Joachim Weickert:
Anisotropic Diffusion in Image Processing

cover page

ECMI Series, Teubner-Verlag, Stuttgart, Germany, 1998. Out of print.
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Many recent techniques for digital image enhancement and multiscale image representations are based on nonlinear partial differential equations (PDEs).
This book gives an introduction to the main ideas behind these methods, and it describes in a systematic way their theoretical foundations, numerical aspects, and applications. A large number of references enables the reader to acquire an up-to-date overview of the original literature.
The central emphasis is on anisotropic nonlinear diffusion filters. Their flexibility allows to combine smoothing properties with image enhancement qualities. A general framework is explored covering well-posedness and scale-space results not only for the continuous, but also for the algorithmically important semidiscrete and fully discrete settings. The presented examples range from applications in medical image analysis to problems in computer aided quality control.

Click here to have a look at some images which have been filtered by nonlinear diffusion processes.


  1. Image Smoothing and Restoration by PDEs
    • Physical Background of Diffusion Processes
    • Linear Diffusion Filtering
    • Nonlinear Diffusion Filtering
    • Methods of Diffusion-Reaction Type
    • Classic Morphological Processes
    • Curvature-Based Morphological Processes
    • Total Variation Methods
    • Conclusions and Further Scope of the Book
  2. Continuous Diffusion Filtering
    • General Model
    • The Structure Tensor
    • Theoretical Results
    • Scale-Space Properties
  3. Semidiscrete Diffusion Filtering
    • General Model
    • Theoretical Results
    • Scale-Space Properties
    • Relation to Semidiscrete Models
  4. Discrete Diffusion Filtering
    • General Model
    • Theoretical Results
    • Scale-Space Properties
    • Relation to Semidiscrete Models
  5. Examples and Applications
    • Edge-Enhancing Diffusion
    • Coherence-Enhancing Diffusion
  6. Conclusions and Perspectives
  7. Bibliography (453 references)
  8. Index (about 500 entries)


With more than 3700 citations, this book is one of the most cited monographs in the field of Mathematical Image Analysis.

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The book is out of print and cannot be ordered.
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