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Displaying similar documents to “A blind definition of shape”

Instability of the eikonal equation and shape from shading

Ian Barnes, Kewei Zhang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In the shape from shading problem of computer vision one attempts to recover the three-dimensional shape of an object or landscape from the shading on a single image. Under the assumptions that the surface is dusty, distant, and illuminated only from above, the problem reduces to that of solving the eikonal equation on a domain in ℝ 2 . Despite various existence and uniqueness theorems for smooth solutions, we show that this problem is unstable, which is catastrophic for general numerical...

An optimal matching problem

Ivar Ekeland (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Given two measured spaces ( X , μ ) and ( Y , ν ) , and a third space , given two functions  and , we study the problem of finding two maps s : X → Z and t : Y → Z such that the images s ( μ ) and t ( ν ) coincide, and the integral ∫ X u ( x , s ( x ) ) d μ - ∫ Y v ( y , t ( y ) ) d ν is maximal. We give condition on and for which there is a unique solution.