Convex Histogram-Based Joint Image Segmentation with Regularized Optimal Transport Cost

We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match statistical distributions of features. In practice, global multidimensional histograms are estimated from the segmented image regions, and are compared to referring models that are either fixed histograms given a priori, or directly inferred in the non-supervised case. The different convex problems studied are solved efficiently using primal-dual algorithms. The proposed approach is generic and enables multi-phase segmentation as well as co-segmentation of multiple images.