Invariant Features for 3D-Data based on Group Integration using Directional Information and Spherical Harmonic Expansion

Due to the increasing amount of 3D data for various applications there is a growing need for classification and search in such databases. As the representation of 3D objects is not canonical and objects often occur at different spatial position and in different rotational poses, the question arises how to compare and classify the objects. One way is to use invariant features. Group integration is a constructive approach to generate invariant features. Several variants of group integration features are already proposed. In this paper we present two main extensions, we include local directional information and use the spherical harmonic expansion to compute more descriptive features. We apply our methods to 3D-volume data (pollen grains) and 3D-surface data (Princeton shape benchmark)