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 , 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...

On the -stabilization of the double integrator subject to input saturation

Yacine Chitour (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider a finite-dimensional control system ( Σ ) x ˙ ( t ) = f ( x ( t ) , u ( t ) ) , such that there exists a feedback stabilizer that renders x ˙ = f ( x , k ( x ) ) globally asymptotically stable. Moreover, for with an output map and 1 p q , we assume that there exists a 𝒦 -function such that H ( x u ) q α ( u p ) , where is the maximal solution of ( Σ ) k x ˙ ( t ) = f ( x ( t ) , k ( x ( t ) ) + u ( t ) ) , corresponding to and to the initial condition . Then, the gain function G ( H , p , q ) of given by 14.5cm G ( H , p , q ) ( X ) = def sup u p = X H ( x u ) q , is well-defined. We call profile of for any 𝒦 -function which is of the same order of magnitude...