On Nonlocal Mathematical Morphology

Santiago Velasco-Forero (1) , Jesus Angulo (2)

1 Fraunhofer ITWM - Fraunhofer Institute of Industrial Mathematics
2 CMM - Centre de Morphologie Mathématique

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finally, we recommend a sparse version to introduce an efficient algorithm that computes these operators in reasonable computational time.

Domaines: Traitement d'image; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Santiago Velasco-Forero, Jesus Angulo. On Nonlocal Mathematical Morphology. 11th International Symposium, ISMM 2013, May 2013, Uppsala, Sweden. pp.219-230, ⟨10.1007/978-3-642-38294-9_19⟩. ⟨hal-00834641⟩