Multiple View Geometry in Computer Vision

How to reconstruct scenes from images using geometry and algebra, with applications to computer vision.

Richard Hartley (Author), Andrew Zisserman (Author)

9780521540513, Cambridge University Press

Paperback, published 25 March 2004

670 pages, 36 colour illus. 35 tables 124 exercises
24.8 x 17.5 x 3.6 cm, 1.465 kg

'The new edition features an extended introduction covering the key ideas in the book (which itself have been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.' Zentralblatt MATH

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction covering the key ideas in the book (which itself has been updated with additional examples and appendices) and significant new results which have appeared since the first edition. Comprehensive background material is provided, so readers familiar with linear algebra and basic numerical methods can understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

1. Introduction - a tour of multiple view geometry
Part 0. The Background: Projective Geometry, Transformations and Estimation: 2. Projective geometry and transformations of 2D
3. Projective geometry and transformations of 3D
4. Estimation - 2D projective transforms
5. Algorithm evaluation and error analysis
Part I. Camera Geometry and Single View Geometry: 6. Camera models
7. Computation of the camera matrix
8. More single view geometry
Part II. Two-View Geometry: 9. Epipolar geometry and the fundamental matrix
10. 3D reconstruction of cameras and structure
11. Computation of the fundamental matrix F
12. Structure computation
13. Scene planes and homographies
14. Affine epipolar geometry
Part III. Three-View Geometry: 15. The trifocal tensor
16. Computation of the trifocal tensor T
Part IV. N -View Geometry: 17. N-linearities and multiple view tensors
18. N-view computational methods
19. Auto-calibration
20. Duality
21. Chirality
22. Degenerate configurations
Part V. Appendices: Appendix 1. Tensor notation
Appendix 2. Gaussian (normal) and chi-squared distributions
Appendix 3. Parameter estimation. Appendix 4. Matrix properties and decompositions
Appendix 5. Least-squares minimization
Appendix 6. Iterative Estimation Methods
Appendix 7. Some special plane projective transformations
Bibliography
Index.

Subject Areas: Computer vision [UYQV], Robotics [TJFM1]