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The flag of best fit as a representative for a collection of linear subspaces

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dc.contributor.authorMarrinan, Timothy P., author
dc.contributor.authorKirby, Michael, advisor
dc.contributor.authorBates, Dan, committee member
dc.contributor.authorDraper, Bruce, committee member
dc.contributor.authorPeterson, Chris, committee member
dc.date.accessioned2007-01-03T06:11:31Z
dc.date.available2007-01-03T06:11:31Z
dc.date.issued2013
dc.description.abstractThis thesis will develop a technique for representing a collection of subspaces with a flag of best fit, and apply it to practical problems within computer vision and pattern analysis. In particular, we will find a nested sequence of subspaces that are central, with respect to an optimization criterion based on the projection Frobenius norm, to a set of points in the disjoint union of a collection of Grassmann manifolds. Referred to as the flag mean, this sequence can be computed analytically. Three existing subspace means in the literature, the Karcher mean, the extrinsic manifold mean, and the L2-median, will be discussed to determine the need and relevance of the flag mean. One significant point of separation between the flag mean and existing means is that the flag mean can be computed for points that lie on different Grassmann manifolds, under certain constraints. Advantages of this distinction will be discussed. Additionally, results of experiments based on data from DARPA's Mind's Eye Program will be compared between the flag mean and the Karcher mean. Finally, distance measures for comparing flags to other flags, and similarity scores for comparing flags to subspaces will be discussed and applied to the Carnegie Mellon University, 'Pose, Illumination, and Expression' database.
dc.format.mediumborn digital
dc.format.mediummasters theses
dc.identifierMarrinan_colostate_0053N_12038.pdf
dc.identifierETDF2013500397MATH
dc.identifier.urihttp://hdl.handle.net/10217/81042
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectflag manifold
dc.subjectflag mean
dc.subjectGrassmann manifold
dc.subjectKarcher mean
dc.subjectsubspace average
dc.subjectSVD
dc.titleThe flag of best fit as a representative for a collection of linear subspaces
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (M.S.)

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