Shape Analysis of Breast Masses in Mammograms via the Fractal Dimension

Masses due to benign breast diseases and tumors due to breast cancer present significantly different shapes on mammograms. In general, malignant tumors appear with rough and complex boundaries or contours, whereas benign masses present smooth, round, or oval contours. Fractal analysis may be used to derive shape features to perform pattern classification of breast masses and tumors. Several procedures have been proposed to compute the fractal dimension of various types of objects or regions of interest in biomedical images, among which the box-counting and ruler methods are popular. In this study, we applied the two methods mentioned above to compute the fractal dimension of both the two-dimensional (2D) contours of breast masses and tumors, as well as their one-dimensional (1D) signatures. A comparative analysis was performed to assess the performance of the two methods of computing the fractal dimension and the two methods of representing the boundaries of masses. It was observed that analysis of the 2D contour representation with the ruler method resulted in the highest classification accuracy of up to 0.946, as indicated by the area under the receiver operating characteristics (ROC) curve. The results indicate that the fractal dimension can serve as a good shape feature for the benign-versus-malignant classification of breast masses in mammograms.