A unifying framework for non-linear registration of 3D objects

An extension of our earlier work is proposed to find a non-linear aligning transformation between a pair of deformable 3D objects. The basic idea is to set up a system of nonlinear equations whose solution directly provides the parameters of the aligning transformation. Each equation is generated by integrating a nonlinear function over the object´s domains. Thus the number of equations is determined by the number of adopted nonlinear functions yielding a flexible mechanism to generate sufficiently many equations. While classical approaches would establish correspondences between the shapes, our method works without landmarks. Experiments with 3D polynomial and thin plate spline deformations confirm the performance of the framework.