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

arXiv: https://arxiv.org/abs/2402.16825 · HTML: https://mlsanity.com/paper/2402.16825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 30 of 35)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [U-Mamba: Enhancing Long-range Dependency for Biomedical Image Segmentation](https://mlsanity.com/paper/2401.04722/) (2024)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [SegMamba: Long-range Sequential Modeling Mamba For 3D Medical Image Segmentation](https://mlsanity.com/paper/2401.13560/) (2024)
- [MedNeXt: Transformer-driven Scaling of ConvNets for Medical Image Segmentation](https://mlsanity.com/paper/2303.09975/) (2023)
- [DeepOrgan: Multi-level Deep Convolutional Networks for Automated Pancreas Segmentation](https://mlsanity.com/paper/1506.06448/) (2015)
- [UNETR++: Delving into Efficient and Accurate 3D Medical Image Segmentation](https://mlsanity.com/paper/2212.04497/) (2022)
- [Scale-Equivariant Steerable Networks](https://mlsanity.com/paper/1910.11093/) (2019)
- [STU-Net: Scalable and Transferable Medical Image Segmentation Models Empowered by Large-Scale Supervised Pre-training](https://mlsanity.com/paper/2304.06716/) (2023)
- [3D UX-Net: A Large Kernel Volumetric ConvNet Modernizing Hierarchical Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2209.15076/) (2022)
- [Rethinking Semi-Supervised Medical Image Segmentation: A Variance-Reduction Perspective](https://mlsanity.com/paper/2302.01735/) (2023)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [Class-Aware Adversarial Transformers for Medical Image Segmentation](https://mlsanity.com/paper/2201.10737/) (2022)
- [Mine yOur owN Anatomy: Revisiting Medical Image Segmentation with Extremely Limited Labels](https://mlsanity.com/paper/2209.13476/) (2022)
- [Beyond Self-Attention: Deformable Large Kernel Attention for Medical Image Segmentation](https://mlsanity.com/paper/2309.00121/) (2023)
- [A Machine Learning Benchmark for Facies Classification](https://mlsanity.com/paper/1901.07659/) (2019)
- [Bootstrapping Semi-supervised Medical Image Segmentation with Anatomical-aware Contrastive Distillation](https://mlsanity.com/paper/2206.02307/) (2022)
- [DCFNet: Deep Neural Network with Decomposed Convolutional Filters](https://mlsanity.com/paper/1802.04145/) (2018)
- [RIC-CNN: Rotation-Invariant Coordinate Convolutional Neural Network](https://mlsanity.com/paper/2211.11812/) (2022)
- [Scaling-Translation-Equivariant Networks with Decomposed Convolutional Filters](https://mlsanity.com/paper/1909.11193/) (2019)
- [RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks](https://mlsanity.com/paper/1805.06846/) (2018)
- [Scaling Up 3D Kernels with Bayesian Frequency Re-parameterization for Medical Image Segmentation](https://mlsanity.com/paper/2303.05785/) (2023)
- [Implicit Anatomical Rendering for Medical Image Segmentation with Stochastic Experts](https://mlsanity.com/paper/2304.03209/) (2023)
- [Implicit Convolutional Kernels for Steerable CNNs](https://mlsanity.com/paper/2212.06096/) (2022)

## Abstract (arXiv)

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.