Lattice image processing: A unification of morphological and fuzzy algebraic systems

Maragos, P

dc.contributor.author	Maragos, P	en
dc.date.accessioned	2014-03-01T01:22:33Z
dc.date.available	2014-03-01T01:22:33Z
dc.date.issued	2005	en
dc.identifier.issn	0924-9907	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16615
dc.subject	Fuzzy logic	en
dc.subject	Lattices	en
dc.subject	Mathematical morphology	en
dc.subject	Minimax algebra	en
dc.subject.classification	Computer Science, Artificial Intelligence	en
dc.subject.classification	Computer Science, Software Engineering	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Fuzzy sets	en
dc.subject.other	Image analysis	en
dc.subject.other	Mathematical morphology	en
dc.subject.other	Mathematical operators	en
dc.subject.other	Signal processing	en
dc.subject.other	Statistical methods	en
dc.subject.other	Algebraic systems	en
dc.subject.other	Fuzzy image operators	en
dc.subject.other	Lattices	en
dc.subject.other	Minimax algebra	en
dc.subject.other	Image processing	en
dc.title	Lattice image processing: A unification of morphological and fuzzy algebraic systems	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10851-005-4897-z	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10851-005-4897-z	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	This paper explores some aspects of the algebraic theory of mathematical morphology from the viewpoints of minimax algebra and translation-invariant systems and extends them to a more general algebraic structure that includes generalized Minkowski operators and lattice fuzzy image operators. This algebraic structure is based on signal spaces that combine the sup-inf lattice structure with a scalar semi-ring arithmetic that possesses generalized 'additions' and -'multiplications'. A unified analysis is developed for: (i) representations of translation-invariant operators compatible with these generalized algebraic structures as nonlinear sup- convolutions, and (ii) kernel representations of increasing translation-invariant operators as suprema of erosion-like nonlinear convolutions by kernel elements. The theoretical results of this paper develop foundations for unifying large classes of nonlinear translation-invariant image and signal processing systems of the max or min type. The envisioned applications lie in the broad intersection of mathematical morphology, minimax signal algebra and fuzzy logic. © 2005 Springer Science + Business Media, Inc.	en
heal.publisher	SPRINGER	en
heal.journalName	Journal of Mathematical Imaging and Vision	en
dc.identifier.doi	10.1007/s10851-005-4897-z	en
dc.identifier.isi	ISI:000229018500014	en
dc.identifier.volume	22	en
dc.identifier.issue	2	en
dc.identifier.spage	333	en
dc.identifier.epage	353	en