Abstract
Models parameterized by Convolutional Neural Networks (CNNs), reportedly, have garnered a commanding position in learning based multidimensional signal processing. This feat is achieved to a large extent through the translation equivariance property of the convolutional filters employed. While popular, the required optimum level of model parameters, the limited availability of signal datasets, robustness of the model to input signal transformations, and generalization to out of distribution signal sets are some of the challenges of CNN models. The incorporation of equivariance or consistency to symmetry transformations in which invariance is a special case, have been suggested to not only alleviate these challenges but also bring about model interpretability. This work presents a systematic survey of the equivariant convolutional filter design for convolutional neural networks in image processing applications with the aim of bringing forth design methods in terms of group theory, discrete Fourier transform, discrete cosine transform, and wavelet transform. The theoretical foundations for translation, rotation, scale and affine equivariance under nonlinear transform, their efficient implementations especially in natural image processing applications has been thoroughly discussed.
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Habte, S.B., Ibenthal, A., Bekele, E.T., Debelee, T.G. (2023). Convolution Filter Equivariance/Invariance in Convolutional Neural Networks: A Survey. In: Girma Debelee, T., Ibenthal, A., Schwenker, F. (eds) Pan-African Conference on Artificial Intelligence. PanAfriCon AI 2022. Communications in Computer and Information Science, vol 1800. Springer, Cham. https://doi.org/10.1007/978-3-031-31327-1_11
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