Image segmentation using multiresolution wavelet analysis and expectation-maximization (EM) algorithm for digital mammography

This article presents a novel algorithm for image segbeen developed for classification purposes. In addition, many mentation via the use of the multiresolution wavelet analysis and the authors have discovered significant advantages in the use of the expectation maximization (EM) algorithm. The development of a multiresolution concept [4,5] . Brazkovic and Neskovic presented multiresolution wavelet feature extraction scheme is based on the the Gaussian pyramid and fuzzy linking method for the adaptive Gaussian Markov random field (GMRF) assumption in mammodetection of cancerous changes in mammograms [6]. graphic image modeling. Mammographic images are hierarchically Recently, as a result of cross-fertilization of innovative ideas decomposed into different resolutions. In general, larger breast lefrom image processing, spatial statistics, and statistical physics, sions are characterized by coarser resolutions, whereas higher resolua significant amount of research activity on image modeling and tions show finer and more detailed anatomical structures. These hierarchical variations in the anatomical features displayed by multiresolusegmentation has also been concentrated on the two-dimensional tion decomposition are further quantified through the application of (2D) Markov random field (MRF). Although many of the potenthe Gaussian Markov random field. Because of its uniqueness in localtials of MRF had been envisioned by the early works of Levy ity, adaptive features based on the nonstationary assumption of [7] , McCormick and Jayaramamrhy [8], and Abend et al. [9] , GMRF are defined for each pixel of the mammogram. Fibroadenomas exploitation of the powers of the MRF was not possible until are then segmented via the fuzzy C-means algorithm using these significant recent advances occurred in the appropriate mathematlocalized features. Subsequently, the segmentation results are further ical and computational tools. Chellappa and Kashyap [10] sucenhanced via the introduction of a maximum a posteriori (MAP) segcessfully applied the noncausal autoregressive (NCAR) model mentation estimation scheme based on the Bayesian learning paraor the Gaussian Markov random field (GMRF) to the characterdigm. Gibbs priors or Gibbs random fields have also been incorporated into the learning scheme of the present research with very effecization of real-world textural images. Woods [11] introduced 2D tive outcomes. In this article, the EM algorithm for MAP estimation is discrete Markovian fields with applications to spectral estimation. formulated. The EM algorithm provides an iterative and computationAs a result of the MRF and Gibbs distribution (GD) equivalence ally simple algorithm based on the incomplete data concept. q 1997 [12,13], Cross and Jain [14], Geman and Geman [15], and Derin John Wiley & Sons, Inc. Int J Imaging Syst Technol, 8, 491–504, 1997 and Elliott [16] also demonstrated substantial successes in image segmentation and restoration.