Geometric computing for perception action systems: concepts, algorithms, and scientific applications
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 235 S. Ill., graph. Darst. |
| ISBN: | 0387951911 |
Staff View
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Record in the Search Index
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| adam_text | EDUARDO BAYRO CORROCHANO GEOMETRIC COMPUTING FOR PERCEPTION ACTION
SYSTEMS CONCEPTS, ALGORITHMS, AND SCIENTIFIC APPLICATIONS WITH 73
ILLUSTRATIONS SPRINGER CONTENTS PREFACE V PART I. FUNDAMENTAL CONCEPTS
1. MATHEMATICAL PRELIMINARIES 3 1.1 INTRODUCTION 3 1.2 GEOMETRIC PRODUCT
AND MULTIVECTORS 3 1.3 THE GEOMETRIC ALGEBRA OF THE N-D SPACE 5 1.3.1
DUAL BLADES AND DUALITY IN THE GEOMETRIC PRODUCT 6 1.3.2 REVERSION AND
MAGNITUDE OF MULTIVECTORS 6 1.4 GEOMETRIC ALGEBRA OF GENERAL COMPLEX
NUMBERS 7 1.5 2D GEOMETRIC ALGEBRAS OF THE PLANE 8 1.6 GEOMETRIC ALGEBRA
OF EUCLIDEAN 3D SPACE 9 1.6.1 THE ALGEBRA OF ROTORS 10 1.6.2
QUATERNIONIC REPRESENTATIONS AND FUNCTIONS 13 1.7 4D GEOMETRIC ALGEBRA
FOR 3D KINEMATICS 14 1.8 4D GEOMETRIC ALGEBRA FOR PROJECTIVE 3D SPACE 15
1.9 CONCLUSION 16 1.10 EXERCISES 16 2. KINEMATICS OF THE 2D AND 3D
SPACES 19 2.1 INTRODUCTION 19 2.2 MOTOR ALGEBRA 19 2.2.1 MOTORS, ROTORS,
AND TRANSLATORS IN QT,O,X 20 2.2.2 PROPERTIES OF MOTORS . . 23 2.3
REPRESENTATION OF POINTS, LINES, AND PLANES USING 3D GEOMETRIC ALGEBRA
25 2.4 REPRESENTATION OF POINTS, LINES, AND PLANES USING MOTOR ALGEBRA
26 2.5 REPRESENTATION OF POINTS, LINES, AND PLANES USING 4D GEOMETRIC
ALGEBRA 27 2.6 MOTION OF POINTS, LINES, AND PLANES IN 3D GEOMETRIC
ALGEBRA 28 2.7 MOTION OF POINTS, LINES, AND PLANES USING MOTOR ALGEBRA
... 29 XII CONTENTS 2.8 MOTION OF POINTS, LINES, AND PLANES USING 4D
GEOMETRIC ALGEBRA 30 2.9 INCIDENCE RELATIONS BETWEEN POINTS, LINES, AND
PLANES 31 2.9.1 FLAGS OF POINTS, LINES, AND PLANES 32 2.10 CONCLUSION 33
2.11 EXERCISES 33 3. LIE ALGEBRAS AND ALGEBRA OF INCIDENCE USING THE
NULL CONE AND AFFINE PLANE 39 3.1 INTRODUCTION 39 3.2 GEOMETRIC ALGEBRA
OF RECIPROCAL NULL CONES 39 3.2.1 RECIPROCAL NULL CONES 40 3.2.2 THE
UNIVERSAL GEOMETRIC ALGEBRA Q N ,N 41 3.2.3 THE STANDARD BASES OF *,*
41 3.2.4 REPRESENTATIONS AND OPERATIONS USING BIVECTOR MATRICES 42 3.2.5
BIVECTOR REPRESENTATION OF LINEAR OPERATORS 43 3.3 HOROSPHERE AND
N-DIMENSIONAL AFFINE PLANE 44 3.4 THE GENERAL LINEAR GROUP 46 3.4.1 THE
GENERAL LINEAR ALGEBRA GL(AF) OF THE GENERAL LINEAR LIE GROUP GL{M) 48
3.4.2 THE ORTHOGONAL GROUPS 49 3.5 COMPUTING RIGID MOTION IN THE AFFINE
PLANE 52 3.6 THE LIE ALGEBRA OF THE AFFINE PLANE 53 3.7 THE ALGEBRA OF
INCIDENCE 57 3.7.1 INCIDENCE RELATIONS IN THE AFFINE N-PLANE 59 3.7.2
DIRECTED DISTANCES 60 3.7.3 INCIDENCE RELATIONS IN THE AFSNE 3-PLANE 61
3.7.4 GEOMETRIC CONSTRAINTS AS FLAGS 62 3.8 CONCLUSION 63 3.9 EXERCISES
63 4. GEOMETRIC ALGEBRA OF COMPUTER VISION 67 4.1 INTRODUCTION 67 4.2
THE GEOMETRIC ALGEBRAS OF 3D AND 4D SPACES 67 4.2.1 3D SPACE AND THE 2D
IMAGE PLANE 68 4.2.2 THE GEOMETRIC ALGEBRA OF 3D EUCLIDEAN SPACE 70
4.2.3 A 4D GEOMETRIC ALGEBRA FOR PROJECTIVE SPACE 70 4.2.4 PROJECTIVE
TRANSFORMATIONS 71 4.2.5 THE PROJECTIVE SPLIT 72 4.3 THE ALGEBRA OF
INCIDENCE 74 4.3.1 THE BRACKET 75 4.3.2 THE DUALITY PRINCIPLE AND MEET
AND JOIN OPERATIONS ... 76 4.3.3 LINEAR ALGEBRA 77 4.4 ALGEBRA IN
PROJECTIVE SPACE 78 CONTENTS XIII 4.4.1 INTERSECTION OF A LINE AND A
PLANE 79 4.4.2 INTERSECTION OF TWO PLANES 80 4.4.3 INTERSECTION OF TWO
LINES 80 4.4.4 IMPLEMENTATION OF THE ALGEBRA 81 4.5 VISUAL GEOMETRY OF
N-UNCALIBRATED CAMERAS 81 4.5.1 GEOMETRY OF ONE VIEW 81 4.5.2 GEOMETRY
OF TWO VIEWS 85 4.5.3 GEOMETRY OF THREE VIEWS 87 4.5.4 GEOMETRY OF
N-VIEWS 89 4.6 CONCLUSION 90 4.7 EXERCISES 90 PART II. PRACTICAL
APPLICATIONS 5. COMPUTING THE KINEMATICS OF ROBOT MANIPULATORS 95 5.1
INTRODUCTION 95 5.2 ELEMENTARY TRANSFORMATIONS OF ROBOT MANIPULATORS 95
5.2.1 THE DENAVIT-HARTENBERG PARAMETERIZATION 96 5.2.2 REPRESENTATIONS
OF PRISMATIC AND REVOLUTE TRANSFORMATIONS 98 5.2.3 GRASPING BY USING
CONSTRAINT EQUATIONS 100 5.3 DIRECT KINEMATICS OF ROBOT MANIPULATORS 101
5.3.1 MAPLE PROGRAM FOR MOTOR ALGEBRA COMPUTATIONS .... 103 5.4 INVERSE
KINEMATICS OF ROBOT MANIPULATORS 104 5.4.1 THE RENDEZVOUS METHOD 104
5.4.2 COMPUTING 9 , 62, AND ^3 USING A POINT REPRESENTATION 105 5.4.3
COMPUTING 64, AND 65 USING A LINE REPRESENTATION 108 5.4.4 COMPUTING 6 6
USING A PLANE REPRESENTATION 109 5.4.5 INVERSE KINEMATIC COMPUTING USING
THE 3D AFFINE PLANE 111 5.5 CONCLUSION 113 6. IMAGE PROCESSING 115 6.1
INTRODUCTION 115 6.2 IMAGE ANALYSIS IN THE FREQUENCY DOMAIN 116 6.2.1
QUATERNIONIC FOURIER TRANSFORM 116 6.2.2 2D ANALYTIC SIGNALS 117 6.2.3
PROPERTIES OF THE QFT 121 6.2.4 DISCRETE QFT 124 6.3 IMAGE ANALYSIS
USING THE PHASE CONCEPT 125 6.3.1 2D GABOR FILTERS 125 6.3.2 THE PHASE
CONCEPT 126 6.4 LIE FILTERS IN THE AFFINE PLANE 127 6.4.1 THE DESIGN OF
AN IMAGE FILTER 128 6.4.2 RECOGNITION OF HAND GESTURES 130 XIV CONTENTS
6.5 COLOR IMAGE PROCESSING 131 6.5.1 ROTOR EDGE DETECTOR 131 6.5.2
MODIFIED ROTOR EDGE DETECTOR 133 6.6 CONCLUSION 134 7. APPLICATIONS IN
COMPUTER VISION 137 7.1 INTRODUCTION 137 7.2 CONIES AND PASCAL S THEOREM
138 7.3 COMPUTING INTRINSIC CAMERA PARAMETERS 141 7.4 PROJECTIVE
INVARIANTS 142 7.4.1 THE ID CROSS-RATIO 143 7.4.2 2D GENERALIZATION OF
THE CROSS-RATIO 144 7.4.3 3D GENERALIZATION OF THE CROSS-RATIO 146 7.4.4
GENERATION OF 3D PROJECTIVE INVARIANTS 146 7.5 3D PROJECTIVE INVARIANTS
FROM MULTIPLE VIEWS 151 7.5.1 PROJECTIVE INVARIANTS USING TWO VIEWS 151
7.5.2 PROJECTIVE INVARIANT OF POINTS USING THREE UNCALIBRATED CAMERAS
153 7.5.3 COMPARISON OF THE PROJECTIVE INVARIANTS 154 7.6 VISUALLY
GUIDED GRASPING 156 7.6.1 PARALLEL ORIENTING 157 7.6.2 CENTERING 158
7.6.3 GRASPING 159 7.6.4 HOLDING THE OBJECT 159 7.7 CAMERA
SELF-LOCALIZATION 159 7.8 PROJECTIVE DEPTH 160 7.9 SHAPE AND MOTION 163
7.9.1 THE JOIN-IMAGE 163 7.9.2 THE SVD METHOD 164 7.9.3 COMPLETION OF
THE 3D SHAPE USING GEOMETRIC INVARIANTS 165 7.10 CONCLUSION 167 8. RIGID
MOTION ESTIMATION USING LINE OBSERVATIONS 169 8.1 INTRODUCTION 169 8.2
BATCH ESTIMATION USING SVD TECHNIQUES 169 8.2.1 SOLVING AX = XB USING
MOTOR ALGEBRA 171 8.2.2 ESTIMATION OF THE HAND-EYE MOTOR USING SVD 174
8.3 EXPERIMENTAL RESULTS 176 8.4 DISCUSSION 179 8.5 RECURSIVE ESTIMATION
USING KALMAN FILTER TECHNIQUES 180 8.5.1 THE KALMAN FILTER 180 8.5.2 THE
EXTENDED KALMAN FILTER 182 8.5.3 THE ROTOR-EXTENDED KALMAN FILTER 184
8.6 THE MOTOR EXTENDED KALMAN FILTER 187 CONTENTS XV 8.6.1
REPRESENTATION OF THE LINE MOTION MODEL IN LINEAR ALGEBRA 188 8.6.2
LINEARIZATION OF THE MEASUREMENT MODEL 189 8.6.3 ENFORCING A GEOMETRIC
CONSTRAINT 191 8.6.4 OPERATION OF THE MEKF ALGORITHM 192 8.6.5
ESTIMATION OF THE RELATIVE POSITIONING OF 6A ROBOT END-EFFECTOR 195 8.7
CONCLUSION 200 9. GEOMETRIC NEURALCOMPUTING 201 9.1 INTRODUCTION 201 9.2
REAL-VALUED NEURAL NETWORKS 202 9.3 COMPLEX MLP AND QUATERNIONIC MLP 203
9.4 GEOMETRIC ALGEBRA NEURAL NETWORKS 204 9.4.1 THE ACTIVATION FUNCTION
204 9.4.2 THE GEOMETRIC NEURON 205 9.4.3 FEEDFORWARD GEOMETRIC NEURAL
NETWORKS 206 9.4.4 GENERALIZED GEOMETRIC NEURAL NETWORKS 208 9.5 THE
LEARNING RULE 209 9.5.1 MULTIDIMENSIONAL BACK-PROPAGATION TRAINING RULE
209 9.5.2 SIMPLIFICATION OF THE LEARNING RULE USING THE DENSITY THEOREM
210 9.5.3 LEARNING USING THE APPROPRIATE GEOMETRIC ALGEBRAS .... 211 9.6
EXPERIMENTS USING GEOMETRIC FEEDFORWARD NEURAL NETWORKS 212 9.6.1
LEARNING A HIGH NONLINEAR MAPPING 212 9.6.2 ENCODER-DECODER PROBLEM 213
9.6.3 PREDICTION 215 9.7 SUPPORT VECTOR MACHINES IN GEOMETRIC ALGEBRA
215 9.7.1 SUPPORT VECTOR MACHINES 216 9.7.2 SUPPORT MULTIVECTOR MACHINES
217 9.7.3 GENERATING SMVMS WITH DIFFERENT KERNELS 218 9.7.4 MULTIVECTOR
REGRESSION 218 9.8 EXPERIMENTAL ANALYSIS OF SUPPORT MULTIVECTOR MACHINES
219 9.8.1 FINDING SUPPORT MULTIVECTORS 219 9.8.2 ESTIMATION OF 3D RIGID
MOTION 221 9.9 CONCLUSION 223 REFERENCES 225 INDEX 231
|
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| id | DE-604.BV013987332 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:55:36Z |
| institution | BVB |
| isbn | 0387951911 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009573105 |
| oclc_num | 45799490 |
| open_access_boolean | |
| owner | DE-29T DE-384 DE-634 |
| owner_facet | DE-29T DE-384 DE-634 |
| physical | XV, 235 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| spelling | Bayro Corrochano, Eduardo Verfasser (DE-588)123058538 aut Geometric computing for perception action systems concepts, algorithms, and scientific applications Eduardo Bayro Corrochano New York [u.a.] Springer 2001 XV, 235 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Apprentissage automatique Clifford, Algèbres de Géométrie - Informatique Datenverarbeitung Clifford algebras Geometry Data processing Machine learning Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Clifford-Algebra (DE-588)4199958-7 gnd rswk-swf Geometrische Algebra (DE-588)4156707-9 gnd rswk-swf Maschinelles Sehen (DE-588)4129594-8 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 s Geometrische Algebra (DE-588)4156707-9 s DE-604 Maschinelles Sehen (DE-588)4129594-8 s Clifford-Algebra (DE-588)4199958-7 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009573105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bayro Corrochano, Eduardo Geometric computing for perception action systems concepts, algorithms, and scientific applications Apprentissage automatique Clifford, Algèbres de Géométrie - Informatique Datenverarbeitung Clifford algebras Geometry Data processing Machine learning Bildverarbeitung (DE-588)4006684-8 gnd Clifford-Algebra (DE-588)4199958-7 gnd Geometrische Algebra (DE-588)4156707-9 gnd Maschinelles Sehen (DE-588)4129594-8 gnd |
| subject_GND | (DE-588)4006684-8 (DE-588)4199958-7 (DE-588)4156707-9 (DE-588)4129594-8 |
| title | Geometric computing for perception action systems concepts, algorithms, and scientific applications |
| title_auth | Geometric computing for perception action systems concepts, algorithms, and scientific applications |
| title_exact_search | Geometric computing for perception action systems concepts, algorithms, and scientific applications |
| title_full | Geometric computing for perception action systems concepts, algorithms, and scientific applications Eduardo Bayro Corrochano |
| title_fullStr | Geometric computing for perception action systems concepts, algorithms, and scientific applications Eduardo Bayro Corrochano |
| title_full_unstemmed | Geometric computing for perception action systems concepts, algorithms, and scientific applications Eduardo Bayro Corrochano |
| title_short | Geometric computing for perception action systems |
| title_sort | geometric computing for perception action systems concepts algorithms and scientific applications |
| title_sub | concepts, algorithms, and scientific applications |
| topic | Apprentissage automatique Clifford, Algèbres de Géométrie - Informatique Datenverarbeitung Clifford algebras Geometry Data processing Machine learning Bildverarbeitung (DE-588)4006684-8 gnd Clifford-Algebra (DE-588)4199958-7 gnd Geometrische Algebra (DE-588)4156707-9 gnd Maschinelles Sehen (DE-588)4129594-8 gnd |
| topic_facet | Apprentissage automatique Clifford, Algèbres de Géométrie - Informatique Datenverarbeitung Clifford algebras Geometry Data processing Machine learning Bildverarbeitung Clifford-Algebra Geometrische Algebra Maschinelles Sehen |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009573105&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bayrocorrochanoeduardo geometriccomputingforperceptionactionsystemsconceptsalgorithmsandscientificapplications |