Geometric properties for incomplete data

393 Pages·2006·3.269 MB·English

by  Reinhard Klette, Ryszard Kozera, Lyle Noakes, Joachim Weickert

Geometric Properties for Incomplete Data
Computational Imaging and Vision
Managing Editor
MAX A. VIERGEVER
Utrecht University, Utrecht, The Netherlands
Editorial Board
GUNILLABORGEFORS, Centre for Image Analysis, SLU, Uppsala, Sweden
THOMAS S. HUANG, University of Illinois, Urbana, USA
SABURO TSUJI, Wakayama University, Wakayama, Japan
Volume 31
Geometric Properties
for Incomplete Data
Edited by
Reinhard Klette
The University of Auckland,
Auckland, New Zealand
Ryszard Kozera
The University of Western Australia,
Perth, Australia
Lyle Noakes
The University of Western Australia,
Perth, Australia
and
Joachim Weickert
Saarland University,
Saarbrücken, Germany
AC.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-3857-7 (HB)
ISBN-13 978-1-4020-3857-0 (HB)
ISBN-10 1-4020-3858-5 (e-book)
ISBN-13 978-1-4020-3858-7 (e-book)
Published by Springer,
P.O. Box 17, 3300 AADordrecht, The Netherlands.
www.springeronline.com
Printed on acid-free paper
All Rights Reserved
© 2006 Springer
No part of this work 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, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
Printed in the Netherlands.
Contents
Contributors vii
Preface xiii
I Continuous Geometry 1
G. Sommer, B. Rosenhahn and C. Perwass / The Twist
Representation of Free-form Objects 3
C. Perwass and W. Fo¨rstner / Uncertain Geometry with Circles,
Spheres and Conics 23
R.T.FaroukiandC.Y.Han/AlgorithmsforspatialPythagorean-
hodograph curves 43
L. Noakes and R. Kozera / Cumulative Chords, Piecewise-
Quadratics and Piecewise-Cubics 59
L. Noakes / Spherical Splines 77
A. Robles-Kelly and E. R. Hancock / Graph-Spectral Methods for
Surface Height Recovery from Gauss Maps 103
II Discrete Geometry 123
U. Eckhardt / Segmentation of Boundaries into Convex and
Concave Parts 125
H. D¨orksen-Reiter and I. Debled-Rennesson /ConvexandConcave
Parts of Digital Curves 145
T. K. Linh, A. Imiya, and A. Torii / Polygonalisation and
Polyhedralisation by Optimisation 161
S. Weber, Ch. Schn¨orr, Th. Schu¨le, and J. Hornegger / Binary
Tomography by Iterating Linear Programs 183
W. Skarbek, K. Kucharski and M. Bober / Cascade of dual LDA
operators for face recognition 199
v
vi CONTENTS
M. N. Huxley, R. Klette and J. Zˇuni´c / Precision of Geometric
Moments in Picture Analysis 221
A. Tankus, N. Sochen and Y. Yeshurun / Shape-from-Shading by
Iterative Fast Marching for Vertical and Oblique Light Sources 237
A. Imiya / Shape from Shadows 259
III Approximation and Regularization 281
A. Bruhn and J. Weickert / A Confidence Measure for Variational
Optic Flow Methods 283
K. Kanatani and Y. Sugaya / Video Image Sequence Analysis:
Estimating Missing Data and Segmenting Multiple Motions 299
M. Fenn and G. Steidl / Robust local approximation of scattered
data 317
P. Mra´zek, J. Weickert and A. Bruhn / On Robust Estimation
and Smoothing with Spatial and Tonal Kernels 335
M. Mu¨hlich / Subspace Estimation with Uncertain and Correlated
Data 353
A. Obereder, S. Osher and O. Scherzer / On the use of Dual
Norms in Bounded Variation Type Regularization 373
Index 391
Contributors
Mirosl(cid:1)aw Bober
Visual Information Laboratory
Mitsubishi Electric
Guildford, United Kingdom
Andr´es Bruhn
Mathematical Image Analysis Group, Faculty of Mathematics and
Computer Science
Saarland University, Building 27
D–66 041 Saarbru¨cken, Germany
Isabelle Debled-Rennesson
Equipe Adage
LORIA Nancy
Nancy, France
Helene Do¨rksen-Reiter
Faculty of Mathematics
Hamburg University, Bundesstrasse 55
D–20 146 Hamburg, Germany
Ulrich Eckhardt
Faculty of Mathematics
Hamburg University, Bundesstrasse 55
D–20 146 Hamburg, Germany
Rida T. Farouki
Dept. of Mechanical and Aeronautical Engineering
University of California
Davis, CA 95616, USA
Markus Fenn
Dept. of Mathematics and Computer Science
University of Mannheim
D–68 131 Mannheim, Germany
Wolfgang Fo¨rstner
Institute of Photogrammetry
University Bonn, Nußallee 15
D–53 115 Bonn, Germany
vii
viii CONTRIBUTORS
Chang Yong Han
Dept. of Mechanical and Aeronautical Engineering
University of California
Davis, CA 95616, USA
Edwin R. Hancock
Dept. of Computer Science
University of York
York YO1 5DD, United Kingdom
Joachim Hornegger
Dept. of Computer Science
Friedrich-Alexander University Erlangen-Nu¨rnberg
D–91 058 Erlangen, Germany
Martin N. Huxley
School of Mathematics
Cardiff University, 23 Senghennydd Road
Cardiff CF 24 4YH, United Kingdom
Atsushi Imiya
IMIT
Chiba University, Yayoi-cho 1-33, Inage-ku
Chiba 263-8522, Japan
Kenichi Kanatani
Dept. of Information Technology
Okayama University
Okayama 700-8530, Japan
Reinhard Klette
Dept. of Computer Science and CITR
The University of Auckland
Auckland, New Zealand
Ryszard Kozera
School of Computer Science and Software Engineering
The University of Western Australia
Perth, Australia
Krzysztof Kucharski
Institute of Radioelectronics
Warsaw University of Technology
Warsaw, Poland
CONTRIBUTORS ix
Truong Kieu Linh
School of Science and Technology
Chiba University, Yayoi-cho 1-33, Inage-ku
Chiba 263-8522, Japan
Pavel Mra´zek
Institute for Information Theory and Automation
Academy of Sciences of the Czech Republic, Pod vod´arenskou vˇeˇz´ı 4
18208 Praha 8, Czech Republic ([email protected])
Matthias Mu¨hlich
Institut fu¨r Angewandte Physik, Computer Vision Group
J.W. Goethe University
D–60 054 Frankfurt am Main, Germany
Lyle Noakes
School of Mathematics and Statistics
The University of Western Australia
Perth, Australia
Andreas Obereder
Dept. of Computer Science
University of Innsbruck, Technikerstr. 25
A–6020 Innsbruck, Austria
Stanley Osher
Mathematics Department
University of California
Los Angeles, CA 90095-1555, USA
Christian Perwass
Institute of Computer Science
Christian-Albrechts-University
D–24 118 Kiel,Germany
Antonio Robles-Kelly
National ICT Australia
Canberra Laboratory
Canberra ACT 2601, Australia
Bodo Rosenhahn
Dept. of Computer Science and CITR
The University of Auckland
Auckland, New Zealand
x CONTRIBUTORS
Otmar Scherzer
Dept. of Computer Science
University of Innsbruck, Technikerstr 25
A–6020 Innsbruck, Austria
Christoph Schn¨orr
Dept. M&CS, CVGPR-Group
University of Mannheim
D–68 131 Mannheim, Germany
Thomas Schu¨le
Dept. M&CS, CVGPR-Group
University of Mannheim
D–68 131 Mannheim, Germany
Wl(cid:1)adysl(cid:1)aw Skarbek
Institute of Radioelectronics
Warsaw University of Technology
Warsaw, Poland
Nir Sochen
School of Mathematics
Tel-Aviv University
Tel-Aviv, 69978 Israel
Gerald Sommer
Institute of Computer Science
Christian-Albrechts-University
D–24 118 Kiel,Germany
Gabriele Steidl
Dept. of Mathematics and Computer Science
University of Mannheim
D–68 131 Mannheim, Germany
Yasuyuki Sugaya
Dept. of Information Technology
Okayama University
Okayama 700-8530, Japan
Ariel Tankus
School of Computer Science
Tel-Aviv University
Tel-Aviv, 69978 Israel