Coherence of multiscale features and its applications for enhancement of mammograms

Image signals represent aIl extraordinarily large amount of information. In analyzing and interpreting signals or images, the first step is extracting relevant features from them. Most researchers agree that edges and lines are particularly rich sources of information. Organization of these features could provide the basis for an efficient description of an image (or a signal). Unfortunately, features are often corrupted by noise or filtering (blurring) processes that make them hard to detect. For a two-dimensional image, we have more information that does not exist in the one-dimensional cases--orientation. The use of edge (line) detection and enhancement is a common means of aiding in the delineation and visualization of structures within an image.;In this dissertation, an artifact-free enhancement algorithm based on overcomplete multiscale wavelet analysis is presented. First, an image is decomposed using a fast wavelet transform algorithm. At the same time, the energy and phase information at each level are determined using a set of separable steerable filters. Then, a measure of coherence within each level is obtained by weighting an energy measure with the ratio of projections of the energy within a specified window onto the central point of the window with respect to the total energy within each window. Finally, a nonlinear operation, integrating coherence and orientation information, is applied to modify transform coefficients with distinct levels of analysis. These modified coefficients were then reconstructed, via an inverse fast wavelet transform, resulting in an improved visualization of mammographic features. The novelty of this algorithm lies in its detection of directional features and removal of unwanted perturbations. Compared to existing multiscale enhancement approachers, these images processed with this method appear more familiar to radiologists and naturally close to the original mammogram.