FAS-UNet: A Novel FAS-Driven UNet to Learn Variational Image Segmentation

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tuned model parameters. The deep learning methods based on the UNet structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires many parameters and training data, which are not always available for practical problems. In this paper, inspired by the traditional multiphase convexity Mumford–Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (FAS-UNet), which exploits the model and algorithm priors to extract the multiscale 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 multiscale features. Secondly, we further design a convolutional 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 the 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.