arXiv 2402.168252026-01-07cs.CV

高效3D仿射等变CNN及其增强球傅里叶-贝塞尔基的自适应融合

Efficient 3D affinely equivariant CNNs with adaptive fusion of augmented spherical Fourier-Bessel bases

School of Computer and Artificial Intelligence, Nanjing University of Finance and Economics（南京金融学院计算机与人工智能学院）；Interdisciplinary Center for Scientific Computing, Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University（科学计算交叉中心、医学智能系统研究所、曼海姆医学院、海德堡大学）；Computer Assisted Clinical Medicine, Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University（临床医学辅助计算机、医学智能系统研究所、曼海姆医学院、海德堡大学）；Department of Diagnostic and Interventional Radiology, University Hospital Bonn（诊断与介入放射科、波恩大学医院）；Interdisciplinary Center for Scientific Computing, Central Institute for Computer Engineering, CSZ Heidelberg Center for Model-Based AI, Data Analysis and Modeling in Medicine, Mannheim Institute for Intelligent Systems in Medicine, Medical Faculty Mannheim, Heidelberg University（科学计算交叉中心、计算机工程中央研究所、海德堡模型驱动AI中心、医学数据与建模中心、曼海姆医学智能系统研究所、曼海姆医学院、海德堡大学）

Wenzhao Zhao, Steffen Albert, Barbara D. Wichtmann, Angelika Maurer, Ulrike Attenberger, Frank G. Zöllner, Jürgen Hesser

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AI总结：

本文提出一种高效3D仿射群等变CNN，通过自适应融合增强球傅里叶-贝塞尔基，提升体积图像的特征提取与分割性能。

摘要：

基于滤波分解的群等变卷积神经网络（CNNs）在3D图像特征提取中表现出有希望的稳定性和数据效率。然而，这些网络依赖于参数共享和离散变换群，往往在处理具有密集3D纹理的体积图像（如常见的3D医学图像）时，在现代深度神经网络架构中表现不佳。为了解决这些局限性，本文提出了一种高效的非参数共享连续3D仿射群等变神经网络，用于体积图像。该网络使用蒙特卡洛增强的球傅里叶-贝塞尔滤波基的自适应聚合，以提高3D群等变CNN在体积数据中的效率和灵活性。与现有方法仅关注滤波基中的角正交性不同，引入的球贝塞尔傅里叶滤波基结合了角正交性和径向正交性，以提高特征提取。在四个医学图像分割数据集和两个地震数据集上的实验表明，所提出的方法在仿射群等变性和分割准确性方面优于现有3D群等变卷积神经网络层，显著提高了传统CNN层的训练稳定性和数据效率（在0.05显著性水平下）。代码可在https://github.com/ZhaoWenzhao/WMCSFB上获取。

英文摘要：

Filter-decomposition-based group equivariant convolutional neural networks (CNNs) have shown promising stability and data efficiency for 3D image feature extraction. However, these networks, which rely on parameter sharing and discrete transformation groups, often underperform in modern deep neural network architectures for processing volumetric images with dense 3D textures, such as the common 3D medical images. To address these limitations, this paper presents an efficient non-parameter-sharing continuous 3D affine group equivariant neural network for volumetric images. This network uses an adaptive aggregation of Monte Carlo augmented spherical Fourier-Bessel filter bases to improve the efficiency and flexibility of 3D group equivariant CNNs for volumetric data. Unlike existing methods that focus only on angular orthogonality in filter bases, the introduced spherical Bessel Fourier filter base incorporates both angular and radial orthogonality to improve feature extraction. Experiments on four medical image segmentation datasets and two seismic datasets show that the proposed methods achieve better affine group equivariance and superior segmentation accuracy than existing 3D group equivariant convolutional neural network layers, significantly improving the training stability and data efficiency of conventional CNN layers (at 0.05 significance level). The code is available at https://github.com/ZhaoWenzhao/WMCSFB.

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