Abstract
Abstract
A novel variational problem for approximating the distance function (to a domain boundary) is proposed. It is shown that this problem can be efficiently solved by ADMM. A review of several other variational and PDE-based methods for distance function estimation is presented. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments. Applications of the method to the problems of surface curvature estimation and computing the skeleton of a binary image are shown.
Publisher
Springer Science and Business Media LLC
Reference35 articles.
1. Aubert, G., Aujol, J.F.: Poisson skeleton revisited: a new mathematical perspective. J. Math. Imaging Vis. 48(1), 149–159 (2014)
2. Babuška, I., Banerjee, U., Osborn, J.E.: Survey of meshless and generalized finite element methods: a unified approach. Acta Numerica 12, 1–125 (2003)
3. Belyaev, A., Fayolle, P.A.: On variational and PDE-based distance function approximations. Comput. Graph. Forum 34(8), 104–118 (2015)
4. Belyaev, A., Fayolle, P.A., Pasko, A.: Signed Lp-distance fields. Comput. Aided Des. 45, 523–528 (2013)
5. Bhattacharya, T., DiBenedetto, E., Manfredi, J.: Limits as $p\to \infty $ of Δpup = f and related extremal problems. Rend. Sem. Mat. Univ. Pol. Torino, Fascicolo Speciale Nonlinear PDEs, 15–68 (1989)
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