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Efficient Statistical Methods for 3D Shape Inference
, 2008
"... Visual inference is a complex and ambiguous problem, and these properties have presented a significant obstacle to developing effective algorithms for many visual tasks. In this thesis, I begin by developing a methodology for statistical inference that is particularly suited for the complex tasks of ..."
Abstract

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Visual inference is a complex and ambiguous problem, and these properties have presented a significant obstacle to developing effective algorithms for many visual tasks. In this thesis, I begin by developing a methodology for statistical inference that is particularly suited for the complex tasks of visual perception. The approach is based on Belief Propagation, a highly successful inference technique that has lead to notable progress in a number of statistical inference applications. Unfortunately, the computational complexity of belief propagation allows it to be applied to only fairly simple statistical distributions, thus excluding many of the rich statistical problems encountered in computer vision. In this thesis, I introduce a new technique to reduce the computational complexity of belief propagation from exponential to linear in the clique size of the underlying graphical model. These advancements allow us to efficiently solve inference problems that were previously intractable. I then apply this methodology to several visual tasks. In one example, I develop a statistical approach to the problem of estimating 3D shape from
Computer Landscape Generation and Smoothing Masters Comprehensive Exam
"... Due to the prevalence of 3Daccelerated graphics cards in modern computers, the ability to create heightened realism in computer graphics has become more important. Computer landscapes are important in many different fields of computer graphics such as gaming and simulation. Height maps are mentione ..."
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Due to the prevalence of 3Daccelerated graphics cards in modern computers, the ability to create heightened realism in computer graphics has become more important. Computer landscapes are important in many different fields of computer graphics such as gaming and simulation. Height maps are mentioned as a method of using real world data to construct a landscape. Various fractal methods of creating landscapes are also investigated including fractional Brownian motion and recursive subdivision methods such as triangularedge, diamondsquare, and squaresquare subdivision. Often the generated landscape is too jagged for a particular application, so various smoothing methods are investigated. The landscape height matrix can also be viewed as a set of pixel intensities for an image. As such, image filtering techniques such as Fourier and wavelet analysis can be used to process the image. Other methods include erosion simulation, polynomial interpolation, Bézier curves, Bsplines, and Bézier patches. Results of four of these methods are analyzed for their effective smoothness. 1