Displaying similar documents to “Instability of the eikonal equation and shape from shading”

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...

The steepest descent dynamical system with control. Applications to constrained minimization

Alexandre Cabot (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Let be a real Hilbert space, Φ 1 : H → a convex function of class 𝒞 1 that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (  Brézis [CITE]) applied to the non-smooth function  Φ 1 + δ S . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function  Φ 0 : H → whose critical points coincide with  and...