A New 3D Shape Retrieval Method Using Spherical Healpix

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Rapidly spreading 3D shape applications have led to the development of content-based 3D shape retrieval research. In this paper, we propose a new retrieval method using Spherical Healpix. Spherical Healpix is a new framework for efficient discretization and fast analysis or synthesis of functions defined on the sphere. We analyzed the construction process of this structure and defined a new Spherical Healpix Extent Function. We then analyzed this Spherical Healpix Extent Function using an inverse-construction process from the sphere to the Euclidean plane. We transformed the result of inverse-construction to the frequency domain using a 2D Fourier transform, instead of spherical harmonics, a well-known tool in spherical analysis. We obtained the low-frequency component in the frequency domain by using a Butterworth low-pass filter. The power spectrum of the low frequency component can be used as the feature vector to describe a 3D shape. This descriptor is extracted in the canonical coordinate frame; that is, each 3D-model is first normalized. We have examined this method on the Konstanz Shape Benchmark and SHREC data set, and confirmed its efficiency. We also compared this method with other methods on the same Konstanz Shape Benchmark and SHREC data set and evaluated the shape retrieval performance.
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