The transformation of one-dimensional and two-dimensional autoregressive random fields under coordinate scaling and rotation

dc.contributor.authorKennedy, Ian Douglas
dc.date.accessioned2008-11-05T20:30:22Z
dc.date.available2008-11-05T20:30:22Z
dc.date.issued2008-11-05T20:30:22Z
dc.date.submitted2008
dc.description.abstractA practical problem in computer graphics is that of representing a textured surface at arbitrary scales. I consider the underlying mathematical problem to be that of interpolating autoregressive random fields under arbitrary coordinate transformations. I examine the theoretical basis for the transformations that autoregressive parameters exhibit when the associated stationary random fields are scaled or rotated. The basic result is that the transform takes place in the continuous autocovariance domain, and that the spectral density and associated autoregressive parameters proceed directly from sampling the continuous autocovariance on a transformed grid. I show some real-world applications of these ideas, and explore how they allow us to interpolate into a random field. Along the way, I develop interesting ways to estimate simultaneous autoregressive parameters, to calculate the distorting effects of linear interpolation algorithms, and to interpolate random fields without altering their statistics.en
dc.identifier.urihttp://hdl.handle.net/10012/4110
dc.language.isoenen
dc.pendingfalseen
dc.publisherUniversity of Waterlooen
dc.subjectautoregressiveen
dc.subjectrandom fielden
dc.subject.programSystem Design Engineeringen
dc.titleThe transformation of one-dimensional and two-dimensional autoregressive random fields under coordinate scaling and rotationen
dc.typeMaster Thesisen
uws-etd.degreeMaster of Applied Scienceen
uws-etd.degree.departmentSystems Design Engineeringen
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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