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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Computational Modeling and Analysis of Symmetry in Human Movements

Description
Human movement is a complex process influenced by physiological and psychological factors. The execution of movement is varied from person to person, and the number of possible strategies for completing a specific movement task is almost infinite. Different choices of strategies can be perceived by humans as having different degrees…

Human movement is a complex process influenced by physiological and psychological factors. The execution of movement is varied from person to person, and the number of possible strategies for completing a specific movement task is almost infinite. Different choices of strategies can be perceived by humans as having different degrees of quality, and the quality can be defined with regard to aesthetic, athletic, or health-related ratings. It is useful to measure and track the quality of a person's movements, for various applications, especially with the prevalence of low-cost and portable cameras and sensors today. Furthermore, based on such measurements, feedback systems can be designed for people to practice their movements towards certain goals. In this dissertation, I introduce symmetry as a family of measures for movement quality, and utilize recent advances in computer vision and differential geometry to model and analyze different types of symmetry in human movements. Movements are modeled as trajectories on different types of manifolds, according to the representations of movements from sensor data. The benefit of such a universal framework is that it can accommodate different existing and future features that describe human movements. The theory and tools developed in this dissertation will also be useful in other scientific areas to analyze symmetry from high-dimensional signals.
ContributorsWang, Qiao (Author) / Turaga, Pavan (Thesis advisor) / Spanias, Andreas (Committee member) / Srivastava, Anuj (Committee member) / Sha, Xin Wei (Committee member) / Arizona State University (Publisher)
Created2018
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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…

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