Nonlinear PDEs and numerical algorithms for modeling levelings and reconstruction filters

Maragos, P; Meyer, F

dc.contributor.author	Maragos, P	en
dc.contributor.author	Meyer, F	en
dc.date.accessioned	2014-03-01T01:14:53Z
dc.date.available	2014-03-01T01:14:53Z
dc.date.issued	1999	en
dc.identifier.issn	0302-9743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13266
dc.subject	Geometric Feature	en
dc.subject	Image Analysis	en
dc.subject	Large Classes	en
dc.subject	nonlinear pde	en
dc.subject	Numerical Algorithm	en
dc.subject	Numerical Solution	en
dc.subject	partial dierential equation	en
dc.subject	Scale Space	en
dc.subject.classification	Computer Science, Theory & Methods	en
dc.subject.other	EQUATIONS	en
dc.subject.other	MORPHOLOGY	en
dc.subject.other	OPERATORS	en
dc.subject.other	EVOLUTION	en
dc.subject.other	AXIOMS	en
dc.title	Nonlinear PDEs and numerical algorithms for modeling levelings and reconstruction filters	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/3-540-48236-9_32	en
heal.identifier.secondary	http://dx.doi.org/10.1007/3-540-48236-9_32	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	In this paper we develop partial differential equations (PDEs) that model the generation of a large class of morphological filters, the levelings and the openings/closings by reconstruction. These types of filters are very useful in numerous image analysis and vision tasks ranging from enhancement, to geometric feature detection, to segmentation. The developed PDEs are nonlinear functions of the first spatial derivatives and model these nonlinear filters as the limit of a controlled growth starting from an initial seed signal. This growth is of the multiscale dilation or erosion type and the controlling mechanism is a switch that reverses the growth when the difference between the current evolution and a reference signal switches signs. We discuss theoretical aspects of these PDEs, propose discrete algorithms for their numerical solution and corresponding filter implementation, and provide insights via several experiments. Finally, we outline the use of these PDEs for improving the Gaussian scale-space by using the latter as initial seed to generate: multiscale levelings that have a superior preservation of image edges and boundaries.	en
heal.publisher	SPRINGER-VERLAG BERLIN	en
heal.journalName	SCALE-SPACE THEORIES IN COMPUTER VISION	en
heal.bookName	LECTURE NOTES IN COMPUTER SCIENCE	en
dc.identifier.doi	10.1007/3-540-48236-9_32	en
dc.identifier.isi	ISI:000170515400032	en
dc.identifier.volume	1682	en
dc.identifier.spage	363	en
dc.identifier.epage	374	en