A new partial differential equation for image inpainting

Mounder Benseghir; Fatma Zohra Nouri; Pierre Clovis Tauber

doi:10.5269/bspm.41334

Mounder Benseghir Badji Mokhtar University https://orcid.org/0000-0003-4201-2010
Fatma Zohra Nouri Badji Mokhtar University http://orcid.org/0000-0002-0828-5464
Pierre Clovis Tauber Faculty of Medicine INSERM http://orcid.org/0000-0003-4210-7140

Abstract

A considerable interest in the inpainting problem have attracted many researchers in applied mathematics community. In fact in the last decade, nonlinear high order partial dierential equations have payed a central role in high quality inpainting developments. In this paper, we propose a technique for inpainting that combines an anisotropic diusion process with an edge-corner enhancing shock ltering. This technique makes use of a partial differential equation that is based on a nonlinear structure tensor which increases the accuracy and robustness of the coupled diusion and shock ltering. A methodology of partition and adjustment is used to estimate the contrast parameters that control the strength of the diffusivity functions. We focus on restoring large missing regions in grey scale images containing complex geometries parts. Our model is extended to a three dimensional case, where numerical experimentations were carried out on lling brain multiple sclerosis lesions in medical images. The efficiency and the competitiveness of the proposed algorithm is numerically compared to other approaches on both synthetic and real images.

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Author Biographies

Mounder Benseghir, Badji Mokhtar University

Mounder Beseghir is a Phd student, preparing a dotorate on Mathematical techniques in image processing with applications on medical images. He got a master degree from the department of Mathematics, university Badji Mokhtar- Annaba in 2013. He contributed with talks in National and international conferences and publised a conference paper in IEEE in 2016.

Fatma Zohra Nouri, Badji Mokhtar University

Fatma Zohra Nouri graduated in Mathematics at University of Annaba, Algeria in 1983. She received a master degree in Modeling and Numerical Analysis from Oxford University, UK in 1985 and a PhD in 1988 in the department of Applied Mathematics at Strathclyde University, UK. She is currently a full professor at Badji Mokhtar University and Director of the Mathematical Modeling and Numerical Simulation Laboratory. She has written more than 100 scientific and pedagogical publications, including chapters in books, and held positions of invited and visiting professor in Europe, Africa and Middle East. Her current research interest focus on differential equations, numerical analysis, mathematical modeling, image processing and computing. She is also involved in mathematics in industry, medicine, pharmacology and sciences of plant international study groups, since 2009.

Pierre Clovis Tauber, Faculty of Medicine INSERM

Piere Clovis Tauber is senior lecturer in applied Mathematics, working in Faculty of Medicine INSERM on image processing and segmentation. His thesis presents a robust model for speckle anisotropic filtering, and a parametric active contour model (B-spline snake) for the segmentation of images affected by speckle in 2005 at the university of Toulouse (France). He publised many papers in this field.

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A new partial differential equation for image inpainting

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