Conformal Geometric Algebra in Stochastic Optimization Problems ...

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268 APPENDIX C. NOTATION [113] R. Swaminathan, M. D. Grossberg, and S. K. Nayar. Caustics of catadioptric cameras. In 8th International Conference on Computer Vision, volume 2, pages 2–9, Vancouver, BC, Canada, July 2001. IEEE Computer Society. [114] R. Swaminathan, M. D. Grossberg, and S. K. Nayar. Non-single viewpoint catadioptric cameras: Geometry and analysis. International Journal of Computer Vision, 66(3):211–229, February 2006. [115] P. Teunissen. Nonlinear least squares. In Manuscripta geodaetica, volume 15, pages 137–150. Springer, Berlin, Heidelberg, 1990. [116] A. Tolvanen, C. Perwass, and G. Sommer. Projective model for central catadioptric cameras using Clifford algebra. In 27. Symposium für Mustererkennung, DAGM 2005, Wien, 29.8.-2.9.005, volume 3663 of LNCS, pages 192– 199. Springer, Berlin, Heidelberg, 2005. [117] I. Tosic, I. Bogdanova, P. Frossard, and P. Vandergheynst. Multiresolution Motion Estimation for Omnidirectional Images. In 13th European. Signal Processing Conference (EUSIPCO), Antalya, Turkey, September 2005. EPFL, The European Association for Signal Processing (EURASIP). [118] B. Vandeportaele, M. Cattoen, and P. Marthon. A fast detector of line images acquired by an uncalibrated paracatadioptric camera. In 18th International Conference on Pattern Recognition (ICPR), volume 3, pages 1042–1045, Hong Kong, China, August 2006. IEEE Computer Society. [119] L. D. Weld. Theory of errors and least squares, a textbook for college students and research workers. New York, MacMillan, 1916. [120] H. Wolf. Das geodätische Gauß-Helmert Modell und seine Eigenschaften. Vermessungswesen, 103:41–43, 1978. [121] H. Wolf. The Helmert Block Method, its Origin and Development. In Proceedings of the Second International Symposium on Problems Related to the Redefinition of North American Geodetic Networks, pages 319–326. US Department of Commerce, Washington, 1978. [122] B. Wrobel. Die ebene Blockausgleichung nach der Anblock-Methode. Nachrichten aus dem öffentlichen Vermessungswesen Nordrhein-Westfalen, pages 203–218, 1971. [123] Y. Yagi. Omnidirectional sensing and its applications. IEICE Transactions on Information and Systems, E82-D(3):568–579, March 1999. INVITED SUR- VEY PAPER Surveys on Image Processing Technologies.
Index κ-vector, 19 3D-epipole, 221 A priori, 150 Adjustment, 10, 152 equations, 154 of observations only, 162 types, 162 Algebra basis, 18 Clifford, 16 degenerate, 18, 240 Dirac, 16 geometric, 18 linear, 235 Anti-commutator, 20, 240 Baker Campbell Hausdorff formula, 130 Barycentric coordinates, 199 Baseline, 221 Basis, 238 null, 85 orthogonalization, 52 sound, 73 Bayes’ theorem, 150 Bilinear form, 21 Bilinearity, 3, 238 of algebra products, 180 of geometric product, 23 Binet-Cauchy identity, 24, 56 Bivector, 19 Blade, 3 basis, 18, 36 definition, 41 null, 72 definition, 48 Calibration paracatadioptric, 218 269 Camera parameters, 135 Catadioptric, 203 image formation, 205 Cholesky decomposition, 156 Circle estimation, 190 great, 206, 218 Clifford algebra, 16 product, 20 Clifford, William Kingdon, 16 Commutator, 20 formalism, 240 identities, 54, 252 Jacobi identity, 242 Leibniz rule, 241 Complex numbers, 1 Conformal circle, 94, 108 degenerate, 110 embedding, 85, 188, 220 geometric algebra, 3, 81 identities, 250 matrix representation, 179, 225 tensor notation, 180 geometry, 81 group, 120 line, 114 mapping, 8 objects, 91 plane, 99 point, 85, 90 point pair, 104, 119 projective point, 107 space, 83 sphere, 90, 96 imaginary, 97 split, 251
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INSTITUT FÜR INFORMATIK Conformal
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Conformal Geometric Algebra in Stoc
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Dedicated to my beloved wife, Steph
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ACKNOWLEDGMENT This thesis as is ca
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3 The Conformal Geometric Algebra 8
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8 Applications in Omnidirectional V
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2 CHAPTER 1. INTRODUCTION with a si
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4 CHAPTER 1. INTRODUCTION three poi
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6 CHAPTER 1. INTRODUCTION Spherical
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80 CHAPTER 2. GEOMETRIC ALGEBRA
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146 CHAPTER 5. PARAMETER ESTIMATION
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