Segmentation and Recovery of Superquadrics

272 Pages·2000·10.38 MB·English

by  Aleš Jaklič, Aleš Leonardis, Franc Solina (auth.)

Segmentation and Recovery of Superquadrics
Computational Imaging and Vision
Managing Editor
MAX A. VIERGEVER
Utrecht University, Utrecht, The Netherlands
Editorial Board
RUZENA BAJCSY, University of Pennsylvania, Philadelphia, USA
MIKE BRADY, Oxford University, Oxford, UK
OLIVIER D. FAUGERAS, INRIA. Sophia-Antipolis, France
JAN J. KOENDERINK, Utrecht University, Utrecht, The Netherlands
STEPHEN M. PIZER, University of North Carolina, Chapel Hill, USA
SABURO TSUJI, Wakayama University, Wakayama, Japan
STEVEN W. ZUCKER, McGill University, Montreal, Canada
Volume 20
Segmentation and Recovery of
Superquadrics
by
Ales Jaklic
Ales Leonardis
and
Franc Solina
Faculty of Computer and Information Science,
University of Ljubljana, Slovenia
Springer-Science+Business Media, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-5574-3 ISBN 978-94-015-9456-1 (eBook)
DOI 10.1007/978-94-015-9456-1
Printed on acid-free paper
All Rights Reserved
© 2000 Springer Science+Business Media Dordrecht
Origina11y published by Kluwer Academic Publishers in 2000.
Softcover reprint ofthe hardcover 1s t edition 2000
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
To our families
Contents
List of Figures
IX
List of Tables
Xlll
Preface
XV
Acknowledgments xvii
Foreword XIX
1. INTRODUCTION 1
1.1 Part-level models 2
1.2 Superquadrics in computer vision 9
1.3 Other applications of superquadrics 10
1.4 Summary 11
2. SUPERQUADRICS AND THEIR GEOMETRIC PROPERTIES 13
2.1 Superellipse 13
2.2 Superellipsoids and superquadries 18
2.3 Superquadrics in general position 24
2.4 Some geometrie properties of superellipsoids 26
2.5 Computation and rendering of superquadrics 37
2.6 Summary 39
3. EXTENSIONS OF SUPERQUADRICS 41
3.1 Global deformations 41
3.2 Local deformations 49
3.3 Hyperquadrics 58
3.4 Ratioquadrics 58
3.5 Summary 60
4. RECOVERY OF INDIVIDUAL SUPERQUADRICS 63
4.1 Overview of superquadric recovery methods 64
4.2 Gradient least-squares minimization 72
4.3 Physics-based reconstruction 91
Vll
vüi SEGMENTATION AND RECOVERY OF SUPERQUADRICS
4.4 Discussion 96
4.5 Summary 101
5. SEGMENTATION WITH SUPERQUADRICS 103
5.1 Overview of segmentation methods 105
5.2 "Recover-and-select" segmentation 111
5.3 Segmentation with surface models 137
5.4 Summary 138
6. EXPERIMENTAL RESULTS 141
6.1 Recover-and-select superquadric segmentation results 142
6.2 Analysis of results 156
6.3 Summary 180
7. APPLICATIONS OF SUPERQUADRICS 181
7.1 A survey of superquadric applications 182
7.2 Range image registration 196
7.3 Summary 215
8. CONCLUSIONS 217
Appendices 221
A- Rendering of Superquadrics in Mathematica 221
B- Superquadric Recovery Code 223
C- Range Image Acquisition 225
D- Minimum Description Length and Maximum A 231
Posteriori Probability
E- Object-Oriented Framework· for Segment at ion 233
(Segmentor)
References 237
Author Index 259
Topic Index 263
List of Figures
1.1 Generalized cylinder 4
1.2 Human figure represented with generalized cylinders 5
1.3 Wooden mannequin represented with superquadrics 6
1.4 Geons 8
1.5 "Classical" versus "Active" vision paradigm 10
2.1 Superellipse 14
2.2 "Superegg" 15
2.3 Nine different types of Lame curves 16
2.4 Spherical product of two 2D curves 18
2.5 Superellipsoids 20
2.6 Superquadrics 22
2.7 Superquadric in general position 24
2.8 Superquadric and its dual superquadric 27
2.9 Radial Euclidean distance 29
2.10 Area of superellipse 31
2.11 Volume of superellipsoid 32
2.12 Volume of superellipsoids as function of EI and E2 34
2.13 Shaded superquadric model 38
3.1 Tapered superquadric 43
3.2 Tapering deformation 44
3.3 Bending plane 46
3.4 Bending deformation 47
3.5 Bent superquadrics 47
3.6 Shape deformations are not commutative 49
3.7 Superquadric as a coarse model 50
3.8 Displacement-based hybrid model 51
3.9 Ratioquadrics 59
4.1 Recovery of superquadrics from 2D contours 66
4.2 Recovery of superquadrics and self-occlusion 75
IX
x SEGMENTATION AND RECOVERY OF SUPERQUADRICS
4.3 Parameter space of the superquadric fitting function 76
4.4 Modified superquadric inside-outside function 78
4.5 Value of the fitting function during model recovery 79
4.6 Shape recovery of a round object 82
4.7 Shape recovery of a cylindric object 83
4.8 Shape recovery of a reet angular object 84
4.9 Shape recovery of a tapered object 88
4.10 Shape recovery of a bent object 89
4.11 Shape recovery of a tapered and bent object 90
5.1 Comparison of surface and volumetrie segmentation 104
5.2 Segmentation by model shrinking 109
5.3 Schema of model-recovery procedure 113
5.4 Recover-then-select strategy 134
5.5 Recover-and-select strategy 134
5.6 Surface segmentation of a complex object 138
5.7 Surface segment at ion of a cube 139
6.1 Range point density depends on surface orientation 143
6.2 Segmentation of non-overlapping grape berries 146
6.3 Segmentation of a bunch of grapes 148
6.4 Inftuence of occlusion on segmentation 150
6.5 Segmentation of a complex scene 152
6.6 Inftuence of range data density on recovered models 154
6.7 Segmentation of an articulated object 160
6.8 Analysis of segmentation for the articulated object 161
6.9 Post-processing of the articulated object 162
6.10 Error distributions for the articulated object 163
6.11 Segmentation of an L-shaped object 164
6.12 Post-processing of the L-shaped object 165
6.13 Error distributions for the L-shaped object 166
6.14 Stability of segmentation 167
6.15 Filtering of outliers 169
6.16 Segmentation of a wooden mannequin 171
6.17 Segmentation of an object that cannot be modeled
weH with superquadrics 174
6.18 Segmentation of aceramie head sculpture 176
6.19 Segmentation with volumetrie and surface models 178
6.20 Segmentation stages for volumetrie and surface models 179
7.1 Model and vision problem complexity 183
7.2 Superquadric model of a fiat postal package 184
7.3 Superquadrics of the same generic shape 188
7.4 CAD system for modeling human bodies 192
7.5 Encoding of segments for object-based video co ding 193
List of Figures xi
7.6 Four different right hand Cartesian coordinate frames 202
7.7 Four possible registration solutions 203
7.8 Object point in canonical coordinate frame 208
7.9 Synthetic range images used in experiments 210
7.10 Registration of range images view-l and view-2 211
7.11 Registration of range images view-l and view-5 212
7.12 Registration of range images view-2 and view-6 213
7.13 Registration of range images view-5 and view-7 214
C.l Structured light range scanner 225
C.2 Light stripe projector and CCD video camera 226
C.3 Light stripe pattern 226
C.4 Principle of structured light range acquisition 227
C.5 Sensitivity to reflectance properties of objects 228
E.l Class diagram of models 234
E.2 Class diagram of world, description, and recover-
and-select class utility 235
E.3 A screen snapshot of a Segmentar session 237