Shape evolution for rigid and nonrigid shape registration and recovery

This paper addresses the problem of rigid and nonrigid shape registration and recovery in the presence of shape deformation, missing parts and/or overlapping of multiple shapes. A novel shape evolution approach based on truncated warping transformation formulated in an Energy-Minimization-Curve-Evolution framework is proposed to solve this problem. We deterministically model the rigid and nonrigid shape deformation/registration as curve evolution by a warping function mapping. We also derive the curve evolution equation of warping to minimize functional energies. Hence, by selecting a prior shape as the initial curve for the curve evolution, the shape evolution for registration is within the shape space generated by the warping transformation of the prior shape. Based on the Fourier shape contour spectrum, local shape contour distortions that result in significant visual impact is considered to be largely contained in the changes of the high frequency components. Thus, the smoothing of the warping function by truncation is performed to recover the true shape. We adopted the Chan-Vese model and a truncated warping function to obtain our algorithm for shape registration and recovery. Experiments validated our model and algorithm quantitatively.