Abstract
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.
C.A.Z. Barcelos—The authors gratefully acknowledge the financial support of CNPQ (National Council for Scientific and Technological Development, Brazil) (Grants \(\sharp 207513/2014-7\), \(\sharp 305812/2013-0\), \(\sharp 475819/2012- 8\)).
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Ferreira, D.P.L., Backes, A.R., Barcelos, C.A.Z. (2015). Bregman Divergence Applied to Hierarchical Segmentation Problems. In: Pardo, A., Kittler, J. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2015. Lecture Notes in Computer Science(), vol 9423. Springer, Cham. https://doi.org/10.1007/978-3-319-25751-8_59
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DOI: https://doi.org/10.1007/978-3-319-25751-8_59
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