FILTRA: Rethinking Steerable CNN by Filter Transform
This work offers a theoretical bridge for researchers in computer vision and machine learning, but it is incremental as it clarifies existing methods rather than introducing new paradigms.
The paper connects the filter transform technique for steerable CNNs with group representation theory, providing a theoretical interpretation and a simple implementation method for steerable convolution operators, validated through experiments on multiple datasets.
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.