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
this https URL

本文描述了一种基于非参数共享的仿射群等变神经网络，用于三维医学图像分割，并基于自适应 Monte Carlo 扩充球形傅里叶 - 贝塞尔滤波基的聚合，通过采用非参数策略的效率和灵活性，首次实现了对体积数据进行高效的三维仿射群等变卷积神经网络的实现，引入的球形贝塞尔傅里叶滤波基结合了角度和半径直交性以实现更好的特征提取，在 BTCV 和 NIH 胰腺数据集上进行的三维图像分割实验表明，所提出的方法在训练稳定性和数据效率方面优于最先进的三维神经网络。