An Elastica-driven Digital Curve Evolution Model for Image Segmentation - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Mathematical Imaging and Vision Year : 2021

An Elastica-driven Digital Curve Evolution Model for Image Segmentation


Geometric priors have been shown to be useful in image segmentation to regularize results. For example, the classical Mumford-Shah functional uses region perimeter as prior. This has inspired much research in the last few decades, with classical approaches like the Rudin-Osher-Fatemi and most graph-cut formulations, which all use a weighted or binary perimeter prior. It has been observed that this prior is not suitable in many applications, for example for segmenting thin objects or some textures, which may have high perimeter/surface ratio. Mumford observed that an interesting prior for natural objects is the Euler Elastical model, which involves the squared curvature. In other areas of science, researchers have noticed that some physical binarization processes, like emulsion unmixing can be well-approximated by curvature-related flow like the Willmore flow. However, curvature-related flows are not easy to compute because curvature is difficult to estimate accurately, and the underlying optimisation processes are not convex. In this article, we propose to formulate a digital flow that approximates an Elastica-related flow using a multigrid-convergent curvature estimator, within a discrete variational framework. We also present an application of this model as a post-processing step to a segmentation framework.
Fichier principal
Vignette du fichier
Antunes_etal_Digital_Elastica.pdf (8.98 Mo) Télécharger le fichier
Origin Files produced by the author(s)
Comment Ce fichier est produit avec le style de l'éditeur mais ne provient pas de l'éditeur. C'est facile de le voir il n'y a aucune indication de page, numéro ou volume.

Dates and versions

hal-03144926 , version 1 (19-02-2021)





Daniel Antunes, Jacques-Olivier Lachaud, Hugues Talbot. An Elastica-driven Digital Curve Evolution Model for Image Segmentation. Journal of Mathematical Imaging and Vision, 2021, 63 (1), pp.1-17. ⟨10.1007/s10851-020-00983-4⟩. ⟨hal-03144926⟩
123 View
76 Download



Gmail Mastodon Facebook X LinkedIn More