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...

Moderate Deviations for I.I.D. Random Variables

Peter Eichelsbacher, Matthias Löwe (2010)

ESAIM: Probability and Statistics

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We derive necessary and sufficient conditions for a sum of i.i.d. random variables ∑ i = 1 n X i / b n – where b n n ↓ 0 , but b n n ↑ ∞ – to satisfy a moderate deviations principle. Moreover we show that this equivalence is a typical moderate deviations phenomenon. It is not true in a large deviations regime.