2D/3D Rotation-Invariant Detection using Equivariant Filters and Kernel Weighted Mapping

Abstract: 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.