Digital Curvature Evolution Model for Image Segmentation

  • Daniel AntunesEmail author
  • Jacques-Olivier Lachaud
  • Hugues Talbot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


Recent works have indicated the potential of using curvature as a regularizer in image segmentation, in particular for the class of thin and elongated objects. These are ubiquitous in biomedical imaging (e.g. vascular networks), in which length regularization can sometime perform badly, as well as in texture identification. However, curvature is a second-order differential measure, and so its estimators are sensitive to noise. The straightforward extensions to Total Variation are not convex, making them a challenge to optimize. State-of-art techniques make use of a coarse approximation of curvature that limits practical applications.

We argue that curvature must instead be computed using a multigrid convergent estimator, and we propose in this paper a new digital curvature flow which mimics continuous curvature flow. We illustrate its potential as a post-processing step to a variational segmentation framework.


Multigrid convergence Digital estimator Curvature Shape optimization Image segmentation 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniel Antunes
    • 1
    Email author
  • Jacques-Olivier Lachaud
    • 1
  • Hugues Talbot
    • 2
  1. 1.Université Savoie Mont Blanc, LAMA, UMR CNRS 5127ChambéryFrance
  2. 2.CentraleSupelec Université Paris-Saclay, équipe Inria GALENParisFrance

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