Texture synthesis and nonparametric resampling of random fields

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dc.creatorLevina, Elizaveta
dc.creatorBickel, Peter J.
dc.date2006-11-09
dc.date.accessioned2026-07-07T08:08:22Z
dc.date.available2026-07-07T08:08:22Z
dc.descriptionThis paper introduces a nonparametric algorithm for bootstrapping a stationary random field and proves certain consistency properties of the algorithm for the case of mixing random fields. The motivation for this paper comes from relating a heuristic texture synthesis algorithm popular in computer vision to general nonparametric bootstrapping of stationary random fields. We give a formal resampling scheme for the heuristic texture algorithm and prove that it produces a consistent estimate of the joint distribution of pixels in a window of certain size under mixing and regularity conditions on the random field. The joint distribution of pixels is the quantity of interest here because theories of human perception of texture suggest that two textures with the same joint distribution of pixel values in a suitably chosen window will appear similar to a human. Thus we provide theoretical justification for an algorithm that has already been very successful in practice, and suggest an explanation for its perceptually good results.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053606000000588 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0611258
dc.identifierhttp://arxiv.org/abs/math/0611258
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 4, 1751-1773
dc.identifierdoi:10.1214/009053606000000588
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131238
dc.subjectStatistics Theory
dc.subject62M40 (Primary) 62G09 (Secondary)
dc.titleTexture synthesis and nonparametric resampling of random fields
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