Dealing with Non-linearity in Shape Modelling of Articulated Objects ⋆ Gr´ egory Rogez ⋆⋆ , Jes´ us Mart´ ınez-del-Rinc´on ⋆⋆⋆ , and Carlos Orrite CVLab, Aragon Institute for Engineering Research, University of Zaragoza, Spain {grogez, jesmar, corrite}@unizar.es http://www.cv.i3a.unizar.es Abstract. We address the problem of non-linearity in 2D Shape mod- elling of a particular articulated object: the human body. This issue is partially resolved by applying a different Point Distribution Model (PDM) depending on the viewpoint. The remaining non-linearity is solved by using Gaussian Mixture Models (GMM). A dynamic-based clustering is proposed and carried out in the Pose Eigenspace. A funda- mental question when clustering is to determine the optimal number of clusters. From our point of view, the main aspect to be evaluated is the mean gaussianity. This partitioning is then used to fit a GMM to each one of the view-based PDM, derived from a database of Silhouettes and Skeletons. Dynamic correspondences are then obtained between gaussian models of the 4 mixtures. Finally, we compare this approach with other two methods we previously developed to cope with non-linearity: Nearest Neighbor (NN) Classifier and Independent Component Analysis (ICA). 1 Introduction Thanks to the structural knowledge, people are able to deduce the pose of an articulated object (e.g. a person) from a simple binary silhouette. Following this statement, our idea was to construct a human model encapsulating within a point distribution model (PDM) [1] body silhouette information given by the 2D Shape (landmarks located along the contour) and the structural information given by the 2D Skeleton joints. In that way, the 2D pose could be inferred from the silhouette. Due to the high non-linearity of the feature space, mainly caused by the rotational deformations inherent to the articulated structure of the human body, we consider in this work the necessity to use non-linear statistical models. They have been previously proposed by Bowden [2] that demonstrated how the 3D structure of an object can be reconstructed from a single view of its outline. In a previous work[3], we presented a first version of the model. The problem of non-linear principal component analysis was partially resolved by applying a different PDM depending on previous pose estimation (4 views were considered: ⋆ Work supported by spanish grant TIC2003-08382-C05-05 (MCyT) and FEDER. ⋆⋆ Funded by FPU grant AP2003-2257 from Spanish Ministry of Education. ⋆⋆⋆ Supported by Spanish Ministry of Education under FPI grant BES-2004-3741. J. Mart´ ı et al. (Eds.): IbPRIA 2007, Part I, LNCS 4477, pp. 63–71, 2007. c  Springer-Verlag Berlin Heidelberg 2007