Convex non-convex image segmentation

Raymond CHAN, Alessandro LANZA, Serena MORIGI*, Fiorella SGALLARI

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

24 Citations (Scopus)


A convex non-convex variational model is proposed for multiphase image segmentation. We consider a specially designed non-convex regularization term which adapts spatially to the image structures for a better control of the segmentation boundary and an easy handling of the intensity inhomogeneities. The nonlinear optimization problem is efficiently solved by an alternating directions methods of multipliers procedure. We provide a convergence analysis and perform numerical experiments on several images, showing the effectiveness of this procedure.

Original languageEnglish
Pages (from-to)635-680
Number of pages46
JournalNumerische Mathematik
Issue number3
Early online date6 Sept 2017
Publication statusPublished - Mar 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag GmbH Deutschland.


  • 47N10
  • 52A41
  • 65K10
  • 65K15
  • 90C26


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