Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations

In its updated 2nd edition, this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. The book is intended for two audiences. First, the mathematical community, showing the contribution of mathematics to this domain, and highlighting some unsolved theoretical questions. The second is the computer vision community, presenting a clear, self-contained and global overview of the mathematics involved in image procesing problems. This work will serve as a source of reference and inspiration for researchers in Applied Mathematics and Computer Vision, as well as being a basis for advanced courses within these fields. The second edition offers a coherent review of progress in the range of image processing applications covered by the PDE framework, and updates the existing material. In addition, the book provides readers with the programming tools to create simulations of their own with minimal effort.