Weighted Monte Carlo augmented spherical Fourier-Bessel convolutional layers for 3D abdominal organ segmentation

Filter-decomposition-based group equivariant convolutional neural networks show promising stability and data efficiency for 3D image feature extraction. However, the existing filter-decomposition-based 3D group equivariant neural networks rely on parameter-sharing designs and are mostly limited to rotation transform groups, where the chosen spherical harmonic filter bases consider only angular orthogonality. These limitations hamper its application to deep neural network architectures for medical image segmentation. To address these issues, this paper describes a non-parameter-sharing affine group equivariant neural network for 3D medical image segmentation based on an adaptive aggregation of Monte Carlo augmented spherical Fourier Bessel filter bases. The efficiency and flexibility of the adopted non-parameter strategy enable for the first time an efficient implementation of 3D affine group equivariant convolutional neural networks for volumetric data. The introduced spherical Bessel Fourier filter basis combines both angular and radial orthogonality for better feature extraction. The 3D image segmentation experiments on two abdominal image sets, BTCV and the NIH Pancreas datasets, show that the proposed methods excel the state-of-the-art 3D neural networks with high training stability and data efficiency. The code will be available at https://github.com/ZhaoWenzhao/WVMS.