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

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SIAM, Sep 1, 2005 - Computers - 400 pages
4 Reviews
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.
  

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direct pde based methods may assume too much regularity in natural images but could still be very powerful in processing highlevel parameteric features. wavelets could also absorb more stochastic info to be closer to Markov models, esp. on multiscale graphical models. these are the topics i feel the authors can further explore and expand in future releases, and will generate even bigger impacts. overall, the authors have been very serious researchers on imaging whose talks and publications are always enthusiastic, innovative, and even somewhat adventurous. the question for the community is to sort out where we are heading given this rich toolkit of modern mathematics.  

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I really enjoyed reading the interesting connection to statistical mechanics, though the physics of various imaging processes has not been explained in details.

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Copyright

Common terms and phrases

Popular passages

Page 392 - L.-Y. Wei and M. Levoy. Fast Texture Synthesis Using Tree-Structured Vector Quantization.
Page 375 - E. Calabi, PJ Olver, C. Shakiban, A. Tannenbaum, and S. Haker. Differential and numerically invariant signature curves applied to object recognition.
Page 391 - Modeling textures with total variation minimization and oscillating patterns in image processing," Journal of Scientific Computing 19(1-3), pp.
Page 387 - S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer- Verlag, New York, 2003. [26] N. Paragios and R. Deriche, "Geodesic active regions: a new framework to deal with frame partition problems in computer vision," Journal of Visual Communication and Image Representation, vol.
Page 388 - Rudin, S. Osher and E. Fatemi, Nonlinear Total Variation Based Noise Removal Algorithms, Physica D., 60 (1992), pp. 259-268. 26. L. Rudin and S. Osher, Total Variation Based Image Restoration with Free Local Constraints, Proc.
Page 392 - Scale space filtering: a new approach to multi-scale description,
Page 384 - Occlusion models for natural images: A statistical study of a scale-invariant dead leaves model.
Page 376 - V. Caselles, J.-M. Morel, and C. Sbert. "An axiomatic approach to image interpolation,
Page 381 - RC Gonzalez and RE Woods, Digital Image Processing, Addison- Wesley, New York, NY, USA 1992.

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About the author (2005)

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: www.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. URL: www.math.umn.edu/~jhshen.

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