A 3D Shape Descriptor: 4D Hyperspherical Harmonics "An Exploration into the Fourth Dimension"

B. Bonvallet, N. Griffin, and J. Li (USA)


shape descriptor, hyperspherical harmonics


Shape matching remains a challenging problem. Most search engines on the internet use textual description to match images. More sophisticated systems use shape descriptors that are automatically constructed from the original 3D shape. In this paper, we propose a novel shape descriptor based on four dimensional (4D) hyperspherical harmonics. Shape descriptor using 3D spherical harmonics present the benefits of being insensitive to noise, orientation, scale, and translation. However, the radii cuts introduce a disadvantage of failing to recognize inner rotations. We address this problem by mapping 3D objects onto the 4D unit hypersphere and applying 4D hyperspherical harmonic decomposition to get the shape descriptor. The 4D hyperspherical harmonics have the same advantages of the 3D spherical harmonics and remove the disadvantage of the 3D spherical harmonics that is associated with the inner radii cuts.

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