Comparison of Specific Fractal and Multifractal Parameters for Certain Regions of Interest from Digital Mammograms

Abstract

Fractal analysis of grey-scale digital image is a recognized tool for detection of irregularities in the image and as measure of complexity of the image. Basic idea of this paper is to explore relation of fractal dimensions and some other related parameters in the chosen regions of interest (ROI) of grey-scale digital medical image with corresponding specific tissue characteristics. If difference of the values for calculated parameters is proven to be statistically significant for ROI of mammograms with different specific characteristics, this kind of analysis can be helpful for computer aided diagnostics. Especially, possibility of automatic detection of microcalcifications is considered. Analysis of mammograms in this manner is not a simple task, as there are four different types of parenchym tissue, there are five grades for microcalcifications according to their malignity (BI-RADS), and there are several different types of microcalcifications. Results of fractal and multifractal analysis of 131 ROIs (150 × 150 pixels) from 60 different mammograms are presented in this paper. Out of total 131, 60 ROIs encloses normal tissue (without dense masses or microcalcifications), and remaining 71 ROIs encloses tissue with microcalcifications. Out of total 60 mammograms concerning parenchym tissue type, 17 mammograms is for ACR 1 structure, 21 ACR 2, i 22 ACR 3 structure. Fractal parameter that is considered is Hurst coefficient, and it is considered how it changes with size of ROI. ${\text{H}}{\ddot{{\text{o}}}}{\text{lder}}$ exponent and multifractal spectra for each ROI is calculated, and corresponding histograms are analyzed. Values of suitable parameters from these histograms are tabulated to check their statistical dependance on ACR and BI-RADS grades. Zero hypothesis that there is no difference between normal ROI and ROI with microcalcifications is tested.