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Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems - [ Mumford-Shah ]

15 years 8 months ago
Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems - [ Mumford-Shah ]
"The purpose of this paper is to introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental problem is to appropriately decompose the domain R of a function g(x, y) of two variables. To explain this problem, we have to start by describing the physical situation whch produces images: assume that a three-dimensional world is observed by an eye or camera from some point P and that g l ( p ) represents the intensity of the light in this world approaching the point P from a direction p. If one has a lens at P focussing this light on a retina or a film-in both cases a plane domain R in which we may introduce coordinates x, y-then let g(x, y) be the strength of the light signal striking R at a point with coordinates ( x , y); g(x, y) is essentially the same as gl( p)-possibly after a simple transformation given by the geometry of the imaging system. The function g(x, y ) defined...
David Mumford and Jayant Shah
Added 01 Apr 2009
Updated 02 Apr 2009
Type Journal
Year 1989
Where Communication on Pure and Applied Math
Authors David Mumford and Jayant Shah
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