Fractal Modeling and Segmentation for the Enhancement of Microcalcifications in Digital Mammograms

Abstract

The objective of this research is to model the mammographic parenchymal, ductal patterns and enhance the microcalcifications using deterministic fractal approach. According to the theory of deterministic fractal geometry, images can be modeled by deterministic fractal objects which are attractors of sets of two dimensional affine transformations. The Iterated Functions Systems and the Collage Theorem are the mathematical foundations of fractal image modeling. In this paper, a methodology based on fractal image modeling is developed to analyze and extract various mammographic textures. We show that general mammographic parenchymal and ductal patterns can be well modeled by a set of parameters of affine transformations. Therefore, microcalcifications can be enhanced by taking the difference between the original image and the modeled image. Our results are compared with those of the partial wavelet reconstruction and morphological operation approaches. The results demonstrate that the fractal modeling method is an effective way to enhance microcalcifications, and thereby facilitate the radiologists' diagnosis. It may also be able to improve detection and classification of microcalcifications in a computer system.