A modification of the mumford-shah functional for segmentation of digital images with fractal objects

Authors:
Carlos Guillén Galván;Daniel Valdés Amaro;Jesus Uriarte Adrián
Affiliations:
Facultad de Ciencias de la Computación, Benemérita Universidad Autónoma de Puebla, Puebla, México;Facultad de Ciencias de la Computación, Benemérita Universidad Autónoma de Puebla, Puebla, México;Facultad de Ciencias de la Computación, Benemérita Universidad Autónoma de Puebla, Puebla, México
Venue:
MICAI'11 Proceedings of the 10th international conference on Artificial Intelligence: advances in Soft Computing - Volume Part II
Year:
2011

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Abstract

In this paper we revisit the Mumford-Shah functional, one of the most studied variational approaches to image segmentation. The contribution of this work is to propose a modification of the Mumford-Shah functional that includes Fractal Analysis to improve the segmentation of images with fractal or semi-fractal objects. Here we show how the fractal dimension is calculated and embedded in the functional minimization computation to drive the algorithm to use both, changes in the image intensities and the fractal characteristics of the objects, to obtain a more suitable segmentation. Experimental results confirm that the proposed modification improves the quality of the segmentation in images with fractal objects or semi fractal such as medical images.