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Nonlinear indicators of malignancy

This paper investigates the use of fractional dimension analysis and nonlinear filters for quantifying the degree of lesion diffusion in mammograms. The fractal method involves computing the fractal dimension over the entire lesion. Based on the observation that malignant lesions usually exhibit rougher intensity profiles and often have more toruous boundaries than benign lesions, the fractal dimension, which is a popular means of quantifying the degree of image/surface roughness, is proposed as a natural tool to assist in the diagnosis of malignancy. In this work, the fractal dimension of the image intensity surface is estimated using the fractional Brownian motion model. The nonlinear analysis was performed on horizontal and vertical lines (one-dimensional data) through the area of interest. These scan lines were also processed by a nonlinear (maximum) transformation as a means of reducing the dimensionality of the data, to aid in clarifying the degree of diffusion present in the data. For benign lesions little diffusion will be present, whereas malignant lesions generally display a higher degree of diffusion. Results of these techniques are applied on several malignant and benign lesions are presented, using mammogram X-rays digitized to a 512 X 512 pixel resolution and 8-bits of gray-scale resolution.