3D Rotation-Invariant Description from Tensor Operation on Spherical HOG Field

Rotation-invariant descriptions are required in many 3D volumetric image analysis tasks. The histogram-of-oriented-gradient (HOG) is widely used in 2D images and proves to be a very robust local description. This paper concentrates on how to use the HOG feature in 3D volumetric images when rotation-invariance is concerned. This is challenging because of the complexity of 3D rotations. We present a decent solution based on the spherical harmonics theory which is an effective tool for analysing 3D rotations, together with the spherical tensor operations which explore high order tensor information in spherical coordinates. The design is quite general and could be used for different applications. It achieves high scores on Princeton Shape Benchmark and SHREC 2009 Generic Shape Benchmark, and also produces promising results when applying on biological microscopy images.