FILTRA: Rethinking Steerable CNN by Filter Transform

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. Filter transform has been an intuitive and widely used technique to construct steerable CNN in the past decades. Recently, group representation theory is used to analyze steerable CNN and 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. Meanwhile, we show that filter transformed kernels can be used to convolve input/output features in different group representation. 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 feasibilty of the proposed approach.