# FAS-UNet: A Novel FAS-driven Unet to Learn Variational Image Segmentation

arXiv: https://arxiv.org/abs/2210.15164 · HTML: https://mlsanity.com/paper/2210.15164/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 56 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [UNet++: Redesigning Skip Connections to Exploit Multiscale Features in Image Segmentation](https://mlsanity.com/paper/1912.05074/) (2019)
- [CHAOS Challenge -- Combined (CT-MR) Healthy Abdominal Organ Segmentation](https://mlsanity.com/paper/2001.06535/) (2020)
- [CE-Net: Context Encoder Network for 2D Medical Image Segmentation](https://mlsanity.com/paper/1903.02740/) (2019)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [LinkNet: Exploiting Encoder Representations for Efficient Semantic Segmentation](https://mlsanity.com/paper/1707.03718/) (2017)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Deep learning for cardiac image segmentation: A review](https://mlsanity.com/paper/1911.03723/) (2019)
- [Deep Learning in Medical Image Registration: A Review](https://mlsanity.com/paper/1912.12318/) (2019)
- [CA-Net: Comprehensive Attention Convolutional Neural Networks for Explainable Medical Image Segmentation](https://mlsanity.com/paper/2009.10549/) (2020)
- [AnatomyNet: Deep Learning for Fast and Fully Automated Whole-volume Segmentation of Head and Neck Anatomy](https://mlsanity.com/paper/1808.05238/) (2018)
- [KiU-Net: Towards Accurate Segmentation of Biomedical Images using Over-complete Representations](https://mlsanity.com/paper/2006.04878/) (2020)
- [Y-Net: Joint Segmentation and Classification for Diagnosis of Breast Biopsy Images](https://mlsanity.com/paper/1806.01313/) (2018)
- [MgNet: A Unified Framework of Multigrid and Convolutional Neural Network](https://mlsanity.com/paper/1901.10415/) (2019)
- [PolyNet: A Pursuit of Structural Diversity in Very Deep Networks](https://mlsanity.com/paper/1611.05725/) (2016)
- [3D Dilated Multi-Fiber Network for Real-time Brain Tumor Segmentation in MRI](https://mlsanity.com/paper/1904.03355/) (2019)
- [Learning Topological Interactions for Multi-Class Medical Image Segmentation](https://mlsanity.com/paper/2207.09654/) (2022)
- [Medical Image Registration Using Deep Neural Networks: A Comprehensive Review](https://mlsanity.com/paper/2002.03401/) (2020)
- [Connections between Numerical Algorithms for PDEs and Neural Networks](https://mlsanity.com/paper/2107.14742/) (2021)
- [RSANet: Recurrent Slice-wise Attention Network for Multiple Sclerosis Lesion Segmentation](https://mlsanity.com/paper/2002.12470/) (2020)
- [RatLesNetv2: A Fully Convolutional Network for Rodent Brain Lesion Segmentation](https://mlsanity.com/paper/2001.09138/) (2020)

## Built on by (most cited first, 2 of 2)

- [PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval](https://mlsanity.com/paper/2309.04171/) (2023)
- [A Multi-scale Generalized Shrinkage Threshold Network for Image Blind Deblurring in Remote Sensing](https://mlsanity.com/paper/2309.07524/) (2023)

## Abstract (arXiv)

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (denoted as FAS-Unet) that exploits the model and algorithm priors to extract the multi-scale features. The proposed model-informed network integrates image data and mathematical models, and implements them through learning a few convolution kernels. Based on the variational theory and FAS algorithm, we first design a feature extraction sub-network (FAS-Solution module) to solve the model-driven nonlinear systems, where a skip-connection is employed to fuse the multi-scale features. Secondly, we further design a convolution block to fuse the extracted features from the previous stage, resulting in the final segmentation possibility. Experimental results on three different medical image segmentation tasks show that the proposed FAS-Unet is very competitive with other state-of-the-art methods in qualitative, quantitative and model complexity evaluations. Moreover, it may also be possible to train specialized network architectures that automatically satisfy some of the mathematical and physical laws in other image problems for better accuracy, faster training and improved generalization.The code is available at urlhttps://github.com/zhuhui100/FASUNet.