Malignant tumors due to breast cancer and masses due to benign disease appear in mammograms
with different shape characteristics: the former usually have rough spiculated or
microlobulated contours whereas the latter commonly have smooth round oval or
macrolobulated contours. Features that characterize shape roughness and complexity can assist
in distinguishing between malignant tumors and benign masses. In spite of the established
importance of shape factors in the analysis of breast tumors and masses difficulties exist in
obtaining accurate and artifact-free boundaries of the related regions from mammograms. Whereas
manually drawn contours could contain artifacts related to hand tremor and are subject to
intra-observer and inter-observer variations automatically detected contours could contain
noise and inaccuracies due to limitations or errors in the procedures for the detection and
segmentation of the related regions. Modeling procedures are desired to eliminate the artifacts
in a given contour while preserving the important and significant details present in the
contour. This book presents polygonal modeling methods that reduce the influence of noise and
artifacts while preserving the diagnostically relevant features in particular the spicules and
lobulations in the given contours. In order to facilitate the derivation of features that
capture the characteristics of shape roughness of contours of breast masses methods to derive
a signature based on the turning angle function obtained from the polygonal model are
described. Methods are also described to derive an index of spiculation an index
characterizing the presence of convex regions an index characterizing the presence of concave
regions an index of convexity and a measure of fractal dimension from the turning angle
function. Results of testing the methods with a set of 111 contours of 65 benign masses and 46
malignant tumors are presented and discussed. It is shown that shape modeling and analysis can
lead to classification accuracy in discriminating between benign masses and malignant tumors
in terms of the area under the receiver operating characteristic curve of up to 0.94. The
methods have applications in modeling and analysis of the shape of various types of regions or
objects in images computer vision computer graphics and analysis of biomedical images with
particular significance in computer-aided diagnosis of breast cancer. Table of Contents:
Analysis of Shape Polygonal Modeling of Contours Shape Factors for Pattern Classification
Classification of Breast Masses
