Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Seeing Behind The Scene: Using Symmetry To Reason About Objects in Cluttered Environments(2017) Ecins, Aleksandrs; Aloimonos, Yiannis; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Rapid advances in robotic technology are bringing robots out of the controlled environments of assembly lines and factories into the unstructured and unpredictable real-life workspaces of human beings. One of the prerequisites for operating in such environments is the ability to grasp previously unobserved physical objects. To achieve this individual objects have to be delineated from the rest of the environment and their shape properties estimated from incomplete observations of the scene. This remains a challenging task due to the lack of prior information about the shape and pose of the object as well as occlusions in cluttered scenes. We attempt to solve this problem by utilizing the powerful concept of symmetry. Symmetry is ubiquitous in both natural and man-made environments. It reveals redundancies in the structure of the world around us and thus can be used in a variety of visual processing tasks. In this thesis we propose a complete pipeline for detecting symmetric objects and recovering their rotational and reflectional symmetries from 3D reconstructions of natural scenes. We begin by obtaining a multiple-view 3D pointcloud of the scene using the Kinect Fusion algorithm. Additionally a voxelized occupancy map of the scene is extracted in order to reason about occlusions. We propose two classes of algorithms for symmetry detection: curve based and surface based. Curve based algorithm relies on extracting and matching surface normal edge curves in the pointcloud. A more efficient surface based algorithm works by fitting symmetry axes/planes to the geometry of the smooth surfaces of the scene. In order to segment the objects we introduce a segmentation approach that uses symmetry as a global grouping principle. It extracts points of the scene that are consistent with a given symmetry candidate. To evaluate the performance of our symmetry detection and segmentation algorithms we construct a dataset of cluttered tabletop scenes with ground truth object masks and corresponding symmetries. Finally we demonstrate how our pipeline can be used by a mobile robot to detect and grasp objects in a house scenario.Item Visual Insight in Geometry(2016) Fletcher, Logan; Carruthers, Peter; Philosophy; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)According to a traditional rationalist proposal, it is possible to attain knowledge of certain necessary truths by means of insight—an epistemic mental act that combines the 'presentational' character of perception with the a priori status usually reserved for discursive reasoning. In this dissertation, I defend the insight proposal in relation to a specific subject matter: elementary Euclidean plane geometry, as set out in Book I of Euclid's Elements. In particular, I argue that visualizations and visual experiences of diagrams allow human subjects to grasp truths of geometry by means of visual insight. In the first two chapters, I provide an initial defense of the geometrical insight proposal, drawing on a novel interpretation of Plato's Meno to motivate the view and to reply to some objections. In the remaining three chapters, I provide an account of the psychological underpinnings of geometrical insight, a task that requires considering the psychology of visual imagery alongside the details of Euclid's geometrical system. One important challenge is to explain how basic features of human visual representations can serve to ground our intuitive grasp of Euclid's postulates and other initial assumptions. A second challenge is to explain how we are able to grasp general theorems by considering diagrams that depict only special cases. I argue that both of these challenges can be met by an account that regards geometrical insight as based in visual experiences involving the combined deployment of two varieties of 'dynamic' visual imagery: one that allows the subject to visually rehearse spatial transformations of a figure's parts, and another that allows the subject to entertain alternative ways of structurally integrating the figure as a whole. It is the interplay between these two forms of dynamic imagery that enables a visual experience of a diagram, suitably animated in visual imagination, to justify belief in the propositions of Euclid’s geometry. The upshot is a novel dynamic imagery account that explains how intuitive knowledge of elementary Euclidean plane geometry can be understood as grounded in visual insight.Item Twist-bulge derivatives and deformations of convex real projective structures on surfaces(2015) Long, Terence Dyer; Wolpert, Scott A; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Let $S$ be a closed orientable surface with genus $g>1$ equipped with a convex $\mathbb{RP}^2$ structure. A basic example of such a convex $\mathbb{RP}^2$ structure on a surface $S$ is the one associated to a hyperbolic structure on $S$, and in this special case Wolpert proved formulas for computing the Lie derivatives $t_{\alpha}l_{\beta}$ and $t_{\gamma}t_{\alpha}l_{\beta}$, where $t_{\alpha}$ is the Fenchel-Nielsen twist vector field associated to the twist along a geodesic $\alpha$, and $l_{*}$ is the hyperbolic geodesic length function. In this dissertation, we extend Wolpert's calculation of $t_{\alpha}l_{\beta}$ and $t_{\gamma}t_{\alpha}l_{\beta}$ in the hyperbolic setting to the case of convex real projective surfaces; in particular, our $t_{\alpha}$ is the twist-bulge vector field along geodesic $\alpha$ coming from the parametrization of the deformation space of convex $\mathbb{RP}^2$ structures on a surface due to Goldman, and our geodesic length function $l_{*}$ is in terms of a generalized cross-ratio in the sense of Labourie. To this end, we use results due to Labourie and Fock-Goncharov on the existence of an equivariant flag curve associated to Hitchin representations, of which convex real projective surfaces are an example. This flag curve allows us to extend the notions arising in the hyperbolic case to that of convex real projective structures and to complete our generalization of Wolpert's formulas.Item Approaches sto Proof in Geometry Textbooks: Comparing Texts from the 1980s and 2000s(2013) Kelley, Genevieve Demos; Edwards, Ann R; Curriculum and Instruction; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Eight American textbooks were studied, four each from the 1980s and the 2000s, with the purpose of identifying differences between the two groups of textbooks in their approaches to teaching proof and proof writing. All of the exercises in each text were coded using parameters established by the author for proofs, types of proof, and other justification and reasoning tasks. Additionally, numbers of proofs in the exposition of each textbook were determined. Thematic analyses of attention to form, presentation of theorems, and introduction to proof and proof writing were also included in the research design. Results suggest both quantifiable and qualitative differences in students' opportunities to engage in and practice proof writing as found in the exercises. Other differences in the newer textbooks include a conjecture-based approach to theorems, greater attention to placing proof in the context of mathematical reasoning, and emphasis on alternatives to the two-column form.Item An Octahedral Tiling on the Ideal Boundary of the Complex Hyperbolic Plane(2006-08-02) Pelzer, Blake Patrick; Schwartz, Richard E; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We present an octahedral tiling on the ideal boundary of the complex hyperbolic plane. The tiling was discovered through the use of a program we wrote called CHAT. We show visual evidence of this tiling and prove some results about embedding a specific tile.Item Structure from Motion on Textures: Theory and Application to Calibration(2005-04-04) Baker, Patrick Terry; Aloimonos, Yiannis J; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation introduces new mathematical constraints that enable us, for the first time, to investigate the correspondence problem using texture rather than point and lines. These three multilinear constraints are formulated on parallel equidistant lines embedded in a plane. We choose these sets of parallel lines as proxies for fourier harmonics embedded on a plane as a sort of ``texture atom''. From these texture atoms we can build up arbitrarily textured surfaces in the world. If we decompose these textures in a Fourier sense rather than as points and lines, we use these new constraints rather than the standard multifocal constraints such as the epipolar or trifocal. We propose some mechanisms for a possible feedback solution to the correspondence problem. As the major application of these constraints, we describe a multicamera calibration system written in C and MATLAB which will be made available to the public. We describe the operation of the program and give some preliminary results.