Degree Type

Dissertation

Date of Award

1993

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Noel A. C. Cressie

Second Advisor

Jennifer L. Davidson

Abstract

This dissertation investigates the use of spatial dependence models to solve problems in image analysis and multivariate geoStatistics and Probability;;In Paper I, a statistical theory, and an algorithm, is presented to identify one-pixel-wide closed object boundaries in gray-scale images. Closed boundary identification is an important problem because boundaries of objects are major features in images. In spite of this, most statistical approaches to image restoration and texture identification place inappropriate stationary model assumptions on the image domain. One way to characterize the structural components present in images is to identify one-pixel-wide closed boundaries that delineate objects. By defining a prior probability model on the space of one-pixel-wide closed boundary configurations and appropriately specifying transition probability functions on this space, a Markov chain Monte Carlo algorithm is constructed that theoretically converges to a statistically optimal closed boundary estimate. Moreover, this approach ensures that any approximation to the statistically optimal boundary estimate will have the necessary property of closure;In Paper II, a Bayesian statistical theory and algorithm based on image segmentation models is presented to identify objects in gray-scale and colored images. Image segmentation algorithms necessitate a priori knowledge of the maximum number of labels to use and estimates of label class parameters. An estimate of these parameters and an initial labeling of the image is obtained using a modified image segmentation algorithm. Then, a Bayesian Markov chain Monte Carlo algorithm is combined with a morphological algorithm to obtain sets of edge pixels that define closed object boundaries;In Paper III, the properties of multivariate spatial prediction under a special class of multivariate spatial dependence models is analyzed. More specifically, the usefulness of covariate information in cokriging is considered under the assumption of multivariate intrinsic coregionalization. It is found that, under the assumption of intrinsic coregionalization with observations available on all components at each sample location, the large-scale parameter space for uniform unbiasedness determines the allowable values for the covariate cokriging weights. An illustration is given using a data set of plutonium and americium concentrations collected from a region of the Nevada Test Site.

DOI

https://doi.org/10.31274/rtd-180813-10035

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Jeffrey Donald Helterbrand

Language

en

Proquest ID

AAI9413982

File Format

application/pdf

File Size

300 pages

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