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.
Highlights
Inpainting is the technique of reconstructing or restoring a damaged part of an image by using available information to filling-in the target region
The results obtained are compared with the ones resulted from Zhang et al [33] (ZH), Shao et al [26] (SH) and Chan et al [9] (TV) algorithms
We proposed an image inpainting approach combining oriented diffusion based on the non-linear structure tensor (NLST), shock filtering and K-means algorithm and a least-square fit (KMLS) algorithm
Summary
Inpainting is the technique of reconstructing or restoring a damaged part of an image by using available information to filling-in the target region. The first are based on searching and copying similar patches in the neighborhood of the damaged region, where the reconstruction is done from the outside to the inside edge of the target area; for example, Criminisi et al [12] adopt an order to fill in the missing region where the patches of the high gradient zones are processed first These methods give very effective solutions for the reconstruction of textures but do not handle very effectively edges and boundaries. The main idea of these approaches is to restore photometric and structural information such as edges, corners, curvatures and junctions In these approaches, the target region is filled by diffusing the information from their surroundings using partial differential equations (PDEs). The last category of approaches, namely ”the hybrid methods”, try to take the advantages of the first two classes of methods to ensure the reconstruction of both the geometric and the textured components
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