Statistical Segmentation of Mammograms

In the past several years there has been tremendous interest in image processing and analysis techniques in mammography. One common approach for detecting abnormalities in mammograms [1, 2] is to use a series of heuristics, e.g. filtering and thresholding, which may include texture analysis to automatically detect abnormalities [3]. These heuristic methods suffer from a lack of robustness when the number of images to be classified is large [4]. Statistical methods have also been developed to address this problem. Brzakovic [5] used fuzzy pyramid linking to identify homogeneous regions in mammograms, and then used a statistical model to classify regions as non-tumor, benign tumor, or malignant tumor. Kegelmeyer [4, 6] extracted a five-dimensional feature vector for each pixel which included edge orientation and the output of four spatial filters. Each feature vector was then classified using a binary decision tree. In this paper we present a new statistical algorithm [7–10] which partitions a mammogram into homogeneous texture regions. Our algorithm assigns each pixel in the mammogram membership to one of a finite number of classes depending upon the statistical properties of the pixel and its neighbors. The individual pixel classifications form a two-dimensional label field which must be estimated from the observed image. Both the mammogram and its label field are modeled as discrete-parameter random fields. We estimate the pixel classes by minimizing the expected value of the number of misclassified pixels, this is known as the “maximizer of the posterior marginals” (MPM) estimate. The expectation-maximization (EM) algorithm is employed to estimate from the observed mammogram the unknown parameters needed for the MPM estimate.