FILTRA: Rethinking Steerable CNN by Filter Transform

TL;DR

This paper bridges the gap between filter transform techniques and group representation theory in steerable CNNs, offering a new, simple implementation method validated through experiments on multiple datasets.

Contribution

It demonstrates that filter transform can be interpreted within group representation theory, unifying theoretical understanding and providing a novel implementation approach.

Findings

Filter transform aligns with group representation theory.

The proposed method improves steerable CNN implementation.

Experimental results confirm the approach's feasibility.

Abstract

Steerable CNN imposes the prior knowledge of transformation invariance or equivariance in the network architecture to enhance the the network robustness on geometry transformation of data and reduce overfitting. It has been an intuitive and widely used technique to construct a steerable filter by augmenting a filter with its transformed copies in the past decades, which is named as filter transform in this paper. Recently, the problem of steerable CNN has been studied from aspect of group representation theory, which reveals the function space structure of a steerable kernel function. However, it is not yet clear on how this theory is related to the filter transform technique. In this paper, we show that kernel constructed by filter transform can also be interpreted in the group representation theory. This interpretation help complete the puzzle of steerable CNN theory and provides a novel and simple approach to implement steerable convolution operators. Experiments are executed on multiple datasets to verify the feasibility of the proposed approach.