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

Description:

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.

Olivier Faugeras is Research Director and head of a computer vision group at INRIA and Adjunct Professor of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. 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 SRI International, California.

 

Table of Contents:

 

Preface	xiii
	Notation	xix
1	A tour into multiple image geometry	1
2	Projective, affine and Euclidean geometries	63
3	Exterior and double or Grassman-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 > 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