On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows |
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Authors: | Antonin Chambolle Jérôme Darbon |
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Affiliation: | (1) CMAP, Ecole Polytechnique, CNRS, 91128 Palaiseau, France;(2) Mathematics Department, UCLA, Los Angeles, USA |
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Abstract: | In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409–422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al.
(SIAM Journal on Control and Optimization 31(2):387–438, 1993) and Luckhaus and Sturzenhecker (Calculus of Variations and Partial Differential Equations 3(2):253–271, 1995), and show how the corresponding problems can be solved with sub-pixel accuracy using Parametric Maximum Flow techniques. This provides interesting algorithms for computing crystalline curvature motion,
possibly with a forcing term.
A. Chambolle’s research supported by ANR project “MICA”, grant ANR-08-BLAN-0082.
J. Darbon’s research supported by ONR grant N000140710810. |
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Keywords: | Crystalline and anisotropic mean curvature flow Variational approaches Total variation Submodular functions Max-flow/min-cut Parametric max-flow algorithms |
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