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VIEWEG+TEUBNER RESEARCH

Tobias Hanning

High Precision Camera Calibration

VIEWEG+TEUBNER RESEARCH

Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.

Habilitation thesis University of Passau, 2009

1st Edition 2011 All rights reserved © Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011 Editorial Office: Ute Wrasmann | Sabine Schöller Vieweg+Teubner Verlag is a brand of Springer Fachmedien. Springer Fachmedien is part of Springer Science+Business Media. www.viewegteubner.de No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright holder. Registered and/or industrial names, trade names, trade descriptions etc. cited in this publication are part of the law for trade-mark protection and may not be used free in any form or by any means even if this is not specifically marked. Cover design: KünkelLopka Medienentwicklung, Heidelberg Printing company: STRAUSS GMBH, Mörlenbach Printed on acid-free paper Printed in Germany ISBN 978-3-8348-1413-5

Contents List of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 4

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Modelling the camera mapping 2.1 Geometric optics for computer vision . . . . . . . . . . 2.1.1 The “thin lens” assumption and first order optics 2.1.2 The circle of confusion . . . . . . . . . . . . . . 2.1.3 Image acquisition . . . . . . . . . . . . . . . . . 2.1.3.1 The sensor array . . . . . . . . . . . . 2.1.3.2 A simplified sensor model . . . . . . . 2.1.3.3 The sensor array as coordinate system 2.2 The pinhole camera model . . . . . . . . . . . . . . . . 2.3 Third order optics and thick lenses . . . . . . . . . . . . 2.4 The pinhole camera model with distortion . . . . . . . . 2.4.1 Definition . . . . . . . . . . . . . . . . . . . . . 2.4.2 Radial distortion . . . . . . . . . . . . . . . . . 2.4.3 Radius transformations . . . . . . . . . . . . . . 2.4.4 Other distortion functions . . . . . . . . . . . . 2.4.4.1 Misaligned thin lens . . . . . . . . . . 2.4.4.2 Misaligned lens systems . . . . . . . . 2.5 Inverting the camera mapping . . . . . . . . . . . . . . 2.6 The pinhole camera model in homogeneous coordinates .

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5 5 5 8 9 9 11 12 13 15 17 17 18 19 21 21 22 23 25

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Error functions for camera calibration and 3D reconstruction 3.1 Introduction . . . . . . . . . .