Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- Creators: Turaga, Pavan
Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms
Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximumentropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021
Description
The depth richness of a scene translates into a spatially variable defocus blur in the acquired image. Blurring can mislead computational image understanding; therefore, blur detection can be used for selective image enhancement of blurred regions and the application of image understanding algorithms to sharp regions. This work focuses on blur detection and its application to image enhancement.
This work proposes a spatially-varying defocus blur detection based on the quotient of spectral bands; additionally, to avoid the use of computationally intensive algorithms for the segmentation of foreground and background regions, a global threshold defined using weak textured regions on the input image is proposed. Quantitative results expressed in the precision-recall space as well as qualitative results overperform current state-of-the-art algorithms while keeping the computational requirements at competitive levels.
Imperfections in the curvature of lenses can lead to image radial distortion (IRD). Computer vision applications can be drastically affected by IRD. This work proposes a novel robust radial distortion correction algorithm based on alternate optimization using two cost functions tailored for the estimation of the center of distortion and radial distortion coefficients. Qualitative and quantitative results show the competitiveness of the proposed algorithm.
Blur is one of the causes of visual discomfort in stereopsis. Sharpening applying traditional algorithms can produce an interdifference which causes eyestrain and visual fatigue for the viewer. A sharpness enhancement method for stereo images that incorporates binocular vision cues and depth information is presented. Perceptual evaluation and quantitative results based on the metric of interdifference deviation are reported; results of the proposed algorithm are competitive with state-of-the-art stereo algorithms.
Digital images and videos are produced every day in astonishing amounts. Consequently, the market-driven demand for higher quality content is constantly increasing which leads to the need of image quality assessment (IQA) methods. A training-free, no-reference image sharpness assessment method based on the singular value decomposition of perceptually-weighted normalized-gradients of relevant pixels in the input image is proposed. Results over six subject-rated publicly available databases show competitive performance when compared with state-of-the-art algorithms.
This work proposes a spatially-varying defocus blur detection based on the quotient of spectral bands; additionally, to avoid the use of computationally intensive algorithms for the segmentation of foreground and background regions, a global threshold defined using weak textured regions on the input image is proposed. Quantitative results expressed in the precision-recall space as well as qualitative results overperform current state-of-the-art algorithms while keeping the computational requirements at competitive levels.
Imperfections in the curvature of lenses can lead to image radial distortion (IRD). Computer vision applications can be drastically affected by IRD. This work proposes a novel robust radial distortion correction algorithm based on alternate optimization using two cost functions tailored for the estimation of the center of distortion and radial distortion coefficients. Qualitative and quantitative results show the competitiveness of the proposed algorithm.
Blur is one of the causes of visual discomfort in stereopsis. Sharpening applying traditional algorithms can produce an interdifference which causes eyestrain and visual fatigue for the viewer. A sharpness enhancement method for stereo images that incorporates binocular vision cues and depth information is presented. Perceptual evaluation and quantitative results based on the metric of interdifference deviation are reported; results of the proposed algorithm are competitive with state-of-the-art stereo algorithms.
Digital images and videos are produced every day in astonishing amounts. Consequently, the market-driven demand for higher quality content is constantly increasing which leads to the need of image quality assessment (IQA) methods. A training-free, no-reference image sharpness assessment method based on the singular value decomposition of perceptually-weighted normalized-gradients of relevant pixels in the input image is proposed. Results over six subject-rated publicly available databases show competitive performance when compared with state-of-the-art algorithms.
ContributorsAndrade Rodas, Juan Manuel (Author) / Spanias, Andreas (Thesis advisor) / Turaga, Pavan (Thesis advisor) / Abousleman, Glen (Committee member) / Li, Baoxin (Committee member) / Arizona State University (Publisher)
Created2019