This paper presents an image-based rendering system using algebraic relations between different views of an object. The system uses pictures of an object taken from known positions. Given three such images it can generate "virtual'' ones as the object would look from any position near the ones that the two input images were taken from. The extrapolation from the example images can be up to about 60 degrees of rotation. The system is based on the trilinear constraints that bind any three view so fan object. As a side result, we propose two new methods for camera calibration. We developed and used one of them. We implemented the system and tested it on real images of objects and faces. We also show experimentally that even when only two images taken from unknown positions are given, the system can be used to render the object from other view points as long as we have a good estimate of the internal parameters of the camera used and we are able to find good correspondence between the example images. In addition, we present the relation between these algebraic constraints and a factorization method for shape and motion estimation. As a result we propose a method for motion estimation in the special case of orthographic projection.

Thesis (Ph.D.) - University of Queensland, 2006. / Includes bibliography.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 1997. / Includes bibliographical references. Also available on the Internet.

This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the <em>q</em>-Kneser graph are the <em>k</em>-dimensional subspaces of a vector space of dimension <em>v</em> over F_<em>q</em>, and two <em>k</em>-subspaces are adjacent if they have trivial intersection. The new results in this thesis involve colouring the <em>q</em>-Kneser graph when <em>k</em>=2. There are two cases. When <em>k</em>=2 and <em>v</em>=4, the chromatic number is <em>q</em>²+<em>q</em>. If <em>k</em>=2 and <em>v</em>>4, the chromatic number is (<em>q</em>^(v-1)-1)/(<em>q</em>-1). In both cases, we characterise the minimal colourings. We develop some theory for colouring the <em>q</em>-Kneser graph in general.

We will discuss three ways to bound the chromatic number on a Cayley graph. 1. If the connection set contains information about a smaller graph, then these two graphs are related. Using this information, we will show that Cayley graphs cannot have chromatic number three. 2. We will prove a general statement that all vertex-transitive maximal triangle-free graphs on <i>n</i> vertices with valency greater than <i>n</i>/3 are 3-colourable. Since Cayley graphs are vertex-transitive, the bound of general graphs also applies to Cayley graphs. 3. Since Cayley graphs for abelian groups arise from vector spaces, we can view the connection set as a set of points in a projective geometry. We will give a characterization of all large complete caps, from which we derive that all maximal triangle-free cubelike graphs on 2ⁿ vertices and valency greater than 2ⁿ/4 are either bipartite or 4-colourable.

This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the <em>q</em>-Kneser graph are the <em>k</em>-dimensional subspaces of a vector space of dimension <em>v</em> over F_<em>q</em>, and two <em>k</em>-subspaces are adjacent if they have trivial intersection. The new results in this thesis involve colouring the <em>q</em>-Kneser graph when <em>k</em>=2. There are two cases. When <em>k</em>=2 and <em>v</em>=4, the chromatic number is <em>q</em>²+<em>q</em>. If <em>k</em>=2 and <em>v</em>>4, the chromatic number is (<em>q</em>^(v-1)-1)/(<em>q</em>-1). In both cases, we characterise the minimal colourings. We develop some theory for colouring the <em>q</em>-Kneser graph in general.

Remotely operated vehicle (ROV) dynamics is affected by hydrodynamic forces such as added mass and viscous drag force. Both of added mass and drag force coefficients can be measured by a set of Planar Motion Mechanism (PMM) tests; however, it is costly. In this study, an economic method for identifying hydrodynamic parameters of ROV is given. A simplified nonlinear ROV dynamics model with twelve unknown hydrodynamic parameters in six degrees of freedom was derived for simulations. The identification is based on experimental data obtained by projective mapping method which is utilized to measure the planar motions of a ROV. Then least-squares optimization is performed by comparison between the theoretical simulations and the actual motion measurements. But, an optimization computation involving a large number of parameters is likely to get trapped in a local minimum. Therefore, to reduce the number of parameters to be optimized, some models of simple motions such as surge, sway, surge and sway, yaw, and heave are decoupled from the ROV dynamic model. A commercial ROV ¡§Seamor¡¨ that equipped with two vertical thrusters, two horizontal thrusters, and a depth sensor is used for identification. The experiments for measuring ROV motions of surge, sway, surge and sway, and yaw were performed in a swimming pool in National Sun Yat-sen University. A video camera is utilized to capture ROV for position estimation using projective mapping method. As for the heave motion of ROV, the experiment was conducted offshore the Shio-Liu-Qiu Island and the ROV depth was measured by an onboard pressure sensor. Then, optimal hydrodynamic parameters are identified in sequence of surge, heave, yaw, sway, and then surge and sway. Verification experiments were performed and the simulation results with the optimum values of hydrodynamic parameters show good agreement with the measured data from verification experiments.

Thesis (Ph. D.)--Ball State University, 2009. / Title from PDF t.p. (viewed on Nov. 12, 2009). "July 16, 2008." Includes bibliographical references (p. 143-152).

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1882. / Vita.

This thesis investigates various rigidity and flexibility phenomena of convex projective structures on hyperbolic manifolds, particularly in dimension 3. Let M[superscipt n] be a finite volume hyperbolic n-manifold where [mathematical equation] and [mathematical symbol] be its fundamental group. Mostow rigidity tells us that there is a unique conjugacy class of discrete faithful representation of [mathematical symbol] into PSO(subscript n, 1). In light of this fact we examine when this representations can be non-trivially deformed into the larger Lie group of PGL[subscript n+1](R) as well as the relationship between these deformations and convex projective structures on M. Specifically, we show that various two-bridge knots do not admit such deformations into PGL[subscript 4](R) satisfying certain boundary conditions. We subsequently use this result to show that certain orbifold surgeries on amphicheiral knot complements do admit deformations. / text