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Guide to Three Dimensional Structure and Motion Factorization [Kõva köide]

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Guide to Three Dimensional Structure and Motion FactorizationSuurem pilt
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Püsilink: https://www.kriso.ee/db/9780857290458.html
Märksõnad:
The problem of structure and motion recovery from image sequences is an important theme in computer vision. Considerable progress has been made in this field during the past two decades, resulting in successful applications in robot navigation, augmented reality, industrial inspection, medical image analysis, and digital entertainment, among other areas. However, many of these methods work only for rigid objects and static scenes. The study of non-rigid structure from motion is not only of academic significance, but also has important practical applications in real-world, nonrigid or dynamic scenarios, such as human facial expressions and moving vehicles.This practical guide/reference provides a comprehensive overview of Euclidean structure and motion recovery, with a specific focus on factorization-based algorithms. The book discusses the latest research in this field, including the extension of the factorization algorithm to recover the structure of non-rigid objects, and presents some new algorithms developed by the authors. Readers require no significant knowledge of computer vision, although some background on projective geometry and matrix computation would be beneficial.Topics and features: presents the first systematic study of structure and motion recovery of both rigid and non-rigid objects from images sequences; discusses in depth the theory, techniques, and applications of rigid and non-rigid factorization methods in three dimensional computer vision; examines numerous factorization algorithms, covering affine, perspective and quasi-perspective projection models; provides appendices describing the mathematical principles behind projective geometry, matrix decomposition, least squares, and nonlinear estimation techniques; includes chapter-ending review questions, and a glossary of terms used in the book.This unique text offers practical guidance in real applications and implementations of 3D modeling systems for practitioners in computer vision and pattern recognition, as well as serving as an invaluable source of new algorithms and methodologies for structure and motion recovery for graduate students and researchers.

This practical guide provides a comprehensive overview of Euclidean structure and motion recovery, with a specific focus on factorization-based algorithms. The text discusses the latest research in the field and presents new algorithms developed by the authors.
1 Introduction to 3D Computer Vision
1(28)
1.1 Introducation
1(1)
1.2 Imaging Geometry and Camera Models
2(5)
1.2.1 Camera Models
2(3)
1.2.2 Single View Imaging Geometry
5(2)
1.3 Single View Metrology and Reconstruction
7(10)
1.3.1 Measurement on Space Planes
8(1)
1.3.2 Camera Calibration from a Single View
9(2)
1.3.3 Measurement in 3D Space
11(3)
1.3.4 Examples of Single View Reconstruction
14(3)
1.4 Two-View Geometry and 3D Reconstruction
17(3)
1.4.1 Epipolar Geometry and Fundamental Matrix
17(1)
1.4.2 Three Dimensional Reconstruction
18(2)
1.5 Reconstruction of Structured Seenes from Two Images
20(6)
1.5.1 Plane Detection Strategy
20(4)
1.5.2 Camera Calibration and Reconstruction
24(2)
1.6 Closure Remarks
26(3)
1.6.1 Conclusion
26(1)
1.6.2 Review Questions
26(1)
References
27(2)
2 Simplified Camera Projection Models
29(14)
2.1 Introduction
29(1)
2.2 Affine Projection Model
30(3)
2.3 Quasi-Perspective Projection Model
33(5)
2.3.1 Quasi-Perspective Projection
33(3)
2.3.2 Error Analysis of Different Models
36(2)
2.4 Experimental Evaluations
38(2)
2.4.1 Imaging Errors
39(1)
2.4.2 Influence of Imaging Conditions
39(1)
2.5 Closure Remarks
40(3)
2.5.1 Conclusion
40(1)
2.5.2 Review Questions
41(1)
References
41(2)
3 Geometrical Properties of Quasi-Perspective Projection
43(20)
3.1 Introduction
43(1)
3.2 One-View Geometrical Property
44(2)
3.3 Two-View Geometrical Property
46(6)
3.3.1 Fundamental Matrix
47(3)
3.3.2 Plane Induced Homography
50(1)
3.3.3 Computation with Outliers
51(1)
3.4 3D Structure Reconstruction
52(1)
3.5 Evaluations on Synthetic Data
53(4)
3.5.1 Fundamental Matrix and Homography
54(1)
3.5.2 Outlier Removal
55(1)
3.5.3 Reconstruction Result
55(2)
3.6 Evaluations on Real Images
57(3)
3.6.1 Test on Stone Dragon Images
57(2)
3.6.2 Test on Medusa Head Images
59(1)
3.7 Closure Remarks
60(3)
3.7.1 Conclusion
60(1)
3.7.2 Review Questions
60(1)
References
61(2)
4 Introduction to Structure and Motion Factorization
63(24)
4.1 Introduction
63(2)
4.2 Problem Definition
65(3)
4.3 Structure and Motion Factorization of Rigid Objects
68(4)
4.3.1 Rigid Factorization Under Orthographic Projection
68(3)
4.3.2 Rigid Factorization Under Perspective Projection
71(1)
4.4 Structure and Motion Factorization of Nonrigid Objects
72(7)
4.4.1 Bregler's Deformation Model
73(1)
4.4.2 Nonrigid Factorization Under Affine Models
74(3)
4.4.3 Nonrigid Factorization Under Perspective Projection
77(2)
4.5 Factorization of Multi-Body and Articulated Objects
79(4)
4.5.1 Multi-Body Factorization
79(3)
4.5.2 Articulated Factorization
82(1)
4.6 Closure Remarks
83(4)
4.6.1 Conclusion
83(1)
4.6.2 Review Questions
83(1)
References
84(3)
5 Perspective 3D Reconstruction of Rigid Objects
87(22)
5.1 Introduction
87(2)
5.2 Previous Works on Projective Depths Recovery
89(2)
5.2.1 Epipolar Geometry Based Algorithm
89(1)
5.2.2 Iteration Based Algorithm
90(1)
5.3 Hybrid Projective Depths Recovery
91(3)
5.3.1 Initialization and Optimization
91(2)
5.3.2 Selection of Reference Frames
93(1)
5.4 Camera Calibration and Euclidean Reconstruction
94(4)
5.4.1 Camera Self-Calibration
94(2)
5.4.2 Euclidean Reconstruction
96(1)
5.4.3 Outline of the Algorithm
97(1)
5.5 Evaluations on Synthetic Data
98(3)
5.5.1 Projective Depths Recovery
98(1)
5.5.2 Calibration and Reconstruction
99(2)
5.6 Evaluations on Real Sequences
101(4)
5.6.1 Test on Model House Sequence
102(1)
5.6.2 Test on Stone Post Sequence
103(1)
5.6.3 Test on Medusa Head Sequence
104(1)
5.7 Closure Remarks
105(4)
5.7.1 Conclusion
105(1)
5.7.2 Review Questions
106(1)
References
106(3)
6 Perspective 3D Reconstruction of Nonrigid Objects
109(16)
6.1 Introduction
109(1)
6.2 Perspective Depth Scales and Nonrigid Factorization
110(2)
6.2.1 Perspective Depth Scales
110(1)
6.2.2 Nonrigid Affine Factorization
111(1)
6.3 Perspective Stratification
112(3)
6.3.1 Linear Recursive Estimation
112(2)
6.3.2 Nonlinear Optimization Algorithm
114(1)
6.4 Evaluations on Synthetic Data
115(3)
6.4.1 Reconstruction Results
116(1)
6.4.2 Convergence and Performance Comparisons
116(2)
6.5 Experiments with Real Sequence
118(3)
6.5.1 Test on Franck Sequence
118(2)
6.5.2 Test on Scarf Sequence
120(1)
6.6 Closure Remarks
121(4)
6.6.1 Conclusion
121(1)
6.6.2 Review Questions
122(1)
References
122(3)
7 Rotation Constrained Power Factorization
125(16)
7.1 Introduction
125(1)
7.2 Power Factorization for Rigid Objects
126(1)
7.3 Power Factorization for Nonrigid Objects
127(5)
7.3.1 Rotation Constrained Power Factorization
128(2)
7.3.2 Initialization and Convergence Determination
130(1)
7.3.3 Sequential Factorization
131(1)
7.4 Evaluations on Synthetic Data
132(3)
7.4.1 Reconstruction Results and Evaluations
132(1)
7.4.2 Convergence Property
133(2)
7.4.3 Influence of Imaging Conditions
135(1)
7.5 Evaluations on Real Sequences
135(2)
7.5.1 Test on Grid Sequence
135(1)
7.5.2 Test on Franck Sequence
136(1)
7.5.3 Test on Quilt Sequence
137(1)
7.6 Closure Remarks
137(4)
7.6.1 Conclusion
137(1)
7.6.2 Review Questions
138(1)
References
139(2)
8 Stratified Euclidean Reconstruction
141(20)
8.1 Introduction
141(1)
8.2 Deformation Weight Constraint
142(5)
8.2.1 Nonrigid Factorization
142(1)
8.2.2 Deformation Weight Constraint
143(2)
8.2.3 Geometrical Explanation
145(2)
8.3 Affine Structure and Motion Recovery
147(2)
8.3.1 Constrained Power Factorization
147(1)
8.3.2 Initialization and Convergence Determination
148(1)
8.4 Segmentation and Stratification
149(3)
8.4.1 Deformation Detection Strategy
149(2)
8.4.2 Stratification to Euclidean Space
151(1)
8.4.3 Implementation Outline
151(1)
8.5 Evaluations on Synthetic Data
152(4)
8.5.1 Reconstruction Results and Evaluations
152(1)
8.5.2 Convergence Property and Segmentation
153(3)
8.6 Evaluations on Real Sequences
156(2)
8.6.1 Test on Grid Sequence
156(1)
8.6.2 Test on Toy Sequence
157(1)
8.7 Closure Remarks
158(3)
8.7.1 Conclusion
158(1)
8.7.2 Review Questions
159(1)
References
159(2)
9 Quasi-Perspective Factorization
161(22)
9.1 Introduction
161(1)
9.2 Background on Factorization
162(2)
9.3 Quasi-Perspective Rigid Factorization
164(6)
9.3.1 Euclidean Upgrading Matrix
164(5)
9.3.2 Algorithm Outline
169(1)
9.4 Quasi-Perspective Nonrigid Factorization
170(3)
9.4.1 Problem Formulation
170(1)
9.4.2 Euclidean Upgrading Matrix
171(2)
9.5 Evaluations on Synthetic Data
173(3)
9.5.1 Evaluation on Rigid Factorization
173(2)
9.5.2 Evaluation on Nonrigid Factorization
175(1)
9.6 Evaluations on Real Image Sequences
176(3)
9.6.1 Test on Fountain Base Sequence
177(1)
9.6.2 Test on Franck Sequence
178(1)
9.7 Closure Remarks
179(4)
9.7.1 Conclusion
179(1)
9.7.2 Review Questions
180(1)
References
180(3)
Appendix A Projective Geometry for Computer Vision
183(8)
A.1 2D Projective Geometry
183(4)
A.1.1 Points and Lines
183(1)
A.1.2 Conics and Duel Conics
184(2)
A.1.3 2D Projective Transformation
186(1)
A.2 3D Projective Geometry
187(4)
A.2.1 Points, Lines, and Planes
187(2)
A.2.2 Projective Transformation and Quadrics
189(2)
Appendix B Matrix Decomposition
191(8)
B.1 Singlular Value Decomposition
191(3)
B.1.1 Properties of SVD Decomposition
192(1)
B.1.2 Low-Rank Matrix Approximation
193(1)
B.2 QR and RQ Decompositions
194(1)
B.3 Symmetric and Skew-Symmetric Matrix
195(4)
B.3.1 Cross Product
195(1)
B.3.2 Cholesky Decomposition
196(1)
B.3.3 Extended Cholesky Decomposition
197(2)
Appendix C Numerical Computation Method
199(8)
C.1 Linear Least Squares
199(3)
C.1.1 Full Rank System
200(1)
C.1.2 Deficient Rank System
201(1)
C.2 Nonlinear Estimation Methods
202(5)
C.2.1 Bundle Adjustment
202(1)
C.2.2 Newton Iteration
203(1)
C.2.3 Levenberg-Marquardt Algorithm
204(3)
References 207(2)
Glossary 209(2)
Index 211