On the Benefits of SO(3)-Equivariant Neural Networks for Spherical Image Processing
Résumé
This paper deals with the use of SO(3)-Equivariant Neural Networks for processing spherical images such as those acquired with bi-directional fish-eye lenses. By using Generative Adversarial Networks trained on the Planesnet dataset to generate augmented training sets, we first confirm recent results according to which the use of SO(3)-equivariance mechanisms is more efficient than training data augmentation techniques for processing data with a native spherical geometry. We then explain how the action of SO(3) on the 2d-sphere can be projected on tangent planes, leading to an equivalent reformulation of the SO(3)-convolution operator in euclidean spaces and allowing to achieve a wider range of robustness properties through the design of appropriate local pooling mechanisms. Finally, we articulate our projected SO(3) convolution with recent works on fish-eye image processing in which SU(1, 1) and SL(2, R) Equivariant Neural Networks are coupled with hyperbolic projection mechanisms, drawing the path toward a consolidated approach for processing inputs represented as signals on homogeneous spaces.
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