Nonlinear registration based on the approximation of radial basis function coefficients

Nonlinear registration is a technique which can accommodate the deformation of structures. It is widely applied to many applications of medical images, such as the analysis of disease characterization and the observation of brain degeneration. This paper presents an efficient approach which can accurately register images. Hierarchical regular meshes of Wendland's radial basis functions are adopted to model the deformation of images from coarse to fine. To efficiently establish the spatial relationship between images, an approximation method is proposed to determine the coefficients of basis functions according to the spatial interpretation in deformation. This results an image registration accomplished by a series of fast optimizations with only three degrees of freedom, and avoids the difficulties of direct searching for all coefficients in a huge optimization space. Experimental results indicate that the proposed method is much more accurate than statistical parametric mapping 2 (SPM2) and is superior to hierarchical attribute matching mechanism for elastic registration (HAMMER) and automatic registration toolbox (ART) in both accuracy and efficiency.