Barbara D. Wichtmann

Wenzhao Zhao, Steffen Albert, Barbara D. Wichtmann et al.

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, 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 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.

Wenzhao Zhao, Barbara D. Wichtmann, Steffen Albert et al.

Group-equivariant convolutional neural networks (G-CNN) heavily rely on parameter sharing to increase CNN's data efficiency and performance. However, the parameter-sharing strategy greatly increases the computational burden for each added parameter, which hampers its application to deep neural network models. In this paper, we address these problems by proposing a non-parameter-sharing approach for group equivariant neural networks. The proposed methods adaptively aggregate a diverse range of filters by a weighted sum of stochastically augmented decomposed filters. We give theoretical proof about how the group equivariance can be achieved by our methods. Our method applies to both continuous and discrete groups, where the augmentation is implemented using Monte Carlo sampling and bootstrap resampling, respectively. Our methods also serve as an efficient extension of standard CNN. The experiments show that our method outperforms parameter-sharing group equivariant networks and enhances the performance of standard CNNs in image classification and denoising tasks, by using suitable filter bases to build efficient lightweight networks. The code will be available at https://github.com/ZhaoWenzhao/MCG_CNN.

Alexander Herold, Daniel Sobotka, Lucian Beer et al.

Background: We aimed to quantify hepatic vessel volumes across chronic liver disease stages and healthy controls using deep learning-based magnetic resonance imaging (MRI) analysis, and assess correlations with biomarkers for liver (dys)function and fibrosis/portal hypertension. Methods: We assessed retrospectively healthy controls, non-advanced and advanced chronic liver disease (ACLD) patients using a 3D U-Net model for hepatic vessel segmentation on portal venous phase gadoxetic acid-enhanced 3-T MRI. Total (TVVR), hepatic (HVVR), and intrahepatic portal vein-to-volume ratios (PVVR) were compared between groups and correlated with: albumin-bilirubin (ALBI) and model for end-stage liver disease-sodium (MELD-Na) score, and fibrosis/portal hypertension (Fibrosis-4 [FIB-4] score, liver stiffness measurement [LSM], hepatic venous pressure gradient [HVPG], platelet count [PLT], and spleen volume). Results: We included 197 subjects, aged 54.9 $\pm$ 13.8 years (mean $\pm$ standard deviation), 111 males (56.3\%): 35 healthy controls, 44 non-ACLD, and 118 ACLD patients. TVVR and HVVR were highest in controls (3.9; 2.1), intermediate in non-ACLD (2.8; 1.7), and lowest in ACLD patients (2.3; 1.0) ($p \leq 0.001$). PVVR was reduced in both non-ACLD and ACLD patients (both 1.2) compared to controls (1.7) ($p \leq 0.001$), but showed no difference between CLD groups ($p = 0.999$). HVVR significantly correlated indirectly with FIB-4, ALBI, MELD-Na, LSM, and spleen volume ($ρ$ ranging from -0.27 to -0.40), and directly with PLT ($ρ= 0.36$). TVVR and PVVR showed similar but weaker correlations. Conclusions: Deep learning-based hepatic vessel volumetry demonstrated differences between healthy liver and chronic liver disease stages and shows correlations with established markers of disease severity.