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.
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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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Chambolle, A., Darbon, J. On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows. Int J Comput Vis 84, 288–307 (2009). https://doi.org/10.1007/s11263-009-0238-9
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DOI: https://doi.org/10.1007/s11263-009-0238-9