Extending the PowerWatershed framework thanks to Γ-convergence

Laurent Najman (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

In this paper, we provide a formal proof of the power-watershed framework relying on the Γ-convergence framework. The main ingredient for the proof is a concept of scale. The proof and the formalism introduced in this paper have the added benefit to clarify the algorithm, and to allow to extend the applicability of the power watershed algorithm to many other types of energy functions. Several examples of applications are provided, including Total Variation and Spectral Clustering.

Mots clés: image segmentation; classification; image filtering; Γ-convergence; Power Watershed; spectral clustering

Domaines: Optimisation et contrôle [math.OC]; Traitement du signal et de l'image [eess.SP]; Mathématique discrète [cs.DM]; Traitement des images [eess.IV]; Théorie spectrale [math.SP]

Laurent Najman. Extending the PowerWatershed framework thanks to Γ-convergence. SIAM Journal on Imaging Sciences, 2017, 10 (4), pp.2275-2292. ⟨10.1137/17M1118580⟩. ⟨hal-01428875v2⟩