Computational Analysis of Visual Motion

242 Pages·1994·4.88 MB·English

by  Amar Mitiche (auth.)

Computational
Analysis of Visual
Motion
ADVANCES IN COMPUTER VISION AND
MACHINE INTELLIGENCE
Series Editor: Martin D. Levine
McGill University
Montreal, Quebec, Canada
COMPUTATIONAL ANALYSIS OF VISUAL MOTION
Amar Mitiche
COMPUTER VISION FOR ELECTRONICS MANUFACTURING
L. F. Pau
HUMAN ENGINEERING IN STEREOSCOPIC VIEWING DEVICES
Daniel B. Diner and Derek H. Fender
PYRAMIDAL ARCHITECTURES FOR COMPUTER VISION
Virginio Cantoni and Marco Ferretti
SIGMA: A Knowledge-Based Aerial Image Understanding System
Takahashi Matsuyama and Vincent Shang-Shouq Hwang
A Continuation Order Plan is available for this series. A continuation order will bring
delivery of each new volume immediately upon publication. Volumes are billed only
upon actual shipment. For further information please contact the publisher.
Computational
Analysis of Visual
Motion
AMAR MITICHE
INRS-Telecommunications
Montreal, Quebec, Canada
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
On file
This document was typeset by A.M5-TEX
ISBN 978-1-4757-9787-9 ISBN 978-1-4757-9785-5 (eBook)
DOI 10.1007/978-1-4757-9785-5
© 1994 Springer Science+Business Media New York
Originally published by Plenum Press, New York in 1994
Softcover reprint of the hardcover 1s t edition 1994
Ali rights reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form
or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise,
without written permission from the Publisher
To Lynda, Karim, and Jojo
to Nora
to my brothers and sisters
to the memory of my parents and of Dj erdj er
Acknowledgments
I am grateful to the following people for reading and commenting on the
manuscript: Patrick Bouthemy, Weige Chen, Tom Henderson, Abdolreza Man
souri, Lynda Mitiche, Pardo Mustillo, Dinesh Nair, J. Radeski, Michael Sabourin,
Machiko Sato, and Danny Thomas. I thank Nancy Gauvin for drawing most of
the geometric figures. I am grateful to INRS for providing support
Figures 1.5, 1.6, 1.7, 1.8, 1.9: from IRISA, Rennes, France, courtesy of Dr.
Patrick Bouthemy,
Figure 1.11: Prof. Janusz Konrad,
Figures 1.10, 9.1: INRS-Telecommunications Visual Communications
group,
Figures 5.11, 5.12, 5.13, were realized in Prof. Cohen's Perception and
Robotics Laboratory, Ecole Polytechnique, Montreal.
vii
Preface
Image motion processing is important to machine vision systems because it can
lead to the recovery of three-dimensional (3D) structure and motion. A chal
lenging goal is robot autonomous interaction with its environment, such as that
involving locomotion and manipulation. In its generality, the problem consists
of relating qualitatively and quantitatively unknown 3D variables (3D structure
and motion) to observable two-dimensional variables (image position and mo
tion). Quantitative evaluation is necessary to any interpretation system aimed at
allowing a physical interaction with the environment. Moreover, a computational
theory of vision can contribute to the understanding of mechanisms of biological
visual systems.
The problem of recovering structure and motion of objects in space from
images is the center of considerable attention for its theoretical as well as practical
challenges. It is of prime importance in application domains such as robotics
(robot autonomous navigation and operation), telecommunications (3D display
television), medicine (reconstruction and display of body structures), surveillance
(target tracking), etc.
Interest in such a problem is evidenced by the regularly important number
of publications in vision journals and conferences and workshops. The most
outstanding demonstration is the ECCV -1 (First European Conference on Com
puter Vision, Antibes, France, May 1990), which had an overwhelming number
of quality papers on image motion processing.
This strong interest by the international vision community justifies a book
that would provide a mathematical treatment of the subject. This book is in
tended to respond to the need. It deals not only with the interpretation of the
discrete cases of point correspondences and straight line correspondences but
with the continuous cases of optical flow and motion of straight lines as well,
and considers interpretation by a knowledge-based system. It provides a formal
ix
X Preface
presentation of the relevant mathematical basis for 3D interpretation (geometric
transformations and kinematics of solids. It also reviews current methods to
compute image motion.
This book is of interest to vision researchers, teachers and students, and to
engineers working in vision related domains.
Contents
1. Introduction: Image Motion in Visual Function 1
1.1. References . . . . . . . . . . . . . . . . . . 9
2. Geometry in Euclidean Space R3: Some Basic Notions 15
2.1. Euclidean 3-space R3 . . . . . . . 15
2.2. Vector Product and Mixed Product 16
2.3. Linear Applications .... 17
2.4. Affine Coordinate Systems . 19
2.5. Isometries .... 19
2.6. Affine Isometries . 21
2. 7. Rotations . . . . . 23
2.8. Reflections . . . . 27
2.9. Projective Relations 28
2.10. Bibliography . . . . 30
3. Rigid Body Kinematics: Some Basic Notions . 31
3 .1. Motion of a Rigid Body . . . . 31
3.2. Fundamental Formula ..... 33
3.3. Instantaneous Axis of Rotation 35
3.4. Equiprojectivity .. . 36
3.5. Scalar Invariant .. . 37
3.6. Translational Motion . 37
3.7. Rotational Motion .. 38
3.8. Composition of Velocities 39
3.9. Acceleration ...... . 40
3.10. Motion of Straight Lines . 41
3.11. Bibliography ...... . 43
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