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 https://github.com/zhuhui100/FASUNet.

本文提出了一种新颖的基于变分模型的网络（称为 FAS-Unet），它利用了模型和算法先验知识来提取多尺度特征，为医学图像分割任务的应用提供了一种简单且有效的方法。