Topology-Preserving Transformation Based on the Correspondence of Control Points Using Radial Basis Functions

Abstract

For point-based image registration, transformations using radial basis functions on scattered points cause problems with topology-preservation. We propose here a topology-preserving transformation based on expansions of radial basis functions. By analyzing the non-preserving transformation given by the corresponding control points, this method computes the main shifting directions of topology non-preserving regions on deformed surfaces. It then determines the control points leading to the topology non-preservation results. Next, it adaptively relaxes these control points based on the spatial relationships of points, and adjusts the transformation function coefficients using relaxation parameters to construct the topology-preserving transformation. We provide here the method for selecting the control points that cause the topology non-preservation results and estimate the optimal relaxation parameters based on the shifting model of the control points. Experimental results on random point sets, artificial images and medical images show that this method is feasible and practicable.