Multifractal signature estimation for textured image segmentation

Fractal theory provides a powerful mathematical tool for texture segmentation. However, in spite of their increasing popularity, traditional fractal features are intrinsically of less accuracy due to the difference between the idea fractal model and the fractal reality of digital images. In this paper, we incorporated the multifractal analysis method into the idea of fractal signature, and thus proposed a novel type of texture descriptor called multifractal signature, which characterizes the variation of multifractal dimensions over spatial scales. In our approach, the local multifractal dimension of each scale was calculated by using the measurement acquired at two successive scales so that the time-consuming and less accurate least square fit was avoided. Based on three popular multifractal measurements, the differential box-counting (DBC) based multifractal signature, relative DBC based multifractal signature, and morphological multifractal signature were presented in this paper. The performance of the proposed texture descriptors was evaluated for segmentation of texture mosaics by comparing to the corresponding multifractal dimensions. The experimental results demonstrated that multifractal signatures can differentiate textured images more effectively and provide more robust segmentations.