Modeling and Analysis of Shape: with Applications in Computer-Aided Diagnosis of Breast Cancer (Synthesis Lectures on Biomedical Engineering)

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 Preface Acknowledgments Symbols and abbreviations 1. Analysis of shape The importance of shape Characteristics of breast tumors Representation of shape Organization of the book 2. Polygonal modeling of contours Review of methods for polygonal modeling Rule-based polygonal modeling of contours Comparative analysis of polygonal models Polygonal approximation of contours based on the turning angle function The TAF of a contour Polygonal model from the TAF Polygonal model from the filtered TAF Illustrations of application Remarks 3. Shape factors for pattern classification Signature based on the filtered TAF Feature extraction from the STAF Derivation of an index of spiculation from the STAF Fractal dimension from the STAF Index of convexity Shape factors from contours Compactness Spiculation index Fractional concavity Fourier factor Fractal analysis Remarks 4. Classification of breast masses Datasets of contours of breast masses Results of shape analysis and classification Remarks References Authors' biographies Index. Symbols and Abbreviations......Page 1 Characteristics of Breast Tumors......Page 21 Representation of Shape......Page 22 Organization of the Book......Page 24 Review of Methods for Polygonal Modeling......Page 29 Rule-based Polygonal Modeling of Contours......Page 31 Comparative Analysis of Polygonal Models......Page 32 Polygonal Approximation of Contours based on the Turning Angle Function......Page 39 Polygonal Model from the TAF......Page 40 Illustrations of Application......Page 47 Remarks......Page 53 Signature Based on the Filtered TAF......Page 61 Fractal Dimension from the STAF......Page 66 Index of Convexity......Page 68 Fourier Factor......Page 69 Fractal Analysis......Page 70 Remarks......Page 71 Results of Shape Analysis and Classification......Page 73 Remarks......Page 83 References......Page 85 Authors' Biographies......Page 93 Index......Page 95