Exploring local rotation invariance in 3D CNNs with steerable filters

Abstract

Locally Rotation Invariant (LRI) image analysis was shown to be fundamental in many\napplications and in particular in medical imaging where local structures of tissues occur\nat arbitrary rotations. LRI constituted the cornerstone of several breakthroughs in texture\nanalysis, including Local Binary Patterns (LBP), Maximum Response 8 (MR8) and\nsteerable lterbanks. Whereas globally rotation invariant Convolutional Neural Networks\n(CNN) were recently proposed, LRI was very little investigated in the context of deep learning.\nWe use trainable 3D steerable lters in CNNs in order to obtain LRI with directional\nsensitivity, i.e. non-isotropic. Pooling across orientation channels after the rst convolution\nlayer releases the constraint on nite rotation groups as assumed in several recent works.\nSteerable lters are used to achieve a ne and ecient sampling of 3D rotations. We only\nconvolve the input volume with a set of Spherical Harmonics (SHs) modulated by trainable\nradial supports and directly steer the responses, resulting in a drastic reduction of trainable\nparameters and of convolution operations, as well as avoiding approximations due to\ninterpolation of rotated kernels. The proposed method is evaluated and compared to standard\nCNNs on 3D texture datasets including synthetic volumes with rotated patterns and\npulmonary nodule classication in CT. The results show the importance of LRI in CNNs\nand the need for a ne rotation sampling.