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Multifractal analysis is becoming more and more popular in image segmentation community, in which the box-counting based multifractal dimension estimations are most commonly used. However, in spite of its computational efficiency, the regular partition scheme used by various box-counting methods intrinsically produces less accurate results. In this paper, a novel multifractal estimation algorithm based on mathematical morphology is proposed and a set of new multifractal descriptors, namely the local morphological multifractal exponents is defined to characterize the local scaling properties of textures. A series of cubic structure elements and an iterative dilation scheme are utilized so that the computational complexity of the morphological operations can be tremendously reduced. Both the proposed algorithm and the box-counting based methods have been applied to the segmentation of texture mosaics and real images. The comparison results demonstrate that the morphological multifractal estimation can differentiate texture images more effectively and provide more robust segmentations.
Date of Publication: March 2006