Extensions of the Formlet Model of Planar Shape

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dc.contributor.advisorElder, James
dc.creatorYakubovich, Alexander
dc.date.accessioned2015-08-28T15:00:11Z
dc.date.available2015-08-28T15:00:11Z
dc.date.copyright2014-10-10
dc.date.issued2015-08-28
dc.date.updated2015-08-28T15:00:10Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelMaster's
dc.degree.nameMA - Master of Arts
dc.description.abstractThis thesis addresses the problem of shape representation using the GRID/formlet theory, a system based on localized diffeomorphisms. While this framework enjoys many desirable properties, it suffers from several limitations: it converges slowly for shapes with elongated parts, and it can be sensitive to parameterization as well as grossly ill-conditioned. Several innovations are proposed to address these problems: 1) The formlet basis is generalized to include oriented deformation, improving convergence for elongated parts. 2) A recent contour remapping method is applied in order to eliminate problems due to drift of the model parameterization during matching pursuit. 3) A regularizing term is introduced in order to limit redundancy in formlet parameters and improve the model’s identifiability. Finally, an algorithm is proposed to hierarchically cluster formlets, and is shown to induce a partial ordering on the representation.
dc.identifier.urihttp://hdl.handle.net/10315/29908
dc.language.isoen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectStatistics
dc.subjectApplied mathematics
dc.subject.keywordsShape
dc.subject.keywordsPlanar shape
dc.subject.keywordsShape analysis
dc.subject.keywordsShape representation
dc.subject.keywordsShape matching
dc.subject.keywordsShape recognition
dc.subject.keywordsDeformation
dc.subject.keywordsSparse coding
dc.subject.keywordsContour completion
dc.subject.keywordsImage representation
dc.subject.keywordsDeformable models
dc.subject.keywordsGenerative models
dc.subject.keywordsTopology
dc.titleExtensions of the Formlet Model of Planar Shape
dc.typeElectronic Thesis or Dissertationen_US

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