Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 16, 2009) Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 18, 2009) Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 174-178).

Spatial vision refers to a general class of perceptual capabilities that allows people to see the structure of objects within an image or visual scene. For example, spatial vision underlies people's abilities to discriminate important objects (or so-called "targets") from less important "background" objects. Spatial vision capabilities, however, are not fixed or unaffected by the physical characteristics of the scene objects. Objects with similar shape, color, or size, for example, are more difficult to perceive than objects differing physically from one another. Likewise, targets surrounded by many physically similar background objects are more difficult to perceive than targets silhouetted against uniformly intensity and uncluttered scene areas (Toet, 1996). The capabilities and limitations of visual target perception have been challenging to study scientifically because the number of variations in targets and backgrounds is large, if not intractable. Thus, the determination of causal relationships between physical properties of objects and human perception of those objects has been limited to relatively simple phenomena, such as the minimum size and luminance contrast needed for visual detection. This dissertation was directed at establishing ways to improve the prediction of target perception performance. Specifically, this research was motivated by the idea that contemporary theories of spatial vision, as well as contemporary digital image analysis techniques, may provide a unified means of classifying the physical properties of targets and backgrounds in real-world scenes. If a unified schema exists or can be derived, the functional relationships between perceptual capabilities and the myriad combinations of target and background properties may be understood and predicted better than that allowed by extant visual psychophysical theories. With this objective, the present work begins the examination of using the quantitative stimulus descriptions of visual masking paradigms as a way to develop a framework for understanding target perception; specifically, target detection and recognition of objects in real-world scenes, such as those relevant to military target acquisition. Visual masking is a psychophysical phenomenon that occurs when "noise" or background (i.e., non-information bearing) objects degrade an observer's ability to perceive target (i.e., task-relevant) objects. Masking occurs because the human eye-brain system processes background features in a manner that degrades (masks) the processing of target features. One example of this phenomenon in military operations is camouflage. Camouflage decreases target visibility by masking target structure and intensity. Psychophysical visual masking studies often employ simple (non-real world) targets and masking stimuli, such as one-dimensional spatial frequency patterns (Wilson, 1995; Wilson, McFarlane & Phillips, 1983; Yang & Stevenson, 1998). A one-dimensional spatial frequency pattern usually consists of a sine- or square-wave grating pattern; that is, the luminance variations in the stimuli oscillate across one dimension of spatial extent. These grating patterns are hypothesized to excite the human visual mechanisms responsible for initial encoding and processing of visual scenes. In this manner, the grating patterns represent a simplification of real-world visual scenes, which are at least two-dimensional (i.e., left-right and up-down dimensions) in spatial (and spatial frequency) content. Past psychophysical research has justified the use of one-dimensional spatial frequency patterns on the basis that more realistic two-dimensional patterns require extensive computational resources. However, with today's affordable computing machines, researchers can implement methodologies readily to explore and exploit the two-dimensional nature of visual imagery, especially the perception of digital images. To begin investing two-dimensional visual processes in target acquisition, it is necessary to establish the existence and functional characteristics of two-dimensional masking phenomena. This dissertation first discusses a preliminary effort to establish a methodology to glean some information on two-dimensional masking effects. Specifically, Experiment 1 provided direct evidence for the existence of masking in the two-dimensional spatial frequency domain. Experiment 2 then demonstrated some functional effects on real-world target perception due to deliberate suppression of selected two-dimensional spatial frequency structure. Lastly, Experiments 3 and 4 extended the findings of the first two experiments using real-world targets and backgrounds. The findings of this dissertation extend existing knowledge on visual masking phenomena into the realm of two-dimensional spatial frequency targets and masking fields, as well as provide a foundation for designing and interpreting more advanced studies of two-dimensional spatial frequency masking effects that may moderate visual target acquisition performance. / Ph. D.

Master of Science / Department of Mathematics / Diego M. Maldonado / In this work we present the main concepts of Fourier Analysis (such as Fourier series, Fourier transforms, Parseval and Plancherel identities, correlation, and convolution) and illustrate them by means of examples and applications. Most of the concepts presented here can be found in the book "A First Course in Fourier Analysis" by David W.Kammler. Similarly, the examples correspond to over 15 problems posed in the same book which have been completely worked out in this report. As applications, we include Fourier's original approach to the heat flow using Fourier series and an application to filtering one-dimensional signals.

While research into improving data quality from analytical instrumentation has gone on for decades, only recently has research been done to improve information extraction methods. One of these methods, correlation analysis, is based upon the shifting of one function relative to another and determining a correlation value for each displacement. The cross correlation algorithm allows one to compare two files and find the similarities that exist, the convolution operation combines two functions two dimensionally (e.g. any input into an analytical instrument convolves with that instrument response to give the output) and deconvolution separates functions that have convolved together. In correlation chromatography, multiple injections are made into a chromatograph at a rate which overlaps the instrument response to each injection. Injection intervals must be set to be as random as possible within limits set by peak widths and number. When the input pattern representation is deconvolved from the resulting output, the effect of that input is removed to give the instrument response to one injection. Since the operation averages all the information in the output, random noise is diminished and signal-to-noise ratios are enhanced. The most obvious application of correlation chromatography is in trace analysis. Signal-to-noise enhancements may be maximized by treating the output data (for example, with a baseline subtraction) before the deconvolution operation. System nonstationarities such as injector nonreproducibility and detector drift cause baseline or "correlation" noise, which limit attainable signal-to-noise enhancements to about half of what is theoretically possible. Correlation noise has been used to provide information about changes in system conditions. For example, a given concentration change that occurs over the course of a multiple injection sequence causes a reproducible correlation noise pattern; doubling the concentration change will double the amplitude of each point in the noise pattern. This correlation noise is much more amenable to computer analysis and, since it is still the result of signal averaging, the effect of random fluctuations and noise is reduced. A method for simulating conventional coupled column separations by means of time domain convolution of chromatograms from single column separations is presented.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1980. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaf 28).

University of Macau / Faculty of Science and Technology / Department of Computer and Information Science

University of Macau / Faculty of Science and Technology / Department of Mathematics