New Algorithm for Fractal Dimension Estimation based on Texture Measurements: Application on Breast Tissue Characterization

Abstract

Abstract-Fractal analysis is currently in full swing in particular in the medical field because of the fractal nature of natural phenomena (vascular system, nervous system, bones, breast tissue ...). For this, many algorithms for estimating the fractal dimension have emerged. Most of them are based on the principle of box counting. In this work we propose a new method for calculating fractal attributes based on contrast homogeneity and energy that have been extracted from gray level co-occurrence matrix. As application we are investigated in the characterization and classification of mammographic images with SuportVectorMachine classifier. We considered in particular images with tumor masses and architectural disorder to compare with normal ones. We calculate, for comparison the fractal dimension obtained by a reference method (triangular prism) and perform a classification similar to the previous. Results obtained with new algorithm are better than reference method (classification rate is 0.91 vs 0.65). Hence new fractal attributes are relevant.

Construction of Fractals based on Catalan Solids

“…They are intensively used in computer graphics for image compression and processing purposes [1][2][3] and modeling of landscapes [4], in description of atomic nets [5], medicine and genetics [6], structural damage identification tasks [7,8] using various formulations of the fractal dimension, etc. They have also found many practical applications, e.g.…”