ECMI Series, Teubner-Verlag, Stuttgart, Germany, 1998. Out of print.
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Synopsis
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.
Contents
- 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
- Continuous Diffusion Filtering
- General Model
- The Structure Tensor
- Theoretical Results
- Scale-Space Properties
- Semidiscrete Diffusion Filtering
- General Model
- Theoretical Results
- Scale-Space Properties
- Relation to Semidiscrete Models
- Discrete Diffusion Filtering
- General Model
- Theoretical Results
- Scale-Space Properties
- Relation to Semidiscrete Models
- Examples and Applications
- Edge-Enhancing Diffusion
- Coherence-Enhancing Diffusion
- Conclusions and Perspectives
- Bibliography (453 references)
- Index (about 500 entries)
Citations
With
more
than 3600 citations, this book is one of the most cited
monographs in the field of Mathematical Image Analysis.
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