On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

Open AccessArticle

DOI: 10.1007/s11263-009-0238-9

Cite this article as:
Chambolle, A. & Darbon, J. Int J Comput Vis (2009) 84: 288. doi:10.1007/s11263-009-0238-9

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.

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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© The Author(s) 2009

Authors and Affiliations

  1. 1.CMAPEcole Polytechnique, CNRSPalaiseauFrance
  2. 2.Mathematics DepartmentUCLALos AngelesUSA