Displaying similar documents to “Asymptotic shape for the chemical distance and first-passage percolation on the infinite Bernoulli cluster”

A blind definition of shape

J. L. Lisani, J. M. Morel, L. Rudin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this note, we propose a general definition of shape which is both compatible with the one proposed in phenomenology (gestaltism) and with a computer vision implementation. We reverse the usual order in Computer Vision. We do not define “shape recognition" as a task which requires a “model" pattern which is searched in all images of a certain kind. We give instead a “blind" definition of shapes relying only on invariance and repetition arguments. Given a set of images ℐ , we call...

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...