Spherical Wavelet Descriptors for Content-based 3D Model Retrieval
The description of 3D shapes with features that possess descriptive power and invariant under similarity transformations is one of the most challenging issues in content based 3D model retrieval. Spherical harmonics-based descriptors have been proposed for obtaining rotation invariant representations. However, spherical harmonic analysis is based on latitude-longitude parameterization of a sphere which has singularities at each pole. Consequently, features near the two poles are over represented while features at the equator are under-sampled, and variations of the north pole affects significantly the shape function. In this paper we discuss these issues and propose the usage of spherical wavelet transform as a tool for the analysis of 3D shapes represented by functions on the unit sphere. We introduce three new descriptors extracted from the wavelet coefficients, namely: (1) a subset of the spherical wavelet coefficients, (2) the $L_1$ and, (3) the $L_2$ energies of the spherical wavelet sub-bands. The advantage of this tool is three fold; First, it takes into account feature localization and local orientations. Second, the energies of the wavelet transform are rotation invariant. Third, shape features are uniformly represented which makes the descriptors more efficient. Spherical wavelet descriptors are natural extension of 3D Zernike moments and spherical harmonics. We evaluate, on the Princeton Shape Benchmark, the proposed descriptors regarding computational aspects and shape retrieval performance.