Maher Moakher

Ecole Nationale d'Ingénieurs de Tunis (ENIT), Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur (LAMSIN), Faculty Member

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James Elkins

School of the Art Institute of Chicago

Elif SERTEL

Istanbul Technical University

Andrej Dujella

University of Zagreb

Amir Manbachi

Johns Hopkins University

Aidy Ali

Universiti Pertahanan Nasional Malaysia

Bihter Erol

Istanbul Technical University

Mikail F Lumentut

National Taiwan University

Aashique Rezwan

University of Wisconsin-Madison

Gomaa Dawod

National Water Research center

Isad Saric

University of Sarajevo

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Papers by Maher Moakher

Symmetric positive definite matrices, e.g. covariance matrices, are constrained by their symmetry, the strict positivity of the diagonal elements (variance) and the Cauchy-Schwarz inequalities bounding the absolute value of the off-diagonal elements: |Cov(xixj)|≤[Var(xj)Var(xj)]1/2, for all i,j∈{...

PLOS ONE, Apr 28, 2015

<p>This topology is easily visualized in case of 2x2 matrices; any 2x2 covariance matrix ca... more <p>This topology is easily visualized in case of 2x2 matrices; any 2x2 covariance matrix can be seen as a point in 3D Euclidean space, with two coordinates given by the two variances (diagonal elements) and the third coordinate given by the covariance (either one of the off-diagonal element). By construction a covariance matrix must stay within the cone boundaries. As soon as the point touches the boundary of the cone, the matrix is no more positive definite.</p

Combined second and fourth-order PDEs model and associated variational problems for geometry images inpainting and denoising

HAL (Le Centre pour la Communication Scientifique Directe), Jan 31, 2020

We consider a Partial Differential Equation model combining second and fourth-order operators for... more We consider a Partial Differential Equation model combining second and fourth-order operators for solving the geometry inpainting and denoising problems. The model allows the accurate recovery of curvatures and the singular set of the reconstructed image (edges, corners). The approach proposed permits a dynamical modelling by constructing a family of simple discrete energies that admit as a Γ-limit a Mumford-Shah-Euler like functionals. The approximation functionals are build within an adaptive strategy, based on two ingredients: a fine location of the singular set using mesh refinement, and second, a local choice of the diffusion coefficients which modify the reconstruction operator. Unlike the usual methods, mostly based on prior guess on the continuous solution and leading to complex and nonlinear systems of PDEs, our method consists in solving linear problems and updating the diffusion coefficients. The high order of the operator allows us to perform simultaneously efficient filtering of the data and the interpolation in the damaged regions. The method turns out to be superior to any second-order model in restoring large gap connections and curvy features. In order to validate this approach, we compare the results of our method with those of some existing one in the fields of geometry-oriented inpainting and we present several numerical examples.

Maher Moakher

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