Mathematical models for local nontexture inpaintings

Tony Chan*, Jianhong Shen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

993 Scopus citations

Abstract

Inspired by the recent work of Bertalmio et al. on digital inpaintings [SIGGRAPH 2000], 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 (TV) denoising model of Rudin, Osher, and Fatemi [Phys. D, 60 (1992), pp. 259-268]. Other models are also discussed based on the Mumford-Shah regularity [Comm. Pure Appl. Math., XLII (1989), pp. 577-685] and curvature driven diffusions (CDD) of Chan and Shen [J. Visual Comm. 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.

Original languageEnglish (US)
Pages (from-to)1019-1043
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume62
Issue number3
DOIs
StatePublished - Jan 1 2002

Keywords

  • Digital zooming
  • Disocclusion
  • Image coding
  • Inpainting
  • Interpolation
  • Prior image models
  • Total variation
  • Variational/PDE method

ASJC Scopus subject areas

  • Applied Mathematics

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