Volume preserving image segmentation with entropy regularized optimal transport and its applications in deep learning

Image segmentation with a volume constraint is an important prior for many real applications. In this work, we present a novel volume preserving image segmentation algorithm, which is based on the entropy and Total Variation (TV) regularized optimal transport theory. The volume and classification constraints can be regarded as two measures preserving constraints in the optimal transport. By studying the dual problem, we develop a simple but efficient dual algorithm for our model. Moreover, to be different from many variational based image segmentation algorithms, the proposed algorithm can be directly unrolled to a new Volume Preserving and TV regularized softmax (VPTV-softmax) layer for semantic segmentation in the popular Deep Convolution Neural Network (DCNN). The experiment results show that our proposed model is very competitive and can improve the performance of many semantic segmentation networks such as the popular U-net and DeepLabv3+.