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Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 36.

Zhao, Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 111-117) and index. / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Objective of the study --- p.2 / Chapter 1.3 --- Challenges and our approach --- p.4 / Chapter 1.4 --- Original contributions --- p.6 / Chapter 1.5 --- Organization of this dissertation --- p.6 / Chapter 2 --- Related Work --- p.9 / Chapter 2.1 --- Critical configuration for motion estimation and projective reconstruction --- p.9 / Chapter 2.1.1 --- Point feature --- p.9 / Chapter 2.1.2 --- Line feature --- p.12 / Chapter 2.2 --- Camera motion estimation --- p.14 / Chapter 2.2.1 --- Line tracking --- p.15 / Chapter 2.2.2 --- Determining camera motion --- p.19 / Chapter 3 --- Preliminaries on Three-View Geometry and Trifocal Tensor --- p.23 / Chapter 3.1 --- Projective spaces P3 and transformations --- p.23 / Chapter 3.2 --- The trifocal tensor --- p.24 / Chapter 3.3 --- Computation of the trifocal tensor-Normalized linear algorithm --- p.31 / Chapter 4 --- Linear Line Structures --- p.33 / Chapter 4.1 --- Models of line space --- p.33 / Chapter 4.2 --- Line structures --- p.35 / Chapter 4.2.1 --- Linear line space --- p.37 / Chapter 4.2.2 --- Ruled surface --- p.37 / Chapter 4.2.3 --- Line congruence --- p.38 / Chapter 4.2.4 --- Line complex --- p.38 / Chapter 5 --- Critical Configurations of Three Views Revealed by Line Correspondences --- p.41 / Chapter 5.1 --- Two-view degeneracy --- p.41 / Chapter 5.2 --- Three-view degeneracy --- p.42 / Chapter 5.2.1 --- Introduction --- p.42 / Chapter 5.2.2 --- Linear line space --- p.44 / Chapter 5.2.3 --- Linear ruled surface --- p.54 / Chapter 5.2.4 --- Linear line congruence --- p.55 / Chapter 5.2.5 --- Linear line complex --- p.57 / Chapter 5.3 --- Retrieving tensor in critical configurations --- p.60 / Chapter 5.4 --- Rank classification of non-linear line structures --- p.61 / Chapter 6 --- Camera Motion Estimation Framework --- p.63 / Chapter 6.1 --- Line extraction --- p.64 / Chapter 6.2 --- Line tracking --- p.65 / Chapter 6.2.1 --- Preliminary geometric tracking --- p.65 / Chapter 6.2.2 --- Experimental results --- p.69 / Chapter 6.3 --- Camera motion estimation framework using EKF --- p.71 / Chapter 7 --- Experimental Results --- p.75 / Chapter 7.1 --- Simulated data experiments --- p.75 / Chapter 7.2 --- Real data experiments --- p.76 / Chapter 7.2.1 --- Linear line space --- p.80 / Chapter 7.2.2 --- Linear ruled surface --- p.84 / Chapter 7.2.3 --- Linear line congruence --- p.84 / Chapter 7.2.4 --- Linear line complex --- p.91 / Chapter 7.3 --- Empirical observation: ruled plane for line transfer --- p.93 / Chapter 7.4 --- Simulation for non-linear line structures --- p.94 / Chapter 8 --- Conclusions and Future Work --- p.97 / Chapter 8.1 --- Summary --- p.97 / Chapter 8.2 --- Future work --- p.99 / Chapter A --- Notations --- p.101 / Chapter B --- Tensor --- p.103 / Chapter C --- Matrix Decomposition and Estimation Techniques --- p.104 / Chapter D --- MATLAB Files --- p.107 / Chapter D.1 --- Estimation matrix --- p.107 / Chapter D.2 --- Line transfer --- p.109 / Chapter D.3 --- Simulation --- p.109

Classical and quantum Chern-Simons with gauge group U(1)N were classified by Belov and Moore in [BM05]. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence is well known between ordinary (2 + 1)-dimensional TQFTs and modular tensor categories. We study group categories and extend them slightly to produce modular tensor categories that correspond to toral Chern-Simons. Group categories have been widely studied in other contexts in the literature [FK93],[Qui99],[JS93],[ENO05],[DGNO07]. The main result is a proof that the associated projective representation of the mapping class group is isomorphic to the one from toral Chern-Simons. We also remark on an algebraic theorem of Nikulin that is used in this paper. / text

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Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.