Résumé
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 lterbanks. 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 lters in CNNs in order to obtain LRI with directional
sensitivity, i.e. non-isotropic. Pooling across orientation channels after the rst convolution
layer releases the constraint on nite rotation groups as assumed in several recent works.
Steerable lters are used to achieve a ne and ecient 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 classication in CT. The results show the importance of LRI in CNNs
and the need for a ne rotation sampling.