Exploring local rotation invariance in 3D CNNs with steerable filters

Vincent Andrearczyk, Julien Fageot, Valentin Oreiller, Xavier Montet, Adrien Depeursinge

Keywords: Local rotation invariance, convolutional neural network, steerable filters, 3D texture

Abstract: Locally Rotation Invariant (LRI) image analysis was shown to be fundamental in many applications and in particular in medical imaging where local structures of tissues occur at arbitrary rotations. LRI constituted the cornerstone of several breakthroughs in texture analysis, including Local Binary Patterns (LBP), Maximum Response 8 (MR8) and steerable filterbanks. Whereas globally rotation invariant Convolutional Neural Networks (CNN) were recently proposed, LRI was very little investigated in the context of deep learning. We use trainable 3D steerable filters in CNNs in order to obtain LRI with directional sensitivity, i.e. non-isotropic filters. Pooling across orientation channels after the first convolution layer releases the constraint on finite rotation groups as assumed in several recent works. Steerable filters are used to achieve a fine and efficient sampling of 3D rotations. We only convolve the input volume with a set of Spherical Harmonics (SHs) modulated by trainable radial supports and directly steer the responses, resulting in a drastic reduction of trainable parameters and of convolution operations, as well as avoiding approximations due to interpolation of rotated kernels. The proposed method is evaluated and compared to standard CNNs on 3D texture datasets including synthetic volumes with rotated patterns and pulmonary nodule classification in CT. The results show the importance of LRI in CNNs and the need for a fine rotation sampling.

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