Survey of fast algorithms for Euler's elastica-based image segmentation

Sung Ha Kang*, Xue-Cheng Tai, Wei Zhu

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingChapterpeer-review

6 Citations (Scopus)


Segmentation has been widely studied and is one of the fundamental and classical tasks of image processing. Starting from Mumford–Shah functional, we review multiphase segmentation using piecewise constant level set approach and relate to phase transition models for multiphase segmentation. In particular, we focus on Euler's elastica-based variational functionals, in the context of fast algorithms for image segmentation problem. Its relation to illusory contour is covered following the phase transition approach. Minimizing the functionals with curvature term helps to capture the geometry of the recovered shape, but introduces complexity due to their nonconvexity and high order derivatives. We review some of fast algorithms developed to efficiently compute the minimum of curvature-based segmentation functionals, such as Euler's elastica segmentation.

Original languageEnglish
Title of host publicationProcessing, Analyzing and Learning of Images, Shapes, and Forms: Part 2
EditorsRon Kimmel, Xue-Cheng Tai
PublisherElsevier B.V.
Number of pages20
ISBN (Electronic)9780444641410
ISBN (Print)9780444641403
Publication statusPublished - 15 Oct 2019

Publication series

NameHandbook of Numerical Analysis
ISSN (Print)1570-8659

Scopus Subject Areas

  • Numerical Analysis
  • Modelling and Simulation
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • 65R10
  • 90C26
  • 94A08
  • Curvature
  • Euler's elastica
  • Fast algorithm
  • Interface model
  • Segmentation augumented Lagrangian method


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