Towards the mathematic formalization of parametric generalized cylinders and initial results in modeling 3D image data

Kechriniotis, AI; Delibasis, KK; Tsonos, C; Assimakis, N; Asvestas, P

dc.contributor.author	Kechriniotis, AI	en
dc.contributor.author	Delibasis, KK	en
dc.contributor.author	Tsonos, C	en
dc.contributor.author	Assimakis, N	en
dc.contributor.author	Asvestas, P	en
dc.date.accessioned	2014-03-01T02:52:13Z
dc.date.available	2014-03-01T02:52:13Z
dc.date.issued	2009	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/35872
dc.subject	Component	en
dc.subject	Genralized cylinders	en
dc.subject	Parametric objct modeling	en
dc.subject.other	3-D image	en
dc.subject.other	3D image data	en
dc.subject.other	Analytical solutions	en
dc.subject.other	Arbitrary points	en
dc.subject.other	Closed curve	en
dc.subject.other	Closed form solutions	en
dc.subject.other	Controlling parameters	en
dc.subject.other	Gaussian noise	en
dc.subject.other	Generalized cylinders	en
dc.subject.other	Global optimization techniques	en
dc.subject.other	Long bone	en
dc.subject.other	Object modeling	en
dc.subject.other	Parametric equation	en
dc.subject.other	Parametric surfaces	en
dc.subject.other	Surface shape	en
dc.subject.other	Three dimensional curves	en
dc.subject.other	Three-dimensional (3D) image	en
dc.subject.other	Two dimensional images	en
dc.subject.other	Unimodality	en
dc.subject.other	Computer vision	en
dc.subject.other	Cylinders (shapes)	en
dc.subject.other	Gaussian noise (electronic)	en
dc.subject.other	Global optimization	en
dc.subject.other	Imaging systems	en
dc.subject.other	Two dimensional	en
dc.subject.other	Three dimensional	en
dc.title	Towards the mathematic formalization of parametric generalized cylinders and initial results in modeling 3D image data	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1109/IWSSIP.2009.5367736	en
heal.identifier.secondary	http://dx.doi.org/10.1109/IWSSIP.2009.5367736	en
heal.identifier.secondary	5367736	en
heal.publicationDate	2009	en
heal.abstract	Generalized cylinders (GCs) have been proposed in computer vision for object modeling in two dimensional images. However approaches so far have not investigated closed form solutions, based on a formal generic definition that covers every possible family of surfaces. In this work we derive the parametric definition of the torus-like surface that is generated when moving a planar closed curve along a three dimensional curve and provide the analytical solution for the distance of an arbitrary point from the surface. As an application, a family of surfaces that approximate a long bone is selected and analytical parametric equations are derived. The measure of match (MoM) between the parametric surface of GC and a three-dimensional (3D) image is defined, using the previously derived analytic parametric equation. The MoM is sampled along pairs of surface shape controlling parameters and its unimodality is evaluated for synthetic 3D image, under various levels of Gaussian noise. Finally, a global optimization technique is applied to determine shape controlling parameter values to fit the synthetic 3D image data. ©2009 IEEE.	en
heal.journalName	2009 16th International Conference on Systems, Signals and Image Processing, IWSSIP 2009	en
dc.identifier.doi	10.1109/IWSSIP.2009.5367736	en