This book details the mathematical developments in total variation based image restauration.  From the reviews: "This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters....The book is written with great care, paying also a lot of attention to the bibliographical and historical notes."-- ZENTRALBLATT MATH

Parabolic Quasilinear Equations Minimizing Linear Growth Functionals (Progress in Mathematics)

Computers & Technology

Andreu-Vaillo, Fuensanta

Caselles, Vicent

Mazón, José M.

Computer Science

Birkhauser

<p>The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems, and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties, empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.</p>

Optimal Transportation Networks: Models and Theory (Lecture Notes in Mathematics, 1955)

Business & Money

Bernot, Marc

Morel, Jean-Michel

Management & Leadership

Springer

Parabolic Quasilinear Equations Minimizing Linear Growth Functionals (Progress in Mathematics, 223)

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