- Page 1 and 2: INSTITUT FÜR INFORMATIK Conformal
- Page 3 and 4: Conformal Geometric Algebra in Stoc
- Page 5: Dedicated to my beloved wife, Steph
- Page 11 and 12: Contents 1 Introduction 1 1.1 Motiv
- Page 13 and 14: 5 Parameter Estimation 145 5.1 Intr
- Page 15 and 16: Chapter 1 Introduction The main con
- Page 17 and 18: 1.1. MOTIVATION GEOMETRIC ALGEBRA 3
- Page 19 and 20: 1.1. MOTIVATION GEOMETRIC ALGEBRA 5
- Page 21 and 22: 1.1. MOTIVATION GEOMETRIC ALGEBRA 7
- Page 23 and 24: 1.2. MOTIVATION STOCHASTICS 9 Fig.
- Page 25 and 26: 1.4. THE THESIS 11 Almost all the v
- Page 27 and 28: 1.4. THE THESIS 13 Omnidirectional
- Page 29 and 30: Chapter 2 Geometric Algebra The beg
- Page 31 and 32: 2.1. AN AXIOMATIC DERIVATION 17 eng
- Page 33 and 34: 2.1. AN AXIOMATIC DERIVATION 19 is
- Page 35 and 36: 2.1. AN AXIOMATIC DERIVATION 21 are
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- Page 41 and 42: 2.1. AN AXIOMATIC DERIVATION 27 Fig
- Page 43 and 44: 2.1. AN AXIOMATIC DERIVATION 29 bui
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- Page 47 and 48: 2.1. AN AXIOMATIC DERIVATION 33 Thi
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- Page 51 and 52: 2.2. BASIC CONCEPTS OF GA 37 Propos
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2.2. BASIC CONCEPTS OF GA 43 have i
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2.2. BASIC CONCEPTS OF GA 45 Coroll
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2.2. BASIC CONCEPTS OF GA 47 (*) A
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2.2. BASIC CONCEPTS OF GA 49 Defini
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2.2. BASIC CONCEPTS OF GA 51 where
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2.2. BASIC CONCEPTS OF GA 53 Exampl
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2.2. BASIC CONCEPTS OF GA 55 As a (
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2.3. EXTENDED CONCEPTS OF GA 57 2.3
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2.3. EXTENDED CONCEPTS OF GA 59 2.3
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2.3. EXTENDED CONCEPTS OF GA 61 The
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2.3. EXTENDED CONCEPTS OF GA 63 2.3
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2.3. EXTENDED CONCEPTS OF GA 65 But
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2.3. EXTENDED CONCEPTS OF GA 67 f(e
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2.3. EXTENDED CONCEPTS OF GA 69 Hen
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2.3. EXTENDED CONCEPTS OF GA 71 whe
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2.3. EXTENDED CONCEPTS OF GA 73 Z
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2.3. EXTENDED CONCEPTS OF GA 75 ort
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2.3. EXTENDED CONCEPTS OF GA 77 In
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2.3. EXTENDED CONCEPTS OF GA 79 is
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Chapter 3 The Conformal Geometric A
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3.2. CONFORMAL SPACE � 4,1 83 in
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3.2. CONFORMAL SPACE � 4,1 85 Hen
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3.3. CONFORMAL ANALYTIC GEOMETRY 87
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3.3. CONFORMAL ANALYTIC GEOMETRY 89
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3.3. CONFORMAL ANALYTIC GEOMETRY 91
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3.3. CONFORMAL ANALYTIC GEOMETRY 93
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3.3. CONFORMAL ANALYTIC GEOMETRY 95
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3.3. CONFORMAL ANALYTIC GEOMETRY 97
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3.3. CONFORMAL ANALYTIC GEOMETRY 99
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3.3. CONFORMAL ANALYTIC GEOMETRY 10
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3.3. CONFORMAL ANALYTIC GEOMETRY 10
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3.3. CONFORMAL ANALYTIC GEOMETRY 10
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3.3. CONFORMAL ANALYTIC GEOMETRY 10
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3.3. CONFORMAL ANALYTIC GEOMETRY 10
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3.3. CONFORMAL ANALYTIC GEOMETRY 11
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3.3. CONFORMAL ANALYTIC GEOMETRY 11
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3.3. CONFORMAL ANALYTIC GEOMETRY 11
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3.3. CONFORMAL ANALYTIC GEOMETRY 11
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3.3. CONFORMAL ANALYTIC GEOMETRY 11
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3.4. THE OPERATORS OF CGA 121 analy
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3.4. THE OPERATORS OF CGA 123 Let P
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3.4. THE OPERATORS OF CGA 125 by an
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3.4. THE OPERATORS OF CGA 127 of Rp
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3.4. THE OPERATORS OF CGA 129 Now l
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3.4. THE OPERATORS OF CGA 131 The o
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3.4. THE OPERATORS OF CGA 133 Given
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Chapter 4 A Primer on Pose Estimati
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4.2. OVERVIEW 137 Since the wolf WE
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4.4. THALES’ THEOREM REVISITED 13
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4.5. THE PERSPECTIVE 3-POINT PROBLE
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4.6. THE PERSPECTIVE N-POINT PROBLE
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Chapter 5 Parameter Estimation The
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5.1. INTRODUCTION 147 As an estimat
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5.1. INTRODUCTION 149 Generalized M
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5.1. INTRODUCTION 151 As the integr
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5.2. LEAST SQUARES ADJUSTMENT 153 (
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5.2. LEAST SQUARES ADJUSTMENT 155 (
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5.2. LEAST SQUARES ADJUSTMENT 157 i
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5.2. LEAST SQUARES ADJUSTMENT 159 o
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5.2. LEAST SQUARES ADJUSTMENT 161 T
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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5.3. GAUSS-HELMERT MODEL BASED ESTI
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Chapter 6 Practical Aspects of Geom
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6.1. GEOMETRIC ALGEBRA AND ITS TENS
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6.2. ERROR PROPAGATION WITH CGA 183
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6.2. ERROR PROPAGATION WITH CGA 185
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6.2. ERROR PROPAGATION WITH CGA 187
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Chapter 7 Applications in Computer
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7.1. FITTING A CIRCLE IN 3D 191 Φ
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7.1. FITTING A CIRCLE IN 3D 193 The
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7.2. ESTIMATING A RIGID BODY MOTION
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7.2. ESTIMATING A RIGID BODY MOTION
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7.3. PERSPECTIVE POSE ESTIMATION 19
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7.3. PERSPECTIVE POSE ESTIMATION 20
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Chapter 8 Applications in Omnidirec
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8.1. OMNIDIRECTIONAL IMAGING 205 8.
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8.2. POSE ESTIMATION 207 Note that,
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8.2. POSE ESTIMATION 209 Fig. 8.5:
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8.2. POSE ESTIMATION 211 the second
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8.2. POSE ESTIMATION 213 8.2.3 Expe
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8.2. POSE ESTIMATION 215 Fig. 8.9:
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8.2. POSE ESTIMATION 217 The result
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8.4. ESTIMATING EPIPOLES 219 can be
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8.4. ESTIMATING EPIPOLES 221 Fig. 8
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8.4. ESTIMATING EPIPOLES 223 Howeve
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8.4. ESTIMATING EPIPOLES 225 F = eo
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8.4. ESTIMATING EPIPOLES 227 Fig. 8
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8.4. ESTIMATING EPIPOLES 229 Fig. 8
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Chapter 9 Conclusion It was intende
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233 implicit use of a conformal emb
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Appendix A Selected Aspects Underly
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A.1. LINEAR ALGEBRA 237 3. Identity
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A.1. LINEAR ALGEBRA 239 x ∈ V is
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A.2. COMMUTATOR AND ANTI-COMMUTATOR
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A.2. COMMUTATOR AND ANTI-COMMUTATOR
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A.3. PROOFS AND DERIVATIONS 245 Pro
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A.3. PROOFS AND DERIVATIONS 247 A.3
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A.3. PROOFS AND DERIVATIONS 249 ind
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A.4. ADDITIONAL NOTES TAILORED TO C
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Appendix B Abbreviations BCH Baker
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Appendix C Notation The following l
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a ∗ b Scalar product of the vecto
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Bibliography [1] S. J. Ahn. Least S
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261 [22] L. Dorst. The representati
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263 [45] C. Gebken, A. Tolvanen, an
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[74] K.-R. Koch. Parameter Estimati
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267 [99] C. Perwass and G. Sommer.
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Index κ-vector, 19 3D-epipole, 221
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Insphere, 110 Intrinsic mean weight
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Shuffle (u,v)-, 54, 243 Signature,