Image Processing and Analysis: Variational, PDE, Wavelet, and Stochastic Methods

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.

Tony F. Chan is Professor of Mathematics and currently also Dean of the Division of Physical Sciences at the University of California, Los Angeles. His research interests include mathematical and computational methods in image processing and computer vision, brain mapping, and VLSI physical design. URL: math.ucla.edu/~imagers. Jianhong (Jackie) Shen is Assistant Professor of Mathematics at the University of Minnesota. In addition to doing extensive research in imaging and vision sciences, he is interested in multiscale structures and patterns in scientific data analysis as well as modeling, analysis, and computation in biological and medical sciences.