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000283020 0247_ $$2doi$$a10.1016/j.inffus.2025.103823
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000283020 1001_ $$00000-0001-5150-3781$$aZhao, Wenzhao$$b0
000283020 245__ $$aEfficient 3D affinely equivariant CNNs with adaptive fusion of augmented spherical Fourier–Bessel bases
000283020 260__ $$aAmsterdam [u.a.]$$bElsevier Science$$c2026
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000283020 500__ $$aThe code is available at https://github.com/ZhaoWenzhao/WMCSFB.
000283020 520__ $$aFilter-decomposition-based group equivariant convolutional neural networks (CNNs) have shown promising stability and data efficiency for 3D image feature extraction. However, these networks, which rely on parameter sharing and discrete transformation groups, often underperform in modern deep neural network architectures for processing volumetric images with dense 3D textures, such as the common 3D medical images. To address these limitations, this paper presents an efficient non-parameter-sharing continuous 3D affine group equivariant neural network for volumetric images. This network uses an adaptive aggregation of Monte Carlo augmented spherical Fourier–Bessel filter bases to improve the efficiency and flexibility of 3D group equivariant CNNs for volumetric data. Unlike existing methods that focus only on angular orthogonality in filter bases, the introduced spherical Bessel Fourier filter base incorporates both angular and radial orthogonality to improve feature extraction. Experiments on four medical image segmentation datasets and two seismic datasets show that the proposed methods achieve better affine group equivariance and superior segmentation accuracy than existing 3D group equivariant convolutional neural network layers, significantly improving the training stability and data efficiency of conventional CNN layers (at 0.05 significance level). 
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000283020 7001_ $$aAlbert, Steffen$$b1
000283020 7001_ $$0P:(DE-2719)9003380$$aWichtmann, Barbara D.$$b2$$udzne
000283020 7001_ $$0P:(DE-2719)2810830$$aSchmitt, Angelika$$b3$$udzne
000283020 7001_ $$aAttenberger, Ulrike$$b4
000283020 7001_ $$aZöllner, Frank G.$$b5
000283020 7001_ $$aHesser, Jürgen$$b6
000283020 773__ $$0PERI:(DE-600)2025632-2$$a10.1016/j.inffus.2025.103823$$gVol. 127, p. 103823 -$$p103823$$tInformation fusion$$v127$$x1566-2535$$y2026
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