3D non-rigid registration for MPU implicit surfaces

Implicit surface representation is well suited for surface reconstruction from a large amount of 3D noisy data points with non-uniform sampling density. Previous 3D non-rigid model registration methods can only be applied to the mesh or volume representations, but not directly to implicit surfaces. To our best knowledge, the previous 3D registration methods for implicit surfaces can only handle rigid transformation and they must keep the data points on the surface. In this paper, we propose a new 3D non-rigid registration algorithm to register two multi-level partition of unity (MPU) implicit surfaces with a variational formulation. The 3D non-rigid transformation between two implicit surfaces is a continuous deformation function, which is determined via an energy minimization procedure. Under the octree structure in the MPU surface, each leaf cell is transformed by an individual affine transformation associated with an energy that is related to the distance between two general quadrics. The proposed algorithm can directly register between two 3D implicit surfaces without sampling on the two signed distance functions or polygonalizing implicit surfaces, which makes our algorithm efficient in both computation and memory requirement. Experimental results on 3D human organ and sculpture models demonstrate the effectiveness of the proposed algorithm.