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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  • Format: Paperback
  • Copyright: 2004-03-01
  • Publisher: Mit Pr
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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.

Author Biography

Olivier Faugeras is Research Director and head of the Robiovis Group at INRIA and Adjunct Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology.

Table of Contents

Prefacep. xiii
Notationp. xix
A tour into multiple image geometryp. 1
Projective, affine and Euclidean geometriesp. 63
Exterior and double or Grassman-Cayley algebrasp. 127
One camerap. 173
Two views: The Fundamental matrixp. 247
Estimating the Fundamental matrixp. 315
Stratification of binocular stereo and applicationsp. 359
Three views: The trifocal geometryp. 409
Determining the Trifocal tensorp. 469
Stratification of n >
views and applicationsp. 501
Self-calibration of a moving camera: From affine or projective calibration to full Euclidean calibrationp. 539
A Appendixp. 593
Referencesp. 597
Indexp. 635
Table of Contents provided by Publisher. All Rights Reserved.

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