Fractal Analysis of Breast Masses in Mammograms

Fractal analysis is useful in digital image processing for the characterization of shape roughness and gray-scale texture or complexity. Breast masses present shape and gray-scale characteristics in mammograms that vary between benign masses and malignant tumors. This book demonstrates the use of fractal analysis to classify breast masses as benign masses or malignant tumors based on the irregularity exhibited in their contours and the gray-scale variability exhibited in their mammographic images. A few different approaches are described to estimate the fractal dimension (FD) of the contour of a mass, including the ruler method, box-counting method, and the power spectral analysis (PSA) method. Procedures are also described for the estimation of the FD of the gray-scale image of a mass using the blanket method and the PSA method. To facilitate comparative analysis of FD as a feature for pattern classification of breast masses, several other shape features and texture measures are described in the book. The shape features described include compactness, spiculation index, fractional concavity, and Fourier factor. The texture measures described are statistical measures derived from the gray-level cooccurrence matrix of the given image. Texture measures reveal properties about the spatial distribution of the gray levels in the given image; therefore, the performance of texture measures may be dependent on the resolution of the image. For this reason, an analysis of the effect of spatial resolution or pixel size on texture measures in the classification of breast masses is presented in the book. The results demonstrated in the book indicate that fractal analysis is more suitable for characterization of the shape than the gray-level variations of breast masses, with area under the receiver operating characteristics of up to 0.93 with a dataset of 111 mammographic images of masses. The methods and results presented in the book are useful for computer-aided diagnosis of breast cancer. Table of Contents: Computer-Aided Diagnosis of Breast Cancer / Detection and Analysis of\newline Breast Masses / Datasets of Images of Breast Masses / Methods for Fractal Analysis / Pattern Classification / Results of Classification of Breast Masses / Concluding Remarks

Thanh Minh Cabral obtained her B.Sc. and M.Sc. degrees from the Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, Canada, in 2004 and 2010, respectively. Her research interests are in the areas of medical image processing and computer-aided diagnosis. She has held research and development positions in several engineering companies. Rangaraj Mandayam Rangayyan is a Professor with the Department of Electrical and Computer Engineering, and an Adjunct Professor of Surgery and Radiology, at the University of Calgary, Calgary, Alberta, Canada. He received a Bachelor of Engineering degree in Electronics and Com munication in 1976 from the University of Mysore at the People’s Education Society College of Engineering, Mandya, Karnataka, India, and a Ph.D. in Electrical Engineering from the Indian Institute of Science, Bangalore, Karnataka, India in 1980. His research interests are in the areas of digital signal and image processing, biomedical signal analysis, biomedical image analysis, and computer-aided diagnosis. He has published more than 140 papers in journals and 250 papers in conference proceedings. His research productivity was recognized with the 1997 and 2001 Research Excellence Awards of the Department of Electrical and Computer Engineering, the 1997 Research Award of the Faculty of Engineering, and by appointment as a “University Professor” in 2003, at the University of Calgary. He is the author of two textbooks: Biomedical Signal Analysis (IEEE/ Wiley, 2002) and Biomedical Image Analysis (CRC, 2005). He has coauthored and coedited several other books, including one on Color Image Processing with Biomedical Applications (SPIE, 2011). He was recognized by the IEEE with the award of the Third Millennium Medal in 2000, and was elected as a Fellow of the IEEE in 2001, Fellow of the Engineering Institute of Canada in 2002, Fellow of the American Institute for Medical and Biological Engineering in 2003, Fellow of SPIE: the In ternational Society for Optical Engineering in 2003, Fellow of the Society for Imaging Informatics in Medicine in 2007, Fellow of the Canadian Medical and Biological Engineering Society in 2007, and Fellow of the Canadian Academy of Engineering in 2009. He has been awarded the Killam Resident Fellowship 3 times (1998, 2002, and 2007) in support of his book-writing projects