A Variational Neural Network for Image Segmentation Based on Chan-Vese Model

The Chan-Vese model for image segmentation is a fundamental region-based model under variational level set framework with a lot of variants for different tasks. Although its solution schemes have been investigated systematically, the segmentation results depend heavily on hand crafted models and algorithms, especially annoying parameter tuning. The computational efficiency is a challenging problem also. Modern deep learning methods based on neural networks are excellent alternatives to deal with these problems, but there are also problems such as un-explanation, discontinuous boundaries, and noise sensitivity. In this paper, we propose a novel deep neural network framework for image segmentation based on algorithm unfolding of Chan-Vese model to inherit the merits of variational models and neural networks without their demerits. Firstly, the original Chan-Vese model is reformulated using a data term of multichannel images and a boundary length term via fields of experts. Secondly, the algorithms are designed based on the splitting method and alternating direction optimization to decompose the original minimization problem into some sub-optimization problems which can be solved iteratively or analytically. Finally, a supervised Chan-Vese network (CVN) is designed based on the corresponding relations of iterative algorithms and network layers, in which the convolutional kernels are designed based on convex combinations of discrete cosine transformation basis, activation functions are parametric soft thresholding formulas. Experiments based on ground truth datasets demonstrate the properties of CVN visually and the advantages of CVN over Chan-Vese model and other existing semantic segmentation networks.