The Cauchy Problem for the Laplace Equation and Application to Image Inpainting | Zendy

Lamia Jaafar Belaid | Zendy; Amel Ben Abda | Zendy; Nawal Al Malki | Zendy

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The Cauchy Problem for the Laplace Equation and Application to Image Inpainting

Author(s) -

Lamia Jaafar Belaid,

Amel Ben Abda,

Nawal Al Malki

Publication year - 2011

Publication title -

isrn mathematical analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-4665

pISSN - 2090-4657

DOI - 10.5402/2011/150979

Subject(s) - inpainting , mathematics , laplace transform , cauchy problem , laplace's equation , cauchy distribution , cauchy boundary condition , moment (physics) , boundary value problem , mathematical analysis , cauchy's convergence test , initial value problem , reciprocity (cultural anthropology) , mathematical optimization , image (mathematics) , computer science , computer vision , neumann boundary condition , social psychology , psychology , physics , classical mechanics

The moment approach to solve the Cauchy problems is investigated. First, we consider the Cauchy problem for the Laplace equation, and we present a moment method for solving it in the case of a flat boundary. Second, we consider the reciprocity gap concept used to solve the problem of crack detection, as a stopping criterion and we study the case of noise data. Finally, we propose an application to the Cauchy problem for the Laplace equation, for the inpainting problem. Some numerical results showing the efficiency of the method proposed are also given.

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