Motion analysis of a homogeneously deformable object using subset correspondences

Abstract

Analysis of generalized motion parameters involves the estimation of translation, rotation and the deformation parameters for a non-rigid object. Most motion analysis methods require a preprocessing step of establishing the feature point correspondence between subsequent time frames. Such a preprocessing of data is computationally demanding, and very often leads to erroneous results. We explore the possibility of relaxing the above requirements for a homogeneously deformable object. A computationally efficient method is proposed here that needs only subset correspondences between 3D feature points on the object at two different time instants, instead of having explicit point correspondence. The deformation parameters are obtained utilizing the changes in the Euclidean distance for individual feature points belonging to different subsets. Under the proposed model, the object may now be transformed into a rigid one utilizing the estimated deformation parameters. The rotation parameters are estimated by considering the invariance properties of the principal moments. Simulation experiments are carried out to evaluate the performance of the proposed method. The applicability of the method is also tested on a real data set.