Invariant Geometric Representation of 3D Point Clouds for Registration and Matching

Though implicit representations of surfaces have often been used for various computer graphics tasks like modeling and morphing of objects, it has rarely been used for registration and matching of 3D point clouds. Unlike in graphics, where the goal is precise reconstruction, we use isosurfaces to derive a smooth and approximate representation of the underlying point cloud which helps in generalization. Implicit surfaces are generated using a variational interpolation technique. Implicit function values on a set of concentric spheres around the 3D point cloud of object are used as features for matching. Geometric-invariance is achieved by decomposing implicit values based feature set into various spherical harmonics. The decomposition provides a compact representation of 3D point clouds while achieving rotation invariance.