These twenty-three contributions focus on the most recent developments in the rapidly evolving field of geometric invariants and their application to computer vision. The introduction summarizes the basics of invariant theory, discusses how invariants are related to problems in computer vision, and looks at the future possibilities, particularly the notion that invariant analysis might provide a solution to the elusive problem of recognizing general curved 3D objects from an arbitrary viewpoint. The remaining chapters consist of original papers that present important developments as well as tutorial articles that provide useful background material. These chapters are grouped into categories covering algebraic invariants, nonalgebraic invariants, invariants of multiple views, and applications. An appendix provides an extensive introduction to projective geometry and its applications to basic problems in computer vision.

Geometric Invariance in Computer Vision (Artificial Intelligence)

Computers & Technology

Zisserman, Andrew

Mundy, Joseph L.

Computer Science

Mit Pr

Visual Reconstruction (Artificial Intelligence)

Visual Reconstruction (Artificial Intelligence Series)

Arts & Photography

Blake, Andrew

Graphic Design

The MIT Press

Visual Reconstruction presents a unified and highly original approach to the treatment of continuity in vision. It introduces, analyzes, and illustrates two new concepts. The first―the weak continuity constraint―is a concise, computational formalization of piecewise continuity. It is a mechanism for expressing the expectation that visual quantities such as intensity, surface color, and surface depth vary continuously almost everywhere, but with occasional abrupt changes. The second concept―the graduated nonconvexity algorithm―arises naturally from the first. It is an efficient, deterministic (nonrandom) algorithm for fitting piecewise continuous functions to visual data. The book first illustrates the breadth of application of reconstruction processes in vision with results that the authors' theory and program yield for a variety of problems. The mathematics of weak continuity and the graduated nonconvexity (GNC) algorithm are then developed carefully and progressively.ContentsModeling Piecewise Continuity • Applications of Piecewise Continuous Reconstruction • Introducing Weak Continuity Constraints • Properties of the Weak String and Membrane • Properties of Weak Rod and Plate • The Discrete Problem • The Graduated Nonconvexity (GNC) Algorithm • Appendixes: Energy Calculations for the String and Membrane • Noise Performance of the Weak Elastic String • Energy Calculations for the Rod and Plate • Establishing Convexity • Analysis of the GNC Algorithm Visual Reconstruction is included in the Artificial Intelligence series, edited by Michael Brady and Patrick Winston.

History & Criticism

MIT Press]

Multiple View Geometry in Computer Vision

A basic problem in computer vision is to understand the structure of a real world scene. This book covers relevant geometric principles and how to represent objects algebraically so they can be computed and applied. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. Richard Hartley and Andrew Zisserman provide comprehensive background material and explain how to apply the methods and implement the algorithms. First Edition HB (2000): 0-521-62304-9

HARTLEY, RICHARD

Cambridge University Press

A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques used in the book for solving this are taken from projective geometry and photogrammetry. The authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. Recent major developments in the theory and practice of scene reconstruction are described in detail in a unified framework. The authors provide comprehensive background material, so a reader familiar with linear algebra and basic numerical methods will be able to understand the projective geometry and estimation algorithms presented, and implement the algorithms directly from the book.

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Books by Zisserman, Andrew