A measure of deformability of shapes, with applications to human motion analysis

In this paper we develop a theory for characterizing how deformable a shape is. We define a term called "deformability index" for shapes. The deformability index is computed from the tracked positions of a sequence of deformable shapes, using a scaled orthographic camera projection model. Our method assumes that a deformable shape sequence can be represented by a linear combination of basis shapes, where the weights assigned to each basis shape changes with time. The tracked points obtained from the shape sequence is transformed to a 3D shape space. Using statistical models to separate out the "true" deformations from those induced by noise in the trajectories, the dimension of this shape space is 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. Rigid 3D transformations of the shape are taken into account in estimating the deformability index; however, the method does not require estimation of 3D structure or motion. Experimental results are shown using motion capture data as well as real imagery of different human activities. The results show that the deformability index is in accordance with our intuitive judgement and corroborates certain hypotheses in human movement analysis studies.