A Convex Approach to Minimal Partitions

  title={A Convex Approach to Minimal Partitions},
  author={Antonin Chambolle and Daniel Cremers and Thomas Pock},
  journal={SIAM J. Imaging Sciences},
We describe a convex relaxation for a family of problems of minimal perimeter partitions. The minimization of the relaxed problem can be tackled numerically, we describe an algorithm and show some results. In most cases, our relaxed problem finds a correct numerical approximation of the optimal solution: we give some arguments to explain why it should be so, and also discuss some situation where it fails. 
Highly Influential
This paper has highly influenced 14 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
Highly Cited
This paper has 145 citations. REVIEW CITATIONS
Recent Discussions
This paper has been referenced on Twitter 1 time over the past 90 days. VIEW TWEETS


Publications citing this paper.
Showing 1-10 of 96 extracted citations

145 Citations

Citations per Year
Semantic Scholar estimates that this publication has 145 citations based on the available data.

See our FAQ for additional information.


Publications referenced by this paper.
Showing 1-10 of 56 references

Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms

  • G. Lawlor, F. Morgan
  • Pacific J. Math., 166(1):55–83,
  • 1994
Highly Influential
6 Excerpts

Soap films and covering spaces

  • K. A. Brakke
  • J. Geom. Anal., 5(4):445–514,
  • 1995
Highly Influential
7 Excerpts

Convex analysis and variational problems, volume 28 of Classics in Applied Mathematics

  • I. Ekeland, R. Témam
  • Society for Industrial and Applied Mathematics…
  • 1999
Highly Influential
7 Excerpts

Convex analysis

  • R. T. Rockafellar
  • Princeton Landmarks in Mathematics. Princeton…
  • 1997
Highly Influential
5 Excerpts

Network flows

  • R. K. Ahuja, T. L. Magnanti, J. B. Orlin
  • Prentice Hall Inc., Englewood Cliffs, NJ,
  • 1993
Highly Influential
3 Excerpts

Similar Papers

Loading similar papers…