dc.contributor.advisor | Owren, Brynjulf | nb_NO |
dc.contributor.author | Viddal, Per Martin | nb_NO |
dc.date.accessioned | 2014-12-19T13:58:09Z | |
dc.date.available | 2014-12-19T13:58:09Z | |
dc.date.created | 2010-09-04 | nb_NO |
dc.date.issued | 2009 | nb_NO |
dc.identifier | 348861 | nb_NO |
dc.identifier | ntnudaim:4519 | nb_NO |
dc.identifier.uri | http://hdl.handle.net/11250/258526 | |
dc.description.abstract | A preliminary study of the papers ``A Cortical Based Model of Perceptual Completion in the Roto-Translation Space'' and ``Minimal Surfaces in the Roto-Translation Group with Applications to a Neuro-Biological Image Completion Model'' is done. The first one, written by Citti and Sarti, describe a perceptual completion model where a part of the visual cortex is modelled using a sub-Riemannian geometry on the Lie group SE(2). The second one, written by Hladky and Pauls, describe a model which completes the interior of a circular hole by spanning the lifted boundary by a minimal surface, presuming such a surface exists. These surfaces are solutions of occluded visual data as described by Citti and Sarti. Based on the models above, we propose a new model. The lifted boundary of an arbitrary hole is spanned by a surface consisting of geodesics between points with matching Dirichlet boundary values. All the three models are based on the sub-Riemannian geometry for the roto-translational space introduced by Citti and Sarti. The basic theory of sub-Riemannian geometries, including the derivation of some flows and operators in this degenerate space, is described. The models are implemented, and numerical results are presented. | nb_NO |
dc.language | eng | nb_NO |
dc.publisher | Institutt for matematiske fag | nb_NO |
dc.subject | ntnudaim | no_NO |
dc.subject | SIF3 fysikk og matematikk | no_NO |
dc.subject | Industriell matematikk | no_NO |
dc.title | Minimal Surfaces in Sub-Riemannian Geometries with Applications to Perceptual Completion | nb_NO |
dc.type | Master thesis | nb_NO |
dc.source.pagenumber | 62 | nb_NO |
dc.contributor.department | Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag | nb_NO |