Show simple item record

dc.contributor.authorHefny, Mohamed Salahaldinen
dc.date2014-01-30 09:49:03.293
dc.date.accessioned2014-01-30T16:33:47Z
dc.date.available2014-01-30T16:33:47Z
dc.date.issued2014-01-30
dc.identifier.urihttp://hdl.handle.net/1974/8597
dc.descriptionThesis (Ph.D, Computing) -- Queen's University, 2014-01-30 09:49:03.293en
dc.description.abstractDiscrete shapes can be described and analyzed using Lie groups, which are mathematical structures having both algebraic and geometrical properties. These structures, borrowed from mathematical physics, are both algebraic groups and smooth manifolds. A key property of a Lie group is that a curved space can be studied, using linear algebra, by local linearization with an exponential map. Here, a discrete shape was a Euclidean-invariant computer representation of an object. Highly variable shapes are known to exist in non-linear spaces where linear analysis tools, such as Pearson's decomposition of principal components, are inadequate. The novel method proposed herein represented a shape as an ensemble of homogenous matrix transforms. The Lie group of homogenous transforms has elements that both represented a local shape and acted as matrix operators on other local shapes. For the manifold, a matrix transform was found to be equivalent to a vector transform in a linear space. This combination of representation and linearization gave a simple implementation for solving a computationally expensive problem. Two medical datasets were analyzed: 2D contours of femoral head-neck cross-sections and 3D surfaces of proximal femurs. The Lie-group method outperformed the established principal-component analysis by capturing higher variability with fewer components. Lie groups are promising tools for medical imaging and data analysis.en
dc.language.isoengen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectStatistical Shape Analysisen
dc.subjectLie Groupsen
dc.titleAnalysis of Discrete Shapes Using Lie Groupsen
dc.typethesisen
dc.description.degreePhDen
dc.contributor.supervisorEllis, Randy E.en
dc.contributor.departmentComputingen
dc.degree.grantorQueen's University at Kingstonen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record