Segmentation by elastica energy with L1 and L2 curvatures: A performance comparison

Xuan He*, Wei Zhu, Xue-Cheng TAI

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


In this paper, we propose an algorithm based on augmented Lagrangian method and give a performance comparison for two segmentation models that use the L1- and L2-Euler's elastica energy respectively as the regularization for image segmentation. To capture contour curvature more reliably, we develop novel augmented Lagrangian functionals that ensure the segmentation level set function to be signed distance functions, which avoids the reinitialization of segmentation function during the iterative process. With the proposed algorithm and with the same initial contours, we compare the performance of these two high-order segmentation models and numerically verify the different properties of the two models.

Original languageEnglish
Pages (from-to)285-311
Number of pages27
JournalNumerical Mathematics
Issue number1
Early online dateSept 2018
Publication statusPublished - Feb 2019

Scopus Subject Areas

  • Modelling and Simulation
  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Augmented Lagrangian method
  • Euler's elastica
  • Image segmentation


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