The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications

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Overview

Over the last forty years, researchers have made great strides in elucidating the laws of image formation, processing, and understanding by animals, humans, and machines. This book describes the state of knowledge in one subarea of vision, the geometric laws that relate different views of a scene. Geometry, one of the oldest branches of mathematics, is the natural language for describing three-dimensional shapes and spatial relations. Projective geometry, the geometry that best models image formation, provides a unified framework for thinking about many geometric problems relevant to vision. The book formalizes and analyzes the relations between multiple views of a scene from the perspective of various types of geometries. A key feature is that it considers Euclidean and affine geometries as special cases of projective geometry.Images play a prominent role in computer communications. Producers and users of images, in particular three-dimensional images,require a framework for stating and solving problems. The book offers a number of conceptual tools and theoretical results useful for the design of machine vision algorithms. It also illustrates these tools and results with many examples of real applications.

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What People Are Saying

From the Publisher
"This is a novel, well-written, thorough presentation of a topic of clear interest in the computer vision field."—Eric Grimson, Bernard Gordon Professor of Medical Engineering,MIT

"This is an excellent book that will be widely read and should serve as a useful reference for the machine vision and computer graphics communities."—Seth Teller, Laboratory ofComputer Science, MIT

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Product Details

  • ISBN-13: 9780262562041
  • Publisher: MIT Press
  • Publication date: 3/1/2004
  • Edition description: New Edition
  • Pages: 668
  • Product dimensions: 8.00 (w) x 9.00 (h) x 1.10 (d)

Meet the Author

Olivier Faugeras is Research Director and head of a computer vision group at INRIA and AdjunctProfessor of Electrical Engineering and Computer Science at the Massachusetts Institute ofTechnology. He is the author of Three-Dimensional Computer Vision (MIT Press,1993).

Quang-Tuan Luong is a computer scientist in the Artifical Intelligence Center at SRIInternational, California.

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Table of Contents

Preface
Notation
1 A tour into multiple image geometry 1
2 Projective, affine and Euclidean geometries 63
3 Exterior and double or Grassmann-Cayley algebras 127
4 One camera 173
5 Two views: The Fundamental matrix 247
6 Estimating the Fundamental matrix 315
7 Stratification of binocular stereo and applications 359
8 Three views: The trifocal geometry 409
9 Determining the Trifocal tensor 469
10 Stratification of n [actual symbol not reproducible] 3 views and applications 501
11 Self-calibration of a moving camera: From affine or projective calibration to full Euclidean calibration 539
A: Appendix 593
References 597
Index 635
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