Handbook of Mathematical Methods in Imaging

Book Preface

Today, computer imaging covers various aspects of data filtering, pattern recognition, feature extraction, computer aided design, and computer aided inspection and diagnosis. Pillars of the field of computer imaging are advanced, stable, and reliable algorithms. In addition, feasibility analysis is required to evaluate practical relevance of the methods. To put these pillars on solid grounds, a significant amount ofmathematical tools are required.

This handbook makes a humble attempt to provide a survey of such mathematical tools. We had the vision that this imaging handbook should contain individual chapters whichcanserve as toolboxes, which, whenaligned, formbackgroundmaterial for complete applied imaging problems.Therefore it should also give an impression on the broad mathematical knowledge required to solve industrial and applied research applications: The image formation process, very frequently, is assigned to the inverse problems community, which is prominently represented in this handbook. The subsequent step is image analysis. Nowadays, advanced Image Analysis, and Image Processing in general, uses sophisticated methods fromGeometry, Differential Geometry, Convex Analysis, Numerical Analysis, to mention just a few. In fact, by the rapid advance of Imaging, the mathematical areas have been pushed forward heavily, and raised their impact in application sciences.

My special thanks go to all individual authors for their valuable contributions and the referees for their help in improving the contributions and making detailed comments. My sincere thanks go to the Springer’s editors and staff, Vaishali Damle, Jennifer Carlson, and Saskia Ellis for their patience, and their constant support and encouragement over the last two years.

Finally, Iwould like to encourage the readers to submit suggestions regarding the handbook’s content. For a project of this size, it is likely that essential topics are missed. In a rapidly evolving area like Imaging it is likely that new areas will appear in a very short time and should be added to the handbook, as well as recent development enforce modifications of existing contributions. We are committed to issuing periodic updates and we look forward to the feedback from the community.