Lai, Rongjie; Tai, Xue-Cheng; Chan, Tony F. A ridge and corner preserving model for surface restoration. (English) Zbl 1266.49080 SIAM J. Sci. Comput. 35, No. 2, A675-A695 (2013). Summary: 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. Cited in 4 Documents MSC: 49Q10 Optimization of shapes other than minimal surfaces 49K20 Optimality conditions for problems involving partial differential equations 90C25 Convex programming 65K10 Numerical optimization and variational techniques Keywords:surface restoration; vectorial total variation; Hessian; augmented Lagrangian Software:RecPF PDFBibTeX XMLCite \textit{R. Lai} et al., SIAM J. Sci. Comput. 35, No. 2, A675--A695 (2013; Zbl 1266.49080) Full Text: DOI Link