A ridge and corner preserving model for surface restoration

Rongjie Lai, Xue Cheng Tai, Tony Chan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

One challenge in surface restoration is to design surface diffusion preserving ridges and sharp corners. In this paper, we propose a new surface restoration model based on the observation that surfaces' implicit representations are continuous functions whose first order derivatives have discontinuities at ridges and sharp corners. Regularized by vectorial total variation on the derivatives of surfaces' implicit representation functions, the proposed model has ridge and corner preserving properties validated by numerical experiments. To solve the proposed fourth order and convex problem efficiently, we further design a numerical algorithm based on the augmented Lagrangian method. Moreover, the theoretical convergence analysis of the proposed algorithm is also provided. To demonstrate the efficiency and robustness of the proposed method, we show restoration results on several different surfaces and also conduct comparisons with the mean curvature flow method and the nonlocal mean method.

Original languageEnglish (US)
JournalSIAM Journal on Scientific Computing
Volume35
Issue number2
DOIs
StatePublished - Jan 1 2013

Keywords

  • Augmented Lagrangian
  • Hessian
  • Surface restoration
  • Vectorial total variation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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