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
Semantic image segmentation has been a key topic in applications involving image processing and computer vision. Owing to the success and continuous research in the field of deep learning, there have been plenty of deep learning-based segmentation architectures that have been designed for various tasks. In this thesis, deep-learning architectures for a specific application in material science; namely the segmentation process for the non-destructive study of the microstructure of Aluminum Alloy AA 7075 have been developed. This process requires the use of various imaging tools and methodologies to obtain the ground-truth information. The image dataset obtained using Transmission X-ray microscopy (TXM) consists of raw 2D image specimens captured from the projections at every beam scan. The segmented 2D ground-truth images are obtained by applying reconstruction and filtering algorithms before using a scientific visualization tool for segmentation. These images represent the corrosive behavior caused by the precipitates and inclusions particles on the Aluminum AA 7075 alloy. The study of the tools that work best for X-ray microscopy-based imaging is still in its early stages.
In this thesis, the underlying concepts behind Convolutional Neural Networks (CNNs) and state-of-the-art Semantic Segmentation architectures have been discussed in detail. The data generation and pre-processing process applied to the AA 7075 Data have also been described, along with the experimentation methodologies performed on the baseline and four other state-of-the-art Segmentation architectures that predict the segmented boundaries from the raw 2D images. A performance analysis based on various factors to decide the best techniques and tools to apply Semantic image segmentation for X-ray microscopy-based imaging was also conducted.
In this thesis, the underlying concepts behind Convolutional Neural Networks (CNNs) and state-of-the-art Semantic Segmentation architectures have been discussed in detail. The data generation and pre-processing process applied to the AA 7075 Data have also been described, along with the experimentation methodologies performed on the baseline and four other state-of-the-art Segmentation architectures that predict the segmented boundaries from the raw 2D images. A performance analysis based on various factors to decide the best techniques and tools to apply Semantic image segmentation for X-ray microscopy-based imaging was also conducted.
ContributorsBarboza, Daniel (Author) / Turaga, Pavan (Thesis advisor) / Chawla, Nikhilesh (Committee member) / Jayasuriya, Suren (Committee member) / Arizona State University (Publisher)
Created2020