Recovery of global nonrigid motion-a model based approach without point correspondences

This paper presents a novel technique for the estimation of global nonrigid motion without using point correspondences. The complete description of the nonrigid motion of an object involves specifying a displacement vector at each point of the object. Such a description provides a large amount of information which needs to be processed further in order to study the global characteristics of the deformation. Nonrigid motion can be studied hierarchically in terms of a global nonrigid motion and point-by-point local nonrigid motion. The technique presented in this paper gives a method for estimating a global affine or polynomial transformation between two objects. The novelty of the technique lies in the fact that it does not use any point correspondences. Our method uses hyperquadric models to model the data and estimate the global deformation. We show that affine or polynomial transformation between two datasets can be recovered from the hyperquadric parameters. The usefulness of the technique is two-fold. First, it paves the way for viewing nonrigid motion hierarchically in terms of global and local motion. Second, it can be used as a front end to other motion-analysis techniques that assume small motion. For instance, most nonrigid motion analyse's algorithms make some assumptions on the type of nonrigid motion (conformal motion, small motion, etc) that are not always satisfied in practice. When the motion between two datasets is large, our algorithm can be used to estimate the affine transformation (which includes scale and shear) or a polynomial transformation between the two datasets which can then be used to warp the first dataset closer to the second so as to satisfy the small motion assumption. We present experiment results with real and synthetic 2D and 3D data.