Image Segmentation Using Multiresolution Wavelet Analysis and Expectation-Maximization (EM) Algorithm for Digital Mammography

This article presents a novel algorithm for image segmentation via the use of the multiresolution wavelet analysis and the expectation maximization (EM) algorithm. The development of a multiresolution wavelet feature extraction scheme is based on the Gaussian Markov random field (GMRF) assumption in mammographic image modeling. Mammographic images are hierarchically decomposed into different resolutions. In general, larger breast lesions are characterized by coarser resolutions, whereas higher resolutions show finer and more detailed anatomical structures. These hierarchical variations in the anatomical features displayed by multiresolution decomposition are further quantified through the application of the Gaussian Markov random field. Because of its uniqueness in locality, adaptive features based on the nonstationary assumption of GMRF are defined for each pixel of the mammogram. Fibroadenomas are then segmented via the fuzzy C-means algorithm using these localized features. Subsequently, the segmentation results are further enhanced via the introduction of a maximum a posteriori (MAP) segmentation estimation scheme based on the Bayesian learning paradigm. Gibbs priors or Gibbs random fields have also been incorporated into the learning scheme of the present research with very effective outcomes. In this article, the EM algorithm for MAP estimation is formulated. The EM algorithm provides an iterative and computationally simple algorithm based on the incomplete data concept.