Sub-riemannian mean curvature flow for image processing

G. Citti, B. Franceschiello, G. Sanguinetti, A. Sarti

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23 Citations (Scopus)
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In this paper we reconsider the sub-Riemannian cortical model of image completion introduced in [G. Citti and A. Sarti, J. Math. Imaging Vision, 24 (2006), pp. 307–326]. This model combines two mechanisms, the sub-Riemannian diffusion and the concentration, giving rise to a diffusion driven motion by curvature. In this paper we give a formal proof of the existence of viscosity solutions of the sub-Riemannian motion by curvature. Furthermore we illustrate the sub-Riemannian finite difference scheme used to implement the model and we discuss some properties of the algorithm. Finally results of completion and enhancement on a number of natural images are shown and compared with other models.

Original languageEnglish
Pages (from-to)212-237
Number of pages26
JournalSIAM Journal on Imaging Sciences
Issue number1
Publication statusPublished - 23 Feb 2016


  • Existence result
  • Image completion
  • Sub-riemannian models


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