Dense Point-to-Point Correspondences Between Genus-Zero Shapes Using Cubic Mapping and Horn-Schunck Optical Flow.

Establishing correspondences is a fundamental and essential task in computer graphics for further processing of shapes. We have proposed an important modification to an existing method to remove several large matching errors in specific regions. The method uses the unit sphere and the regular spherical grid as parameterization spaces to perform registration and obtain the matching map between two three-dimensional genus-zero shapes, considering non-rigid and non-isometric deformations. Although the unit sphere is a suitable parameterization space for rigid alignment, mapping the sphere to a regular spherical grid for non-rigid registration makes the process unstable since it is not a distance-preserving projection. Therefore, it produces large detachments on the grid and for several regions. Replacing the regular spherical grid mapping with Cubic mapping results in smooth displacement and locality for all corresponding vertices on each cube face. Due to our enhancement, the Optical Flow faces a smooth flow field in the non-rigid registration process. Our modification results in the elimination of matches with significant normalized geodesic error and an increase in the accuracy of the correspondence map, compared to the base method and other recently published approaches.