Fast computation of 3D spherical Fourier harmonic descriptors - a complete orthonormal basis for a rotational invariant representation of three-dimensional objects

In this paper we propose to extend the well known spherical harmonic descriptor (SHD) by adding an additional Fourier-like radial expansion to represent volumetric data. Having created an orthonormal basis on the ball with all the gentle properties known from the spherical harmonics theory and Fourier theory, we are able to compute efficiently a multi-scale representation of 3D objects that leads to highly discriminative rotation-invariant features, which will be called spherical Fourier harmonic descriptors (SFHD). Experiments on the challenging Princeton Shape Benchmark (PSB) demonstrate the superiority of SFHD over the ordinary SHD.