Geometric Invariance in Computer Vision

557 Pages·1992·49.511 MB·English

by  Joseph L. Mundy, Andrew Zisserman

Geometric
Invariance in
Computer Vision
Edited by Joseph L. Mundy and Andrew Zisserman
Geometric Invariance in Computer Vision
Geometric Invariance in Computer Vision
edited by
Joseph L. Mundy and Andrew Zisserman
The MIT Press
Cambridge, Massachusetts
London, England
© 1992 Massachusetts Institute of Technology
All rights reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or information
storage and retrieval) without permission in writing from the publisher.
This book was set in by the authors. Camera-ready copy was produced by
Chiron, Inc.
This book was printed and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Geometric invariance in computer vision / edited by Joseph Mundy, Andrew
Zisserman.
p. cm. — (Artificial intelligence)
"Mainly a result of a joint DARPA-ESPRIT workshop . . . held in Reylgavik,
Iceland, March 26-28,1991M—Pref.
Includes bibliographical references (p. ) and index.
ISBN 0-262-13286-0
1. Computer vision. 2. Invariants. I. Mundy, Joseph L. II. Zisserman,
Andrew. III. Series: Artificial intelligence (Cambridge, Mass.)
TA1632.G46 1992
621.39’9—dc20 92-1336
CIP
0262132850
MUNDY
GEOM INVAR COMP VAR
Contents
Series Foreword ix
Preface xi
1 Introduction — Towards a New Framework
for Vision 1
Joseph L. Mundy and Andrew Zisserman
1 FOUNDATIONS
Ia ALGEBRAIC INVARIANTS
2 Invariant Theory and Enumerative
Combinatorics of Young Tableaux 45
Shreeram S. Abhyankar
3 Geometric Interpretation of Joint Conic
Invariants 77
Joseph L. Mundy, Deepak Kapur,
Stephen J. Maybank, Patrick Gros and Long Quan
4 An Experimental Evaluation of Projective
Invariants 87
Christopher Coelho, Aaron Heller, Joseph L. Mundy,
David A. Forsyth and Andrew Zisserman
5 The Projection of Two Non-Coplanar Conics 105
Stephen J. Maybank
6 The Non-Existence of General-Case
View-Invariants 120
J. Brian Burns, Richard S. Weiss and
Edward M. Riseman
Ib invariants of non-algebraic
CURVES
7 Noise Resistant Invariants of Curves 135
Isaac Weiss
8 Semi-Differential Invariants 157
Luc J. Van Gool, Theo Moons, Eric Pauwels and
Andre Onsterlinrk
VI Contents
9 Projective Invariants for Curves in Two and
Three Dimensions 193
Michael H. Brill, Eamon B. Barrett and
Paul M. Payton
10 Numerical Evaluation of Differential and
Semi-Differential Invariants 215
Christopher Brown
11 Recognizing General Curved Objects
Efficiently 228
Andrew Zisserman, David A. Forsyth,
Joseph L. Mundy and Charles A. Rothwell
12 Fitting Affine Invariant Conics to Curves 252
Deepak Kapur and Joseph L. Mundy
13 Projectively Invariant Decomposition of
Planar Shapes 267
Stefan Carlsson
Ic INVARIANTS FROM MULTIPLE VIEWS
14 Invariant Linear Methods in
Photogrammetry and Model-Matching 277
Eamon B. Barrett, Michael H. Brill, Nils N. Haag
and Paul M. Payton
15 Semi-Differential Invariants for Nonplanar
Curves 293
Luc J. Van Gool, Michael H. Brill,
Eamon B. Barrett, Theo Moons and Eric Pauwels
16 Disambiguating Stereo Matches with
Spatio-Temporal Surfaces 310
Olivier Faugeras and Theo Papadopoulo
II APPLICATIONS
17 Transformation Invariant Indexing 335
Haim J. Wolfson and Yehezkel Lamdan
18 Affine Invariants for Model-Based
Recognition 354
John E. Hopcroft, Daniel P. Huttenlocher and
Peter C. Wayner
Contents vii
19 Object Recognition Based on Moment (or
Algebraic) Invariants 375
Gabriel Taubin and David B. Cooper
20 Fast Recognition Using Algebraic Invariants 398
Charles A. Rothwell, Andrew Zisserman,
David A. Forsyth and Joseph L. Mundy
21 Toward 3D Curved Object Recognition from
Image Contours 408
Jean Ponce and David J. Kriegman
22 Relative Positioning with Uncalibrated
Cameras 440
Roger Mohr, Luce Morin and Enrico Grosso
III APPENDIX
23 Appendix — Projective Geometry for
Machine Vision 463
Joseph L. Mundy and Andrew Zisserman
References 521
List of Contributors 535
Index 538

Series Foreword
Artificial intelligence is the study of intelligence using the ideas and
methods of computation. Unfortunately, a definition of intelligence
seems impossible at the moment because intelligence appears to be an
amalgam of so many information processing and information represen¬
tation abilities.
Of course psychology, philosophy, linguistics, and related disciplines
offer various perspectives and methodologies for studying intelligence.
For the most part, however, the theories proposed in these fields are too
incomplete and too vaguely stated to be realized in computational terms.
Something more is needed, even though valuable ideas, relationships,
and constraints can be gleaned from traditional studies of what are,
after all, impressive existence proofs that intelligence is in fact possible.
Artificial intelligence offers a new perspective and a new methodology.
Its central goal is to make computers intelligent, both to make them more
useful and to understand the principles that make intelligence possible.
That intelligent computers will be extremely useful is obvious. The
more profound point is that artificial intelligence aims to understand
intelligence using the ideas and methods of computation, thus offering
a radically new and different basis for theory formation. Most of the
people doing work in artificial intelligence believe that these theories
will apply to any intelligent information processor, whether biological or
solid state.
There are side effects that deserve attention, too. Any program that
will successfully model even a small part of intelligence will be inher¬
ently massive and complex. Consequently, artificial intelligence contin¬
ually confronts the limits of computer science technology. The problems
encountered have been hard enough and interesting enough to seduce
artificial intelligence people into working on them with enthusiasm. It is
natural, then, that there has been a steady flow of ideas from artificial
intelligence to computer science, and the flow shows no sign of abating.
The purpose of this series in artificial intelligence is to provide people
in many areas, both professionals and students, with timely, detailed
information about what is happening on the frontiers in research centers
all over the world.
J. Michael Brady
Daniel Bobrow
Randall Davis