TROPICAL AND MORPHOLOGICAL OPERATORS FOR SIGNALS ON GRAPHS

Samy Blusseau (1) , Santiago Velasco-Forero (1) , Jesus Angulo (1) , Isabelle Bloch (2)

1 CMM - Centre de Morphologie Mathématique
2 LTCI - Laboratoire Traitement et Communication de l'Information

We extend recent work on mathematical morphology for signal processing on weighted graphs, based on discrete tropical algebra. The framework is general and can be applied to any scalar function defined on a graph. We show applications in structure tensors analysis and the regularization of grayscale images.

Mots clés: Mathematical morphology; Signal processing on graphs; Tropical algebra

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement des images [eess.IV]; Mathématique discrète [cs.DM]

Samy Blusseau, Santiago Velasco-Forero, Jesus Angulo, Isabelle Bloch. TROPICAL AND MORPHOLOGICAL OPERATORS FOR SIGNALS ON GRAPHS. 2018. ⟨hal-01799029v1⟩