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Mathematical Image Processing

  • Textbook
  • © 2018

Overview

Authors:
  1. Kristian Bredies

    1. Institute for Mathematics and Scientific, University of Graz, Graz, Austria

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  2. Dirk Lorenz

    1. Braunschweig, Germany

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    You can also search for this author in PubMed   Google Scholar

  • The book sets out pragmatically and sensibly to introduce to the fast field of mathematical techniques in solving many specific problems in image processing
  • Covers also more recent methods based on PDE and variational methods
  • Has the virtues of a good an handy reference manual

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Kristian Bredies, Dirk Lorenz
    Pages 1-13

  3. Mathematical Preliminaries

    • Kristian Bredies, Dirk Lorenz
    Pages 15-53

  4. Basic Tools

    • Kristian Bredies, Dirk Lorenz
    Pages 55-108

  5. Frequency and Multiscale Methods

    • Kristian Bredies, Dirk Lorenz
    Pages 109-170

  6. Partial Differential Equations in Image Processing

    • Kristian Bredies, Dirk Lorenz
    Pages 171-250

  7. Variational Methods

    • Kristian Bredies, Dirk Lorenz
    Pages 251-443

  8. Back Matter

    Pages 445-473
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Keywords

About this book

This book addresses the mathematical aspects of modern image processing methods, with a special emphasis on the underlying ideas and concepts. It discusses a range of modern mathematical methods used to accomplish basic imaging tasks such as denoising, deblurring, enhancing, edge detection and inpainting. In addition to elementary methods like point operations, linear and morphological methods, and methods based on multiscale representations, the book also covers more recent methods based on partial differential equations and variational methods.

Review of the German Edition: The overwhelming impression of the book is that of a very professional presentation of an appropriately developed and motivated textbook for a course like an introduction to fundamentals and modern theory of mathematical image processing. Additionally, it belongs to the bookcase of any office where someone is doing research/application in image processing. It has the virtues of a good and handy reference manual. (zbMATH, reviewer: Carl H. Rohwer, Stellenbosch)

Reviews

“This book is devoted to researches in image processing and can be used for courses of applied mathematics. This book can be treated as a good starting point, since it introduces the reader into the base theory of mathematical image processing and shows the wide spectrum of approaches to typical image processing tasks.” (Agnieszka Lisowska, zbMath 1418.94001, 2019)

Authors and Affiliations

  • Institute for Mathematics and Scientific, University of Graz, Graz, Austria

    Kristian Bredies

  • Braunschweig, Germany

    Dirk Lorenz

About the authors

Dirk Lorenz is professor at TU Braunschweig, Institute for Analysis and Algebra. His research areas are: Inverse Problemes and Mathematical Image Processing.

Kristian Bredies is professor at Karl-Franzens-Universität Graz. His research interests include mathematical imaging, variational methods and numerical optimization.





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