Spherical Wavelet Descriptors for Content-Based 3D Model Retrieval

• Main Authors: Hamid Laga, Hiroki Takahashi, Masayuki Nakajima
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 2006
• Subjects: shape matching; spherical; North Pole; Sion
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.459.6347; http://chihara.naist.jp/people/RESEARCHER/hamid/publications.files/smi2006/hamid_smi2006.pdf

The description of 3D shapes with features that possess descriptive power and invariant under similarity transfor-mations is one of the most challenging issues in content based 3D model retrieval. Spherical harmonics-based de-scriptors have been proposed for obtaining rotation invari-ant representations. However, spherical harmonic analysis is based on latitude-longitude parameterization of a sphere which has singularities at each pole. Consequently, fea-tures near the two poles are over represented while fea-tures 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) theL1 and, (3) the L2 energies of the spher-ical wavelet sub-bands. The advantage of this tool is three fold; First, it takes into account feature localization and lo-cal orientations. Second, the energies of the wavelet trans-form are rotation invariant. Third, shape features are uni-formly represented which makes the descriptors more ef-ficient. Spherical wavelet descriptors are natural exten-sion of 3D Zernike moments and spherical harmonics. We evaluate, on the Princeton Shape Benchmark, the proposed descriptors regarding computational aspects and shape re-trieval performance.