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Mathematical Methods for Camera Self-Calibration in Photogrammetry and Computer Vision

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Mathematical Methods for Camera Self-Calibration in Photogrammetry and Computer Vision Mathematical Methods for Camera Self-Calibration in Photogrammetry and Computer Vision A thesis accepted by the Faculty of Aerospace Engineering and Geodesy of the Universität Stuttgart in partial fulfillment of the requirements for the degree of Doctor of Engineering Sciences (Dr.-Ing.) by Rongfu Tang born in Guangdong, China P. R. Committee Chair: Prof. Dr.-Ing habil. Dieter Fritsch Committee member: Prof. Dr.-Ing habil. Christian Heipke Date of defence: 28.05.2013 Institute of Photogrammetry University of Stuttgart 2013 Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften Reihe C Dissertationen Heft Nr. 703 Rongfu Tang Mathematical Methods for Camera Self-Calibration in Photogrammetry and Computer Vision München 2013 Verlag der Bayerischen Akademie der Wissenschaften in Kommission beim Verlag C. H. Beck ISSN 0065-5325 ISBN 978-3-7696-5115-7 Deutsche Geodätische Kommission bei der Bayerischen Akademie der Wissenschaften Reihe C Dissertationen Heft Nr. 703 Mathematical Methods for Camera Self-Calibration in Photogrammetry and Computer Vision Von der Fakultät Luft- und Raumfahrttechnik und Geodäsie der Universität Stuttgart zur Erlangung der Würde eines Doktors der Ingenieurwissenschaften (Dr.-Ing.) genehmigte Abhandlung Vorgelegt von M.Sc. Rongfu Tang München 2013 Verlag der Bayerischen Akademie der Wissenschaften in Kommission beim Verlag C. H. Beck ISSN 0065-5325 ISBN 978-3-7696-5115-7 Adresse der Deutschen Geodätischen Kommission: Deutsche Geodätische Kommission Alfons-Goppel-Straße 11 ! D – 80 539 München Telefon +49 – 89 – 23 031 1113 ! Telefax +49 – 89 – 23 031 - 1283 / - 1100 e-mail [email protected] ! http://www.dgk.badw.de Hauptberichter: Prof. Dr.-Ing. habil. Dieter Fritsch Mitberichter: Prof. Dr.-Ing. habil. Christian Heipke Tag der mündlichen Prüfung: 28.05.2013 © 2013 Deutsche Geodätische Kommission, München Alle Rechte vorbehalten. Ohne Genehmigung der Herausgeber ist es auch nicht gestattet, die Veröffentlichung oder Teile daraus auf photomechanischem Wege (Photokopie, Mikrokopie) zu vervielfältigen. ISSN 0065-5325 ISBN 978-3-7696-5115-7 3 Contents Zusammenfassung ................................................................................................................................... 6 Abstract ................................................................................................................................................... 8 1 Introduction ...................................................................................................................................... 11 1.1 Basic concepts ................................................................................................................................. 11 1.1.1 Camera coordinate system ........................................................................................................ 11 1.1.2 Central projection ..................................................................................................................... 11 1.1.3 Collinearity equations ............................................................................................................... 12 1.1.4 Projection equation ................................................................................................................... 13 1.1.5 Terminology ............................................................................................................................. 14 1.2 Camera calibration .......................................................................................................................... 15 1.2.1 Camera calibration in photogrammetry .................................................................................... 15 1.2.2 Camera calibration in computer vision ..................................................................................... 16 1.3 Related work on camera self-calibration ......................................................................................... 17 1.3.1 Self-calibration in close range photogrammetry ...................................................................... 17 1.3.2 Self-calibration in aerial photogrammetry................................................................................ 18 1.3.3 Auto-calibration in computer vision ......................................................................................... 19 1.4 Problem settings .............................................................................................................................. 20 1.5 Outline of the thesis ......................................................................................................................... 21 2 Self-Calibration Models in Photogrammetry: Theory ...................................................................... 23 2.1 Self-calibration models .................................................................................................................... 23 2.1.1 Distortion modeling .................................................................................................................. 23 2.1.2 Self-calibration: a mathematical view ...................................................................................... 23 2.1.3 Function approximation theory ................................................................................................ 24 2.1.4 Mathematical basis functions ................................................................................................... 24 2.2 Legendre self-calibration model ...................................................................................................... 26 2.2.1 Orthogonal polynomial approximation .................................................................................... 26 2.2.2 Legendre model ........................................................................................................................ 27 2.2.3 Discussions on polynomial self-calibration models ................................................................. 29 2.3 Fourier self-calibration model ......................................................................................................... 31 2.3.1 Optimal basis functions ............................................................................................................ 31 2.3.2 Fourier model ........................................................................................................................... 32 2.3.3 Discussions on mathematical self-calibration models .............................................................. 34 2.4 Self-calibration models in close range photogrammetry ................................................................. 37 4 Contents 2.4.1 Brown self-calibration model ................................................................................................... 37 2.4.2 Out-of-plane and in-plane distortion ........................................................................................ 38 2.4.3 Correlation analysis .................................................................................................................. 39 2.5 Concluding remarks ........................................................................................................................ 41 3 Self-Calibration Models in Photogrammetry: Tests ......................................................................... 42 3.1 Test datasets .................................................................................................................................... 42 3.1.1 Datasets in aerial photogrammetry ........................................................................................... 42 3.1.2 Datasets in close range photogrammetry .................................................................................. 44 3.2 In-situ airborne camera calibration .................................................................................................. 44 3.2.1 Overall system calibration ........................................................................................................ 45 3.2.2 Evaluation strategies................................................................................................................. 45 3.3 Tests in aerial photogrammetry ....................................................................................................... 47 3.3.1 Tests on Legendre self-calibration model ................................................................................ 47 3.3.2 Tests on Fourier self-calibration model .................................................................................... 50 3.4 Comparisons: airborne camera calibration ...................................................................................... 54 3.4.1 External accuracy ..................................................................................................................... 54 3.4.2 Correlation analyses ................................................................................................................. 55 3.4.3 Calibrations of three IO parameters and IMU misalignments .................................................. 56 3.4.4 Distortion calibration ................................................................................................................ 57 3.4.5 Overparameterization and statistical test .................................................................................. 59 3.5 Tests in close range photogrammetry .............................................................................................
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