Bayesian Modeling of Uncertainty in Low-Level Vision
Vision has to deal with uncertainty. The sensors are noisy, the prior knowledge is uncertain or inaccurate, and the problems of recovering scene information from images are often ill-posed or underconstrained. This research monograph, which is based on Ri
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THE KLUWER INTERNATIONAL SERIES IN ENGINEERING AND COMPUTER SCIENCE ROBOTICS: VISION, MANIPULATION AND SENSORS Consulting Editor Takeo Kanade Carnegie Mellon University Other books in the series: Robotic Grasping and Fine Manipulation, M. Cutkosky ISBN 0-89838-200-9 Shadows and Silhouettes in Computer Vision, S. Shafer ISBN 0-89838-167-3 Perceptual Organization and Visual Recognition, D. Lowe ISBN 0-89838-172-X Robot Dynamics Algorithms, R. Featherstone ISBN 0-89838-230-0 Three Dimensional Machine Vision, T. Kanade (editor) ISBN 0-89838-188-6 Kinematic Modeling, Identification and Control of Robot Manipulators, H.W. Stone ISBN 0-89838-237-8 Object Recognition Using Vision and Touch, P.K. Allen ISBN 0-89838-245-9 Integration, Coordination and Control of Multi-Sensor Robot Systems, H.F. Durrant-Whyte ISBN 0-89838-247-5 Motion Understanding: Robot and Human Vision, W.N. Martin and 1.K. Aggrawal (Editors) ISBN 0-89838-258-0
BAYESIAN MODELING OF UNCERTAINTY IN LOW-LEVEL VISION
by
Richard Szeliski Carnegie Mellon University
with a foreword by Takeo Kanade
1rII...
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KLUWER ACADEMIC PUBLISHERS
Boston/Dordrecht/London
Distributors for North America: Kluwer Academic Publishers tOl Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA Distributors for all other countries: Kluwer Academic Publishers Group Distribution Centre Post Office Box 322 3300 AH Dordrecht, THE NETHERLANDS
Library of Congress Cataloging-in-Publication Data Szeliski, Richard. 1958Bayesian modeling of uncertainty in low-level vision I Richard Szeliski ; foreword by Takeo Kanade. p. cm. - (The Kluwer international series in engineering and computer science; #79) ISBN-13: 978-1-4612-8904-3 DOl: 10.1007/978-1-4613-1637-4
e-ISBN-13: 978-1-4613-1637-4
1. Computer vision-Mathematical models. I. Title. II. Series: Kluwer international series in engineering and computer science: SECS 79. 89-15632 TA1632.S94 1989 CIP
Copyright © 1989 by Kluwer Academic Publishers Softcover reprint of the hardcover 1st edition 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Kluwer Academic Publishers, tOl Philip Drive, Assinippi Park, Norwell, Massachusetts 02061. .
To my parents, Zdzislaw Ludwig Szeliski and Jadwiga Halina Szeliska, who have always encouraged my academic aspirations, and whose integrity and love have been a lifelong inspiration.
Contents Foreword by Takeo Kanade
xiii
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xv
1 Introduction .
1 2 5 9 12
Preface
1.1
1.2 1.3 1.4 2
Modeling uncertainty in low-level vision Previous work . . . Overview of results Organization . . . .
Representations for low-level vision . 2.1 Visible surface representations . 2.2 Visible surface algorithms . . . . 2.2.1 Regularization . . . . . . 2.2.2 Finite element discretization . 2.2.3 Relaxation . . . . . . . 2.3 Multiresolution representations 2.3.1 Multigrid algorithms . . 2.3.2 Relative repre
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