Methods for Detection and Reconstruction of Sharp Features in Point Cloud Data [Elektronische Ressource] / Christopher Weber. Betreuer: Hans Hagen

© Christopher Dominik Weber, Technische Universität Kaiserslautern, Department Of Computer Science

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• Informatik

Informations

• Publié par: technische_universitat_kaiserslautern
• Publié le: 01 janvier 2011
• Nombre de lectures: 41
• Langue: English
• Poids de l'ouvrage: 28 Mo

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M E T H O D S F O R D E T E C T I O N A N D R E C O N S T R U C T I O N O F
S H A R P F E AT U R E S I N P O I N T C L O U D D ATA
vom Fachbereich Informatik der
Technischen Universität Kaiserslautern
zur Verleihung des akademischen Grades
Doktor der Naturwissenschaften (Dr. rer. nat.)
genehmigte Dissertation
von
Dipl.-Inf. Christopher Dominik Weber
Erster Berichterstatter:
Prof. Dr. Hans Hagen
Zweiter
Prof. Dr. Stefanie Hahmann
Vorsitzender der Prüfungskommision:
Prof. Dr. Klaus Schneider
Dekan des Fachbereichs:
Prof. Dr. Arnd Poetzsch-Heffter
Datum der wissenschaftlichen Aussprache: 23. August 2011
D 386M E T H O D S F O R D E T E C T I O N A N D R E C O N S T R U C T I O N O F S H A R P
F E AT U R E S I N P O I N T C L O U D D ATA
christopher dominik weber
Computer Graphics and HCI Group
Department of Computer Science
Technische Universität Kaiserslautern
Advisors:
Prof. Dr. Hans Hagen
Prof. Dr. Stefanie Hahmann
April 2011
D 386Christopher Dominik Weber: Methods for Detection and Reconstruction of Sharp Features in
Point Cloud Data, , © April 2011A C K N O W L E D G M E N T S
I would like to thank all the people around me that made it possible to write this thesis
with their help and support. Above all, I would like to thank my family, especially
my parents and sister. They all gave me the support and backing I needed during the
research and writing of this thesis.
This thesis would not have been possible without the help, support and patience of my
1 2supervisors Prof. Dr. Hans Hagen and Prof. Dr. Stefanie Hahmann . They were always
an invaluable source of advice and knowledge for which I am extremely grateful. I would
also like to acknowledge the financial, academic and technical support of the IRTG 1131
of the German Research Foundation and the Technische Universität Kaiserslautern and
its staff as well as my friends and colleagues at the Computer Graphics and HCI Group
and the IRTG. Our open meetings and dicussions were always a huge inspiration for the
solution of upcoming problems.
Last but not least I would like to mention and thank the sources for the examples and
datasets I used in this thesis. The vase model is provided courtesy of INRIA, the fandisk,
the ocata-flower and the trim-star are provided courtesy of MPII, all by the AIM@SHAPE
Shape Repository. The drill model is courtesy of Sergei Azernikov, Siemens Corporate
Research, Princeton.
1 Technische Universität Kaiserslautern, Computer Graphics and HCI Group, Germany
2 Université de Grenoble, Laboratoire Jean Kuntzmann, France
vC O N T E N T S
i introduction 1
1 introduction 3
ii basics 9
2 basics 11
2.1 Point sets 11
2.1.1 Simple points 12
2.1.2 Oriented points 12
2.1.3 Splats 12
2.1.4 Point set algorithms 13
2.1.5 Generation of unorganized point sets 15
2.2 Scattered Data interpolation and approximation methods 17
2.2.1 Shepard’s Method 17
2.2.2 Radial Basis Functions 18
2.3 An Introduction to Moving least squares 19
2.3.1 Standard Least Squares 19
2.3.2 Towards Moving Least Squares 20
2.4 Introduction to NURBS 26
iii detection of sharp features in point clouds 31
3 detection of sharp features in point clouds 33
3.1 Abstract 33
3.2 Problem Description 34
3.3 State of the art 36
3.3.1 Mesh based feature detection 36
3.3.2 Point based feature 38
3.3.3 Reconstruction based methods 40
3.3.4 Our method 40
3.4 Feature extraction 41
3.4.1 Data structure 41
3.4.2 Neighborhood analysis 45
vii3.4.3 Discrete Gauss map 45
3.5 Choice of parameters 51
3.5.1 Size of neighborhood 51
3.5.2 Sensitivity parameter for Gauss map clustering 52
3.6 Local-Adaptive Method 54
3.7 Results 57
3.7.1 Robustness w/r to varying angles 58
3.7.2 Comparison between global and local-adaptive method 58
3.7.3 Global method 60
3.7.4 Local-adaptive method 60
3.7.5 Robustness to noise 61
3.7.6 Complex point-sampled surfaces 63
3.7.7 Comparison to PCA methods 65
3.8 Conclusions 67
iv sharp feature reconstruction using moving least squares 69
4 sharp feature reconstruction using moving least squares 71
4.1 Abstract 71
4.2 Moving least squares and sharp features - State of the art 72
4.3 Our method - MLS with Neighborhood modification 78
4.3.1 An overview of the algorithm 78
4.3.2 MLS Notations 80
4.3.3 Local feature line construction 81
4.3.4 Feature lines error analysis 85
4.3.5 Modification of neighborhood 86
4.3.6 ofhood in the special case of corner fea-
tures 88
4.4 Results 93
4.4.1 Feature lines: robustness w/r to noise 95
4.4.2 Choice of Parameters for the MLS 98
4.4.3 Error analysis 101
4.4.4 Surface reconstruction: robustness w/r to noise 101
4.4.5 Comparison to known methods 104
4.4.6 Nonuniform sampling 107
4.5 conclusion 108
viiiv blending mls-surfaces with nurbs 109
5 blending mls-surfaces with nurbs 111
5.1 Abstract 111
5.2 Problem description 112
5.3 Some related works 112
5.4 Blending NURBS with MLS-Surfaces 114
5.4.1 Short description and notations 114
5.4.2 Blending 115
5.4.3 Combination with sharp features 128
5.5 Results 129
5.5.1 Examples 129
5.5.2 Varying the ’collar’ 131
5.5.3 Noise 135
5.6 Conclusion 136
bibliography 137
ixL I S T O F F I G U R E S
Figure 1 Examples for sharp feature detection 4
Figure 2 for the sharp feature MLS-reconstruction 5
Figure 3 Examples for blending of a NURBS- and a MLS-surface 6
Figure 4 From left to right: simple point, oriented point, splat, elliptical
splat 13
Figure 5 Different shape approximations from left to right: irregular trian-
gles, regular triangles, circular splats, elliptical splats. Image taken
from [28] 14
Figure 6 Comparison: splats and point set. Top row: 350k points, bottom
row 30k circular splats, Image taken from [28] 15
Figure 7 2D example for an interpolating moving least squares fit with an
linear basis function 22
Figure 8 2D example for an interpolating moving least squares fit with an
quadratic basis function 22
Figure 9 2D example for a moving least squares fit with an approximating
weight function,=0.5 23
Figure 10 2D example for a moving least squares fit with an interpolating
weight function,=0 24
Figure 11 The basis MLS projection procedure: First, a local reference domain
H for the red pointr is generated. The projection ofr ontoH defines
its originq (green). After this, the local polynomial approximation
g to the heightsf of pointsp overH is computed. The blue pointi i
finally is the projection ofr ontog. 25
Figure 12 Tagged Point cloud: the left side of this figure shows the original
point cloud data; The right shows the tagged data. 34
Figure 13 The left side shows examples without the adaption method; the
right side examples use the adaptive method 35
x