Discriminative Spherical Wavelet Features for Content-Based 3D Model Retrieval

The description of 3D shapes using features that possess descriptive power and are 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 a latitude-longitude parameterization of the sphere which has singularities at each pole, and therefore, variations of the north pole affect significantly the shape function. In this paper we discuss these issues and propose the usage of spherical wavelet transforms 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 L1 and, (3) the L2 energies of the spherical wavelet sub-bands. The advantage of this tool is threefold; 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 extensions of spherical harmonics and 3D Zernike moments. We evaluate, on the Princeton Shape Benchmark, the proposed descriptors regarding computational aspects and shape retrieval performance.