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Mathematical models for local nontexture inpaintings. (English) Zbl 1050.68157

Summary: Inspired by the recent work of Bertalmio et al. (2000) on digital inpaintings, we develop general mathematical models for local inpaintings of nontexture images. On smooth regions, inpaintings are connected to the harmonic and biharmonic extensions, and inpainting orders are analyzed. For inpaintings involving the recovery of edges, we study a variational model that is closely connected to the classical total variation denoising model of L. Rudin, S. Osher, and E. Fatemi [Physica D 60, 259–268 (1992; Zbl 0780.49028)]. Other models are also discussed based on the Mumford-Shah regularity [D. Mumford and J. Shah, Commun. Pure Appl. Math. 42, 577–685 (1989; Zbl 0691.49036)] and curvature driven diffusions (CDD) of T. F. Chan and J. Shen [J. Visual Commun. Image Rep. 12 (2001)]. The broad applications of the inpainting models are demonstrated through restoring scratched old photos, disocclusion in vision analysis, text removal, digital zooming, and edge-based image coding.

MSC:

68U10 Computing methodologies for image processing
65K10 Numerical optimization and variational techniques
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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