Bregman Divergence Applied To Hierarchical Segmentation Problems

Image segmentation is one of the first steps in any process concerning digital image analysis and its accuracy will go on to determine the quality of this analysis. A classic model used in image segmentation is the Mumford-Shah functional, which includes both the information to pertaining the region and the length of its borders. In this work, by using the concept of loss in Bregman Information a functional is defined which is a generalization of the Mumford-Shah functional, once it is obtained from the proposed function by means of the Squared Euclidean distance as a measure of similarity. The algorithm is constructed by using a fusion criterion, which minimizes the loss in Bregman Information. It is shown that the proposed hierarchical segmentation method generalizes the algorithm which minimizes the piecewise constant Mumford-Shah functional. The results obtained through use of the Generalized I-Divergence, Itakura-Saito and Squared Euclidean distance, show that the algorithm attained a good performance.