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Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences (Springer)) (v. 147) Hardcover – November 9, 2001

ISBN-13: 978-0387953267 ISBN-10: 0387953264 Edition: 1st

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Product Details

  • Series: Applied Mathematical Sciences (Springer) (Book 147)
  • Hardcover: 286 pages
  • Publisher: Springer; 1 edition (November 9, 2001)
  • Language: English
  • ISBN-10: 0387953264
  • ISBN-13: 978-0387953267
  • Product Dimensions: 9.2 x 6.6 x 0.8 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #3,210,607 in Books (See Top 100 in Books)

Editorial Reviews

Review

From the reviews:

MATHEMATICAL REVIEWS

"The authors have substantially contributed to many aspects of the subject…The level of the book is advanced, and the exposition very clear, developed in depth, and to some extent self-contained. The proofs of the main theorems are usually given in detail; when necessary there is also a precise reference to the ample literature on the specific topic. This book will certainly interest both mathematicians (some interesting, still open theoretical questions there are highlighted) and researchers in computer vision…The books substantial and up-to-date body for reference is a detailed guide to the literature on the many aspects of image processing."

 

G. Aubert and P. Kornprobst

Mathematical Problems in Image Processing

Partial Differential Equations and the Calculus of Variations

"This book is devoted to a detailed presentation of several aspects of mathematical problems in image processing . . . The authors have substantially contributed to many aspects of their subject . . . The level of the book is advanced, and the to some extent self-contained . . . This book will certainly interest both mathematicians (some interesting, still open theoretical questions here are highlighted) and researchers in computer vision."—MATHEMATICAL REVIEWS

From the Back Cover

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. The goals of this book are to present a variety of image analysis applications, the precise mathematics involved and how to discretize them. Thus, this book is intended for two audiences. The first is the mathematical community by showing the contribution of mathematics to this domain. It is also the occasion to highlight some unsolved theoretical questions. The second is the computer vision community by presenting a clear, self-contained and global overview of the mathematics involved in image processing problems. This work will serve as a useful source of reference and inspiration for fellow researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields.

During the four years since the publication of the first edition, there has been substantial progress in the range of image processing applications covered by the PDE framework. The main goals of the second edition are to update the first edition by giving a coherent account of some of the recent challenging applications, and to update the existing material. In addition, this book provides the reader with the opportunity to make his own simulations with a minimal effort. To this end, programming tools are made available, which will allow the reader to implement and test easily some classical approaches.

Reviews of the earlier edition:

"Mathematical Problems in Image Processing is a major, elegant, and unique contribution to the applied mathematics literature, oriented toward applications in image processing and computer vision.... Researchers and practitioners working in the field will benefit by adding this book to their personal collection. Students and instructors will benefit by using this book as a graduate course textbook."

-- SIAM Review

"The Mathematician -- and he doesn't need to be a 'die-hard' applied mathematician -- will love it because there are all these spectacular applications of nontrivial mathematical techniques and he can even find some open theoretical questions. The numerical analyst will discover many challenging problems and implementations. The image processor will be an eager reader because the book provides all the mathematical elements, including most of the proofs.... Both content and typography are a delight. I can recommend the book warmly for theoretical and applied researchers."

-- Bulletin of the Belgian Mathematics

--This text refers to the Paperback edition.

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9 of 11 people found the following review helpful By Chunming Li on June 30, 2004
Format: Hardcover
This book not only includes the state-of-art image processig techniques using math methods, but also provides very good numerical schemes for these methods. This book is written by mathematicians, but engineers still can easily implemente many commonly used image processing algorithm, just follow the detailed numerical difference schemes provided in the appendix.
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Format: Hardcover Verified Purchase
This is book is rarely excellent. I have always desired a book with strong mathematics and this meets my expectation
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