Algebraic and PDE approaches for multiscale image operators with global constraints: Reference semilattice erosions and levelings

Maragos, P

dc.contributor.author	Maragos, P	en
dc.date.accessioned	2014-03-01T01:16:07Z
dc.date.available	2014-03-01T01:16:07Z
dc.date.issued	2001	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13923
dc.subject	Geometric Feature	en
dc.subject	Global Constraint	en
dc.subject	Image Analysis	en
dc.subject	Large Classes	en
dc.subject	Local Computation	en
dc.subject	Morphological Operation	en
dc.subject	Numerical Solution	en
dc.subject	Scale Space	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	FILTERS	en
dc.title	Algebraic and PDE approaches for multiscale image operators with global constraints: Reference semilattice erosions and levelings	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/3-540-47778-0_12	en
heal.identifier.secondary	http://dx.doi.org/10.1007/3-540-47778-0_12	en
heal.language	English	en
heal.publicationDate	2001	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 axe useful in numerous image analysis and vision tasks ranging from simplification, to geometric feature detection, to segmentation. 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 reference 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 a PDE that generates geodesic levelings. Further, we develop PDEs that can model and generate continuous-scale semilattice erosions, as a special case of the leveling PDE. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution which are proved to converge as iterations of triphase operators, and provide insights via image experiments.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	SCALE-SPACE AND MORPHOLOGY IN COMPUTER VISION, PROCEEDINGS	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.doi	10.1007/3-540-47778-0_12	en
dc.identifier.isi	ISI:000174659600012	en
dc.identifier.volume	2106	en
dc.identifier.spage	137	en
dc.identifier.epage	148	en