A Solution to the Similarity Registration Problem of Volumetric Shapes

This paper provides a novel solution to the volumetric similarity registration problem usually encountered in statistical study of shapes and shape-based image segmentation. Here, shapes are implicitly represented by characteristic functions (CFs). By mapping shapes to a spherical coordinate system, shapes to be registered are projected to unit spheres and thus, rotation and scale parameters can be conveniently calculated. Translation parameter is computed using standard phase correlation technique. The method goes through intensive tests and is shown to be fast, robust to noise and initial poses, and suitable for a variety of similarity registration problems including shapes with complex structures and various topologies.