Solid Spherical Energy (SSE) CNNs for Efficient 3D Medical Image Analysis

Invariance to local rotation, to differentiate from the global rotation of images and objects, is required in various texture analysis problems. It has led to several breakthrough methods such as local binary patterns, maximum response and steerable filterbanks. In particular, textures in medical images often exhibit local structures at arbitrary orientations. Locally Rotation Invariant (LRI) Convolutional Neural Networks (CNN) were recently proposed using 3D steerable filters to combine LRI with Directional Sensitivity (DS). The steerability avoids the expensive cost of convolutions with rotated kernels and comes with a parametric representation that results in a drastic reduction of the number of trainable parameters. Yet, the potential bottleneck (memory and computation) of this approach lies in the necessity to recombine responses for a set of predefined discretized orientations. In this paper, we propose to calculate invariants from the responses to the set of spherical harmonics projected onto 3D kernels in the form of a lightweight Solid Spherical Energy (SSE) CNN. It offers a compromise between the high kernel specificity of the LRI-CNN and a low memory/operations requirement. The computational gain is evaluated on 3D synthetic and pulmonary nodule classification experiments. The performance of the proposed approach is compared with steerable LRI-CNNs and standard 3D CNNs, showing competitive results with the state of the art.