N-ary Mathematical Morphology

• Main Authors: Chevallier, Emmanuel, Chevallier, Augustin, Angulo, Jesus
• Other Authors: Centre de Morphologie Mathématique (CMM), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL), École normale supérieure - Cachan (ENS Cachan)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2015
• Subjects: [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing; Iceland
• Online Access: https://hal.science/hal-01104191; https://hal.science/hal-01104191/document; https://hal.science/hal-01104191/file/n-aryMorphology_ismm15_v4.pdf; https://doi.org/10.1007/978-3-319-18720-4_29

International audience Mathematical morphology on binary images can be fully de-scribed by set theory. However, it is not sucient to formulate mathe-matical morphology for grey scale images. This type of images requires the introduction of the notion of partial order of grey levels, together with the denition of sup and inf operators. More generally, mathemati-cal morphology is now described within the context of the lattice theory. For a few decades, attempts are made to use mathematical morphology on multivariate images, such as color images, mainly based on the no-tion of vector order. However, none of these attempts has given fully satisfying results. Instead of aiming directly at the multivariate case we propose an extension of mathematical morphology to an intermediary situation: images composed of a nite number of independent unordered categories.