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Title: Inpainting method based on variational calculus and sparse matrices
Authors: Forero, Manuel G.
Navarro, Andrés F.
Miranda, Sergio L.
Keywords: Photo restoration
Sparse matrices
Image restoration
Scratch remotion
Issue Date: 1-Aug-2021
Publisher: Proceedings of SPIE - The International Society for Optical Engineering
Citation: Manuel G. Forero, Andrés F. Navarro, and Sergio L. Miranda "Inpainting method based on variational calculus and sparse matrices", Proc. SPIE 11842, Applications of Digital Image Processing XLIV, 118421F (1 August 2021);
Abstract: Photo restoration is one of the most popular tasks in digital image processing, required when an image has stains, scratches or any unwanted object. Inpainting is the name given to this type of method, which is based on modifying the areas, where the unwanted information is, in an imperceptible way. The concept of Inpainting was born in the early twentieth century, due to the need to replace or remove an object from a photograph, this was possible through manual brushstrokes of an editor or painter. From the above and the theory of Poisson's image editing, a new technique based on variational calculus and the use of sparse matrices is developed. In this technique, a functional is proposed, which is subsequently minimized, thus achieving that the union between the filled region and the image to be repaired is visually imperceptible. The results obtained were compared with those of the bilinear interpolation, isophote, Orthogonal Matching Pursuit (OMP) and KSVD techniques, the latter two being techniques based on sparse models. Then, the difference between the original and the resulting image was calculated considering only the areas of interest to find the number of distinct pixels and the root mean square error (RMSE). The proposed method presents better results than bilinear interpolation, Orthogonal Matching Pursuit and K-SVD, and very similar to those obtained with the Isotope technique.
ISSN: 0277-786X
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