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

Olivier Faugeras (Author), Quang-Tuan Luong (Author), Theo Papadopoulo (Contributor)

Book Description

Publication Date: January 30, 2004

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.

Editorial Reviews

Review

"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 of Computer Science, MIT

About the Author

This 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.

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

Product Details

• Paperback: 668 pages
• Publisher: The MIT Press; New Ed edition (January 30, 2004)
• Language: English
• ISBN-10: 0262562049
• ISBN-13: 978-0262562041
• Product Dimensions: 8.8 x 7.6 x 1.1 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,487,516 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

11 of 12 people found the following review helpful:

5.0 out of 5 stars Thought Provoking, October 4, 2006

By 

O. Burak Okan (Cambridge, MA USA) - See all my reviews
(REAL NAME)   

This review is from: The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications (Paperback)

My interest in this item largely stems from its use of the language of differential forms in its treatment of the mathematics of vision and the geometry of image formation. The index free tensorial background is a very natural framework for geometry albeit its heavy use has been limited to those in the theoretical physics community hitherto. In this respect this is pretty much the only treatment on the uses of those methods in vision and image construction. It is, however, a very solid text. In addition to the exterior calculus language used, it is a nice refresher of geometry in general. I figured out that my understanding of the concept of perspective was rather limited prior to reading it. Moreover, the treatment of the affine and projective geometries is very well motivated and would benefit anyone whose work partially or fully make use of those concepts. I wish visual art students could also dig into it and take out as much as they could.

In the final analysis, the nature of image formation is a very fundamental issue in vision and in this respect the rigorous use of geometric tools is instrumental and instructive. With that said, this is a rather well written account of the mathematical foundations of image formation. The price is very enticing as well. Not to be missed by anyone who is moved by the marvels of geometry.