Algebraic and PDE approaches for lattice scale-spaces with global constraints

Maragos, P

dc.contributor.author	Maragos, P	en
dc.date.accessioned	2014-03-01T01:18:37Z
dc.date.available	2014-03-01T01:18:37Z
dc.date.issued	2003	en
dc.identifier.issn	0920-5691	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15109
dc.subject	Lattice operators	en
dc.subject	Levelings	en
dc.subject	Morphology	en
dc.subject	Nonlinear scale-spaces	en
dc.subject	PDEs	en
dc.subject.classification	Computer Science, Artificial Intelligence	en
dc.subject.other	Algorithms	en
dc.subject.other	Computer vision	en
dc.subject.other	Constraint theory	en
dc.subject.other	Convergence of numerical methods	en
dc.subject.other	Feature extraction	en
dc.subject.other	Image analysis	en
dc.subject.other	Image enhancement	en
dc.subject.other	Image segmentation	en
dc.subject.other	Linear algebra	en
dc.subject.other	Mathematical operators	en
dc.subject.other	Object recognition	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Image simplification	en
dc.subject.other	Lattice operators	en
dc.subject.other	Motion analysis	en
dc.subject.other	Nonlinear scale spaces	en
dc.subject.other	Object detection	en
dc.subject.other	Shape analysis	en
dc.subject.other	Mathematical morphology	en
dc.title	Algebraic and PDE approaches for lattice scale-spaces with global constraints	en
heal.type	journalArticle	en
heal.identifier.primary	10.1023/A:1022999923439	en
heal.identifier.secondary	http://dx.doi.org/10.1023/A:1022999923439	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	This paper begins with analyzing the theoretical connections between levelings on lattices and scale-space erosions on reference semilattices. They both represent large classes of self-dual morphological operators that exhibit both local computation and global constraints. Such operators are useful in numerous image analysis and vision tasks including edge-preserving multiscale smoothing, image simplification, feature and object detection, segmentation, shape and motion analysis. Previous definitions and constructions of levelings were either discrete or continuous using a PDE. We bridge this gap by introducing generalized levelings based on triphase operators that switch among three phases, one of which is a global constraint. The triphase operators include as special cases useful classes of semilattice erosions. Algebraically, levelings are created as limits of iterated or multiscale triphase operators. The subclass of multiscale geodesic triphase operators obeys a semigroup, which we exploit to find PDEs that can generate geodesic levelings and continuous-scale semilattice erosions. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution which converge as iterations of triphase operators, and provide insights via image experiments.	en
heal.publisher	KLUWER ACADEMIC PUBL	en
heal.journalName	International Journal of Computer Vision	en
dc.identifier.doi	10.1023/A:1022999923439	en
dc.identifier.isi	ISI:000181764500004	en
dc.identifier.volume	52	en
dc.identifier.issue	2-3	en
dc.identifier.spage	121	en
dc.identifier.epage	137	en