Partial differential equations (PDEs) and variational methods
were introduced into image processing about fifteen years ago.
Since then, intensive research has been carried out. The goals of
this book are to present a variety of image analysis applications,
the precise mathematics involved and how to discretize them.
Thus, this book is intended for two audiences. The first is the
mathematical community by showing the contribution of mathematics
to this domain. It is also the occasion to highlight some unsolved
theoretical questions. The second is the computer vision community
by presenting a clear, self-contained and global overview of the
mathematics involved in image processing problems. This work will
serve as a useful source of reference and inspiration for fellow
researchers in Applied Mathematics and Computer Vision, as well as
being a basis for advanced courses within these fields.
During the four years since the publication of the first
edition, there has been substantial progress in the range of image
processing applications covered by the PDE framework. The main
goals of the second edition are to update the first edition by
giving a coherent account of some of the recent challenging
applications, and to update the existing material. In addition,
this book provides the reader with the opportunity to make his own
simulations with a minimal effort. To this end, programming tools
are made available, which will allow the reader to implement and
test easily some classical approaches.
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