Elastic Registration of 3D Deformable Objects

A novel correspondence-less approach is proposed to find a non-linear aligning transformation between a pair of deformable 3D objects. Herein, we consider a polynomial deformation model, but our framework can be easily adapted to other common deformations. The basic idea of the proposed method 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. The efficiency of the proposed approach has been demonstrated on a large synthetic dataset as well as in the context of medical image registration.