v ψ(b t ). (4) The pose preserving reonstrution problem using this generative model is the estimation of onfiguration parameter b t, shape style parameter s, and view parameter v at eah new frame given shape y t..3. Pose Preserving Reonstrution When we know the state of the deomposable generative model, we an synthesize the orresponding dynami shapes. For given body pose parameter, we an reonstrut best fitting shape by estimating style and view parameter with preserving the body pose. Similarly, when we know body pose parameter and view parameter, we an reonstrut best fitting shape by estimating style parameter with preserving view and body pose. If we want to synthesize new shape at time t for a given shape normalized input y t, we need to estimate the body pose b t, the view v, and the shape style s whih minimize the reonstrution error E(b t,v,s) = y t A v s ψ(b t ). (5) We assume that the estimated optimal style an be written as a linear ombination of style vetors in the training data. Therefore, we need to solve for linear regression weights α suh that s est = K s k=1 α ks k where eah s k is one of the K s shape style vetors in the training data. Similarly for the view, we need to solve for weights β suh that v est = K v k=1 β kv k where eah v k is one of the K v view lass vetors. If the shape style and view fators are known, then equation 5 redues to a nonlinear 1-dimensional searh problem

4 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models for a body pose b t on the kinematis manifold that minimizes the error. On the other hand, if the body pose and the shape style fator are known, we an obtain view onditional lass probabilities p(v k y t,b t,s) whih is proportional to the observation likelihood p(y t b t,s,v k ). Suh the likelihood an be estimated assuming a Gaussian density entered around A v k s ψ(b t ), i.e.,p(y b t,s,v k ) N (C v k s ψ(b t ),Σ vk ). Given view lass probabilities we an set the weights to β k = p(v k y,b t,s). Similarly, if the body pose and the view fator are known, we an obtain the shape style weights by evaluating the shape given eah shape style vetor s k assuming a Gaussian density entered at C v s k ψ(b t ). An iterative proedure similar to a deterministi annealing where in the beginning the eah view and shape style weights are fored to be lose to uniform weights to avoid hard deisions about view and shape style lasses, is used to estimate x t,v,s from given input y t. To ahieve this, we use variables, view and style lass varianes, that are uniform to all lasses and are defined as Σ v = T v σ v I and Σ s = T s σ s I respetively. The parameters T v and T s start with large values and are gradually redued and in eah step and a new onfiguration estimate is omputed. 3. Carrying Objet Detetion We an detet arrying objets by iterative estimation of outlier using the generative model that an synthesize posepreserving shape. In order to ahieve better alignment in normalized shape representation, we performed hole filling and outlier removal for the extrated shape Shape Representation Bakground Subtration: We aptured gait sequene on treadmill with multiple amera. Nonparametri kernel density estimation methods (Elgammal et al., ) are applied for per-pixel bakground models assuming stati amera and employing loal model of intensity. To learn shape deformations in normal walking without arrying objet, we olleted walking sequenes on treadmill for five people with 11 different views around irle in the same amera height. Fig. (a) shows an example of aptured real image. We performed bakground subtration after learning statistial model for the bakground. However, due to lighting around amera and luttered indoor environments, some of the silhouettes are not good as shown in Fig. (b). To ahieve onsistent shape representation in different people and hole filling for inaurate bakground subtration, we orret silhouettes used for training. Normalization of Silhouette Shape: For onsistent representation of shape deformation by variant fators, we (a) Input (b) Silhouette Figure. An example of bakground subtration and silhouette representation: (a) Input image. (b) Bakground subtrated image. () Normalized silhouette. (d) Signed distane representation. normalize silhouette shapes by resizing and re-entering. To be invariant to the distane from amera and different height in eah subjet, we normalized the extrated silhouette height from bakground-subtrated body silhouettes. In addition, the horizontal enter of the shape is re-entered by the enter of gravity of silhouette bloks. We use silhouette bloks whose sizes are larger than speifi threshold value for onsistent entering of shape in spite of small inorret bakground blok from noise and shadow. we perform normalization after morphologial operation and filtering to remove noise spot and small holes. Shape Representation by Signed Distane Funtion: We parameterize shape ontour using signed distane funtion with limitation of maximum distane value for robust shape representation in learning and mathing shape ontour. Impliit funtion z(x) at eah pixel x suh that z(x) = on the ontour, z(x) > inside the ontour, and z(x) < outside the ontour is used, whih is typially used in level-set methods (Osher & Paragios, 3). We add a threshold value as well d T H p () (d) d (x) d T H p x inside d (x) z(x) = x on d (x) x outside d T H n d (x) d T H n, (6) where the d (x) is the distane to the losest point on the ontour with a positive sign inside the ontour and a negative sign outside the ontour. We threshold distane value d (x) by d T H p and d T H n as the distane value beyond er-

5 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models tain distane does not ontain meaningful shape information in similarity measurements. Suh shape representation imposes smoothness on the distane between shapes and robustness to noise and outlier. In addition, by hanging threshold values gradually, we an generate mask to represent inside of the shape for hole filling. Given suh representation, input shape images are points in a d dimensional spae, y i R d,i = 1,,N where all the input shapes are normalized and registered, d is the dimensionality of the input spae, and N is the number of frame in the sequene. 3.. Hole Filling We fill holes in the bakground-subtrated shape to attain more aurate shape representation. When the foreground olor and the bakground olor are the same, most of the bakground subtrated shape silhouettes have holes inside the extrated shape. This auses inaurate desription of shape in signed distane funtion. Hene holes inside shape result in inaurate estimation of the best fitting shape. It an also indue misalignment of shape as the hole an shift enter of gravity for the horizontal axis alignment. From the signed distane representation, we an generate a mask to represent inside of the shape for estimated style, view, and body pose parameters. We an use the mask to fill holes for the original shape. The mask an be generated by thresholds generated from signed distane shape representation like { 1 d (x) d T H hole h(x) hole mask = otherwise, (7) where d T H hole is the threshold value for inner shape to reate mask for hole filling. If the threshold value is zero, the mask will be the same as the silhouette image generated by dynami shape model given style, view and onfiguration. As we don t know the exat shape style, view and onfiguration at the beginning, and the hole auses misalignment, we start from large threshold value, whih generates a small mask of inner shape area and robust to misalignment. We redue the threshold value as estimated model parameters get more aurate. The hole filling operation an be desribed by y hole f illing = z(bin(y) h(y est )), where is logial OR operator to ombine extrated foreground silhouette and mask area, bin( ) onverts signed distane shape representation into binary representation, and z( ) onvert binary representation into signed distane representation with threshold. Fig. 3 shows initial shape normalized silhouette with holes (a), the best estimated shape model (b) whih is generated from the generative model with style and view estimation and onfiguration searh, and the hole mask () when d T H hole = 3, and new shape after hole filling (d). We an improve the best mathing shape by exluding mask area in the omputation of similarity measurement for generated samples in searhing the best fitting body pose. Re-alignment of shape and re-omputation of shape representation after hole filling provide better shape desription for next step Carrying Objet Detetion Carrying objets are deteted by estimating outlier from best mathing normal dynami shape and given input shape. The outlier of a shape silhouette with arrying objets is the mismathing part in input shape ompared with best mathing normal walking shape. Carrying objets are the major soure of mismathing when we ompare with normal walking shape even though other fators suh as inaurate shape extration for bakground subtration, shape misalignment also ause mismathes. For aurate detetion of arrying objet from outlier, we need to remove other soure of outlier suh as hole and misalignment in shape. Hole filling and outlier removal are performed iteratively to improve shape representation for better estimation of the mathing shape. We gradually redue threshold value for outlier detetion to get more preise estimation of outlier progressively. The mismathing error e(x) is measured by Eulidian distane between signed distane input shape and best mathing shape generated from the shape model, e (x) = z (x) z est (x). (8) The error e(x) inreases linearly as the outlier goes away from the mathing shape ontour due to signed distane representation. By thresholds the error distane, we an detet outlier. { 1 e (x) e T H outlier O(x) outlier mask = otherwise, (9) At the beginning, we start from large e T H outlier value and we redue the value gradually. Whenever we detet outlier, we remove the deteted outlier area and perform realignment to redue misalignment due to the outlier. In Fig. 3, for given signed distane input shape (e), we measure mismathing error (f) by omparing with best mathing shape (b). Outlier is deteted (g) with given threshold value e T H outlier = 5, and new shape for next iteration is generated by removing outlier (h). This outlier detetion and removal proedure is ombined with hole filling as both of them help aurate alignment of shape and estimation of best mathing shape Iterative Estimation of Outlier with Hole Filling Iterative estimations of outlier, hole filling, outlier removal, and estimation of shape style, view and onfiguration are performed with threshold value ontrol. The threshold

6 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models (a) (b) () (d) (e) (f) (g) (h) Figure 3. Hole filling using mask from best fitting model : (a) Initial normalized shape with hole. (b) Best mathing shape from generative model. () Overlapping with initial silhouette and mask from best mathing shape by threshold. (d) New shape with redued hole. (e) Initial normalized shape for outlier detetion with signed distane representation. (f) Eulidian distane between best mathing model from the generative model and input shape with signed distane representation. (g) Deteted outlier with threshold value e(x) 5. (h) New shape after removing outlier. value for hole filling and the threshold value for outlier detetion need to be dereased to get more preise in the outlier detetion and hole filling in eah iteration. In addition, we ontrol the number of samples to searh body pose for estimated view and shape style. At the initial stage, as we don t know aurate shape style and view, we use small number of samples along the equally distant manifold points. As the estimation progress, we inrease auray of body pose estimation with inreased number of samples. We summarize the iterative estimation as follows: Input: image shape y i, estimated view v, estimated style s, ore tensor A Initialization: initialize sample num N sp initialize d T H hole, e T H outlier Iterate: Generate N sp samples y sp i b i,i = 1,,N sp Coeffiient C = A s v embedding b i = g(β i ), β i = M i sp Generate hole filling mask h i = h(y sp i ) Update input with hole filling y hole f illing = z(bin(y) h i (y est )) Estimate best fitting shape with hole filling mask: 1-D searh for y est that minimizes E(b i ) = y hole f illing h i (Cψ(b i )) Compute outlier error e (x) = y hole f illing y est (x) Estimate outlier o outlier (x) = e (x) e T H outlier Update: inrease N sp redue d T H hole, e T H outlier Based on the best mathing shape, we ompute the outlier from the initial soure after re-entering initial soure. 4. Experimental Results We evaluated our method using two gait-database. One is from CMU Mobo data set and the other is our own data set for multiple view gait sequene. Robust outlier detetion in spite of hole in the silhouette images was shown learly in CMU database. We olleted our own data set to show arrying objet detetion in ontinuous view variations Carrying Ball Detetion from Multiple Views The CMU Mobo database ontains 5 subjets with 6 different views walking on the treadmill to study human loomotion as a biometri (Gross & Shi, 1). The database provides silhouette sequene extrated based on one bakground image. The bakground subtrated silhouettes in most of the sequenes have holes. We olleted 1(= 4 3) yles to learn dynami shape models with view and style variations from normal slow walking sequenes of 4 subjets with 3 different views. For the training sequenes, we orreted holes manually. Fig. 4 shows deteted arrying objets in two different views from different people. The initial normalized shape has holes with a arrying ball (a)(e). Still the best fitting shape models reover orret body poses after iterative estimations of view and shape style with hole filling and outlier removal (b)(f). Fig. 4 ()(g) show examples of generated masks during iteration for hole filling. Fig. 4 (d) (h) show deteted outlier after iteration. In Fig. 4 (h), the outlier in bottom right orner omes from the inaurate bakground subtration outside the subjet, whih annot be managed by hole filling. The verifiation routine based on temporal harateristis of the outlier similar to (BenAbdelkader & Davis, ) an be used to exlude suh a outlier from deteted arrying objets. 4.. Carrying Objet Detetion with Continuous View Variations We olleted 4 people with 7 different views to learn the pose preserving shape model of normal walking for detetion of arrying objet in ontinuous view variations. In order to ahieve reasonable multiple view interpolation,

7 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models (a) (b) () (d) (e) (f) (g) (h) Figure 4. Outlier detetion in different view: (a) Initial normalized shape for outlier detetion. (b) The best fitting model from the generative model. () Overlapping initial input and hole filling mask at the last iteration. (d) Deteted outlier. (e) (f) (g) (h) : Another view in different person we aptured normal gait sequene on the treadmill with the same height amera position in our lab. The test sequene is aptured separately in outdoor using ommerial amorder. Fig. 5 shows an example sequene of arrying objet detetion in ontinuous hange of walking diretion. The first row shows original input images from the amorder. The seond row shows normalized shape after bakground subtration. We used the nonparametri kernel density estimation method for per-pixel bakground models (Elgammal et al., ). The third row shows best mathing shape estimated after hole filling and outlier removal using dynami shape models with multiple views. The fourth row shows deteted outlier. Most of the dominant outlier omes from the arrying objet. 5. Conlusions We presented shape outlier detetion using pose preserving dynami shape model espeially for arrying objets detetion for given silhouette images. The proposed model may be used for shadow detetion and abnormal body pose detetion, whih is important human motion reognition and event detetion. In the arrying objet detetion, the signed distane representation of shape helps robust mathing in spite of small misalignment and holes. To enhane the auray of alignment and mathing, we preformed hole filling and outlier detetion iteratively with threshold hange. In our experiment, we ontrolled threshold for gradual disriminative estimation of outlier and holes. More expert knowledge, suh as temporal onstraints in body pose transition, periodi harateristis in body limb an be used to enhane outlier detetion and identifiation. Experimental results from CMU Mobo data set show aurate detetion of outlier in multiple fixed views. We also showed the estimation of outlier in ontinuous view variations from our olleted data set. The removal of outlier or arrying objet will be useful for gait reognition as it helps reovering high quality original silhouette, whih is important in gait reognition. We plan to apply the proposed method to test gait reognition with arrying objets and abnormal motion detetion. Aknowledgement This researh is partially funded by NSF award IIS Referenes Baumberg, A., & Hogg, D. (1996). Generating spatiotemporal models from examples. Image and Vision Computing, 14, BenAbdelkader, C., & Davis, L. S. (). Detetion of people arrying objets: A motion-based reognition approah. Pro. of FGR (pp ). Cootes, T. F., Taylor, C. J., Cooper, D. H., & Graham, J. (1995). Ative shape models: Their training and appliations. CVIU, 61, Elgammal, A., Harwood, D., & Davis, L. (). Bakground and foreground modeling using nonparametri kernel density estimation for visual surveillane. IEEE Proeedings, 9, Elgammal, A., & Lee, C.-S. (4a). Inferring 3d body pose from silhouettes using ativity manifold learning. Pro. CVPR (pp ). Elgammal, A., & Lee, C.-S. (4b). Separating style and ontent on a nonlinear manifold. Pro. CVPR (pp ). Gross, R., & Shi, J. (1). The mu motion of body (mobo) database (Tehnial Report TR-1-18). Carnegie Mellon University. Haritaoglu, I., Cutler, R., Harwood, D., & Davis, L. S. (1999). Pakpak: Detetion of people arrying objets using silhouettes. Pro. of ICCV (pp. 1 17). Isard, M., & Blake, A. (1998). Condensation onditional density propagation for visual traking. Int.J.Computer Vision, 9, 5 8.

8 Shape Outlier Detetion Using Pose Preserving Dynami Shape Models Frame 1 Frame 15 Frame 3 Frame 45 Frame 6 Frame 75 Frame 9 Frame 15 Figure 5. Outlier detetion in ontinuous view variations: First row: Input image. Seond row: Extrated silhouette shape. Third row: Best mathing shape. Fourth row: Deteted arrying objet Kimeldorf, G., & Wahba, G. (1971). Some results on thebyheffian spline funtions. J. Math. Anal. Appli., 33, Lathauwer, L. D., de Moor, B., & Vandewalle, J. (). A multilinear singular value deomposiiton. SIAM Journal On Matrix Analysis and Appliations, 1, Leventon, M. E., Grimson, W. E., & Faugeras, O. (). Statistial shape influene in geodesi ative ontours. Pro. of CVPR (pp ). Osher, S., & Paragios, N. (3). Geometri level set methods. Springer. Paragios, N. (3). A level set approah for shape-driven segmentation and traking of the left venttile. IEEE Trans. on Medial Imaging,. Rousson, M., & Paragios, N. (). Shape priors for level set representations. Pro. ECCV, LNCS 351 (pp. 78 9). Roweis, S., & Saul, L. (). Nonlinear dimensionality redution by loally linar embedding. Siene, 9, Sarkar, S., Phillips, P. J., Liu, Z., Vega, I. R., Grother, P., & Bowyer, K. W. (5). The humanid gait hallenge problem: Data sets, performane, and analysis. IEEE Trans. PAMI, 7, Shlkopf, B., & Smola, A. (). Learning with kernels: Support vetor mahines, regularization, optimization and beyond. MIT Press. Toyama, K., & Blake, A. (1). Probabilisti traking in a metri spae. ICCV (pp. 5 59). Tsai, A., Yezzi, A., Wells, W., Tempany, C., Tuker, D., Fan, A., & Grimson, W. E. (3). A shape-based approah to the segmentation of medial imagery using level sets. IEEE Trans. on Medial Imaging,. Vasilesu, M. A. O., & Terzopoulos, D. (3). Multilinear subspae analysis of image ensembles. Pro. of CVPR. Wang, Q., Xu, G., & Ai, H. (3). Learning objet intrinsi struture for robust visual traking. CVPR (pp. 7 33).