Thesis advisor: Martin Bridgeman / We begin this dissertation by studying the relationship between the Poincaré metric of a simply connected domain Ω ⊂ ℂ and the geometry of Dome(Ω), the boundary of the convex hull of its complement. Sullivan showed that there is a universal constant K[subscript]eq[subscript] such that one may find a conformally natural K[subscript]eq[subscript]-quasiconformal map from Ω to Dome(Ω) which extends to the identity on ∂Ω. Explicit upper and lower bounds on K[subscript]eq[subscript] have been obtained by Epstein, Marden, Markovic and Bishop. We improve upon these upper bounds by showing that one may choose K[subscript]eq[subscript] ≤ 7.1695. As part of this work, we provide stronger criteria for embeddedness of pleated planes. In addition, for Kleinian groups Γ where N = ℍ³/Γ has incompressible boundary, we give improved bounds for the average bending on the convex core of N and the Lipschitz constant for the homotopy inverse of the nearest point retraction. In the second part of this dissertation, we prove an extension of Basmajian's identity to n-Hitchin representations of compact bordered surfaces. For 3-Hitchin representations, we provide a geometric interpretation of this identity analogous to Basmajian's original result. As part of our proof, we demonstrate that for a closed surface, the Lebesgue measure on the Frenet curve of an n-Hitchin representation is zero on the limit set of any incompressible subsurface. This generalizes a classical result in hyperbolic geometry. In our final chapter, we prove the Bridgeman-Kahn identity for all finite volume hyperbolic n-manifolds with totally geodesic boundary. As part of this work, we correct a commonly referenced expression of the volume form on the unit tangent bundle of ℍⁿ in terms of the geodesic end point parametrization. / Thesis (PhD) — Boston College, 2016. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Thesis (Nav.Arch and S.M.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1975. / Includes bibliographical references. / Nav.Arch and S.M.

Classification learning is dominated by systems which induce large numbers of small axis-orthogonal decision surfaces. This strongly biases such systems towards particular hypothesis types but there is reason believe that many domains have underlying concepts which do not involve axis orthogonal surfaces. Further, the multiplicity of small decision regions mitigates against any holistic appreciation of the theories produced by these systems, notwithstanding the fact that many of the small regions are individually comprehensible. This thesis investigates modeling concepts as large geometric structures in n-dimensional space. Convex hulls are a superset of the set of axis orthogonal hyperrectangles into which axis orthogonal systems partition the instance space. In consequence, there is reason to believe that convex hulls might provide a more flexible and general learning bias than axis orthogonal regions. The formation of convex hulls around a group of points of the same class is shown to be a usable generalisation and is more general than generalisations produced by axis-orthogonal based classifiers, without constructive induction, like decision trees, decision lists and rules. The use of a small number of large hulls as a concept representation is shown to provide classification performance which can be better than that of classifiers which use a large number of small fragmentary regions for each concept. A convex hull based classifier, CH1, has been implemented and tested. CH1 can handle categorical and continuous data. Algorithms for two basic generalisation operations on hulls, inflation and facet deletion, are presented. The two operations are shown to improve the accuracy of the classifier and provide moderate classification accuracy over a representative selection of typical, largely or wholly continuous valued machine learning tasks. The classifier exhibits superior performance to well-known axis-orthogonal-based classifiers when presented with domains where the underlying decision surfaces are not axis parallel. The strengths and weaknesses of the system are identified. One particular advantage is the ability of the system to model domains with approximately the same number of structures as there are underlying concepts. This leads to the possibility of extraction of higher level mathematical descriptions of the induced concepts, using the techniques of computational geometry, which is not possible from a multiplicity of small regions.

Recovering a volumetric model of a person, car, or other object of interest from a single snapshot would be useful for many computer graphics applications. 3D model estimation in general is hard, and currently requires active sensors, multiple views, or integration over time. For a known object class, however, 3D shape can be successfully inferred from a single snapshot. We present a method for generating a ``virtual visual hull''-- an estimate of the 3D shape of an object from a known class, given a single silhouette observed from an unknown viewpoint. For a given class, a large database of multi-view silhouette examples from calibrated, though possibly varied, camera rigs are collected. To infer a novel single view input silhouette's virtual visual hull, we search for 3D shapes in the database which are most consistent with the observed contour. The input is matched to component single views of the multi-view training examples. A set of viewpoint-aligned virtual views are generated from the visual hulls corresponding to these examples. The 3D shape estimate for the input is then found by interpolating between the contours of these aligned views. When the underlying shape is ambiguous given a single view silhouette, we produce multiple visual hull hypotheses; if a sequence of input images is available, a dynamic programming approach is applied to find the maximum likelihood path through the feasible hypotheses over time. We show results of our algorithm on real and synthetic images of people.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, December 2003. / Thesis advisor(s): Fotis Papoulias. Includes bibliographical references (p. 73). Also available online.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, December 2003. / Thesis advisor(s): Fotis Papoulias. Includes bibliographical references (p. 67-69). Also available online.

We describe our overall approach to building robot vision systems, and the conceptual systems architecture as a network of agents, which run in parallel, and cooperate to achieve the system’s goals. We present the current state of the 3D Feature-Based Tracker, a robot vision system for tracking and segmenting the 3D motion of objects using image input from a calibrated stereo pair of video cameras. The system runs in a multi-level cycle of prediction and verification or correction. The currently modelled 3D positions and velocities of the feature points are extrapolated a short time into the future to yield predictions of 3D position. These 3D predictions are projected into the two stereo views, and are used to guide a fast and highly focused visual search for the feature points. The image positions at which the features are re-acquired are back-projected in 3D space in order to update the 3D positions and velocities. At a higher level, features are dynamically grouped into clusters with common 3D motion. Predictions from the cluster level can be fed to the lower level to correct errors in the point-wise tracking.

Recovering a volumetric model of a person, car, or other objectof interest from a single snapshot would be useful for many computergraphics applications. 3D model estimation in general is hard, andcurrently requires active sensors, multiple views, or integration overtime. For a known object class, however, 3D shape can be successfullyinferred from a single snapshot. We present a method for generating a``virtual visual hull''-- an estimate of the 3D shape of an objectfrom a known class, given a single silhouette observed from an unknownviewpoint. For a given class, a large database of multi-viewsilhouette examples from calibrated, though possibly varied, camerarigs are collected. To infer a novel single view input silhouette'svirtual visual hull, we search for 3D shapes in the database which aremost consistent with the observed contour. The input is matched tocomponent single views of the multi-view training examples. A set ofviewpoint-aligned virtual views are generated from the visual hullscorresponding to these examples. The 3D shape estimate for the inputis then found by interpolating between the contours of these alignedviews. When the underlying shape is ambiguous given a single viewsilhouette, we produce multiple visual hull hypotheses; if a sequenceof input images is available, a dynamic programming approach isapplied to find the maximum likelihood path through the feasiblehypotheses over time. We show results of our algorithm on real andsynthetic images of people.

Thesis (Masters Diploma (Mechanical Engineering)) -- Cape Technikon, Cape Town,1996 / A need exists whereby the preliminary power requirement of a ship can be rapidly estimated. Because the majority of methods available for this purpose are manual and consist of a number of independent components, they are tedious and time consuming to use. With the advent of the personal computer and its widespread acceptance, it was logical to examine the various components involved to determine their suitability for computerisation and general accuracy. In total eleven hull resistance prediction methods were examined, eight of which were computerised. Model test data of four vessels were used to evaluate these eight programs. The methodproviding the best results was selected to form the core of an integrated Power Prediction program. Factors such as appendage resistance, fouling and hull roughness were examined and appropriate methods selected for inclusion into the integrated program. Various propeller series were examined and evaluated against a variety of examples and model data. Two propeller optimisation programs were written and a general method for determining the optimum characteristics from Kr-KQ polynomials is described. Methods for determining propulsion coefficients were examined and their results compared with those obtained from model tests. The method providing the best overall results was incorporated into the Power Prediction program Added resistance due to sea state was broken down into two components, namely wind and wave resistance. Only the head sea and wind conditions were considered. Various methods for estimating wind resistance were examined and a program developed capable of providing resistance estimates regardless of wind direction. The problem of added resistance due to waves was examined and two programs written around the methods examined. To facilitate prediction estimates, sea state was chosen as the prime function. Wave height is estimated for the appropriate sea state and wind speed in turn from the wave height Actual sea trial data ofa twin screw channel ship is used to determine the overall accuracy ofthe Power Prediction Program

An investigation was directed at determining whether the Submarine Control System Test Vehicle (CSTV), could be used as the underwater hull for the Monoform (a small waterplane area ship). Hydrostatic and static stability considerations formed a basis for obtaining an optimum strut configuration for the hull. Two hull forms were. considered. The model was scaled to a 2000-ton prototype to obtain the necessary geometry for a full scale vessel. Two computer programs were developed and are outlined together with the derived formulae used in them. Stability curves help establish the design's conformance with requirements laid down by the US Navy. The results indicate that not only could the CSTV be effectively used as the underwater hull for the Monoform but also that the chosen design exhibits exceptionally good stability characteristics. A set of model experiments designed to assess the Monoform's performance in calm water and waves (seakeeping) as well as to ascertain the speed-power relationships are also recommended in this report. / M.S.