Harmonic Filters in 3D - Theory and Applications

This report proposes a concept for SE(3)-equivariant non-linear filters for multiple purposes, especially in the context of feature and object detection. The idea of the approach is to compute local descriptors as projections onto a local harmonic basis. These descriptors are mapped in a non-linear way onto new local harmonic representations, which then contribute to the filter output in a linear way. This approach may be interpreted as a kind of voting procedure in the spirit of the generalized Hough transform, where the local harmonic representations are interpreted as a voting function. On the other hand, the filter has similarities with classical low-level feature detectors (like corner/blob/line detectors), just extended to the generic feature/object detection problem. The proposed approach fills the gap between low-level feature detectors and high-level object detection systems based on the generalized Hough transform. As an introductory example we use the proposed approach for edge preserving denoising. Secondly, we will apply the proposed filter to a feature detection task on confocal microscopical images of airborne pollen and compare the results to a 3D-extension of a popular GHT-based approach and to a classification per voxel solution.