A new partial differential equation for image inpainting

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.