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

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

by Olivier Faugeras, Quang-Tuan Luong
     
 

ISBN-10: 0262562049

ISBN-13: 9780262562041

Pub. Date: 03/01/2004

Publisher: MIT Press

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

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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.

The MIT Press

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Product Details

ISBN-13:
9780262562041
Publisher:
MIT Press
Publication date:
03/01/2004
Edition description:
New Edition
Pages:
668
Sales rank:
1,258,253
Product dimensions:
8.00(w) x 9.00(h) x 1.10(d)
Age Range:
18 Years

Table of Contents

Preface
Notation
1A tour into multiple image geometry1
2Projective, affine and Euclidean geometries63
3Exterior and double or Grassmann-Cayley algebras127
4One camera173
5Two views: The Fundamental matrix247
6Estimating the Fundamental matrix315
7Stratification of binocular stereo and applications359
8Three views: The trifocal geometry409
9Determining the Trifocal tensor469
10Stratification of n [actual symbol not reproducible] 3 views and applications501
11Self-calibration of a moving camera: From affine or projective calibration to full Euclidean calibration539
A: Appendix593
References597
Index635

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