In many vision problems, rotation-invariant analysis is necessary or preferred. Popular solutions are mainly based on pose normalization or brute-force learning, neglecting the intrinsic properties of rotations. In this paper, we present a rotation invariant detection approach built on the equivariant filter framework, with a new model for learning the filtering behavior. The special properties of the harmonic basis, which is related to the irreducible representation of the rotation group, directly guarantees rotation invariance of the whole approach. The proposed kernel weighted mapping ensures high learning capability while respecting the invariance constraint. We demonstrate its performance on 2D object detection with in-plane rotations, and a 3D application on rotation-invariant landmark detection in microscopic volumetric data.

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.