Divergências de Bregman e total Bregman aplicadas na análise de imagens

Abstract

The Bregman and Total Bregman divergences are useful for determining the similarity of complex data and have been used in various applications. Fundamental algorithms and data structures have been generalizes offering thus meta-algorithms that can be applied using any Bregman divergences. Considering the relevance of generalizations methods using Bregman and Total Bregman divergences, since they are not metric dissimilarity measures, it is proposed in this work, new methods of image analysis deĄned for these class of Bregman divergence measures. In this perspective, we have developed new functional energy that enables the generalization of the hierarchical segmentation method based on functional Mumford Shah and the generalization of the variational method used in image registration. Conditions and treatments suitable to support similarity search defined by these divergences were established. Both the functional and the treatments were employed in the analysis of real and synthetic images. The results demonstrate the viability of implementing the defined functionals and show that the treatments, considering the characteristics and diferences of application domains, provide optimization of the methods used in image analysis.