Towards a measure of deformability of shape sequences

In this paper we develop a theory for characterizing how deformable a shape is given a sequence of its observations. We define a term called ‘‘deformability index’’ (DI) for shapes. The novelty of the proposed method lies in its ability to separate the effects of observation noise from the underlying non-rigid deformation process. The DI is computed from the tracked positions of a sequence of deformable shapes, using an affine camera model. Our method assumes that a deformable shape sequence can be represented by a linear combination of rigid basis shapes, where the weights assigned to each basis shape change with time. The tracked points obtained from the 2D shape sequence are transformed to a 3D shape space, whose dimension is then estimated using spectral analysis methods. The dimension of this shape space determines the number of basis shapes needed to represent the shape sequence, which, in turn, determines the deformability index. Our method is different from existing techniques since it is non-iterative, does not require setting an arbitrary threshold and is able to precisely model the effects of noise in the feature positions. Rigid 3D transformations of the shape are taken into account in estimating the DI; however, the method does not require estimation of 3D structure or motion. Experimental results show that the DI is in accordance with our intuitive judgment. Applications and comparative analysis on 3D deformable object modeling are also presented. 2007 Elsevier B.V. All rights reserved.