Geometric modeling and mesh generation from scanned images

352 Pages·2016·236.444 MB·English

by  Zhang, Yongjie

Geometric Modeling and
Mesh Generation from
Scanned Images
Chapman & Hall/CRC
Mathematical and Computational
Imaging Sciences
Series Editors
Chandrajit Bajaj Guillermo Sapiro
Center for Computational Visualization Department of Electrical
The University of Texas at Austin and Computer Engineering
Duke University
Aims and Scope
This series aims to capture new developments and summarize what is
known over the whole spectrum of mathematical and computational imaging
sciences. It seeks to encourage the integration of mathematical, statistical and
computational methods in image acquisition and processing by publishing a
broad range of textbooks, reference works and handbooks. The titles included
in the series are meant to appeal to students, researchers and professionals
in the mathematical, statistical and computational sciences, application areas,
as well as interdisciplinary researchers involved in the field. The inclusion of
concrete examples and applications, and programming code and examples, is
highly encouraged.
Published Titles
Image Processing for Cinema
by Marcelo Bertalmío
Image Processing and Acquisition using Python
by Ravishankar Chityala and Sridevi Pudipeddi
Statistical and Computational Methods in Brain Image Analysis
by Moo K. Chung
Rough Fuzzy Image Analysis: Foundations and Methodologies
by Sankar K. Pal and James F. Peters
Variational Methods in Image Processing
by Luminita A. Vese and Carole Le Guyader
Theoretical Foundations of Digital Imaging Using MATLAB®
by Leonid P. Yaroslavsky
Geometric Modeling and Mesh Generation from Scanned Images
by Yongjie Jessica Zhang
Proposals for the series should be submitted to the series editors above or directly to:
CRC Press, Taylor & Francis Group
3 Park Square, Milton Park, Abingdon, OX14 4RN, UK
Chapman & Hall/CRC
Mathematical and Computational Imaging Sciences
Geometric Modeling and
Mesh Generation from
Scanned Images
Yongjie Jessica Zhang
Carnegie Mellon University
Pittsburgh, Pennsylvania, USA
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Contents
Preface vii
1 Introduction and Pipelines 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Pipelines and Five Topics . . . . . . . . . . . . . . . . . . . . 2
1.3 Challenges and Advances . . . . . . . . . . . . . . . . . . . . 5
2 Review of Numerical Methods 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Linear and Nonlinear Algebraic Equations . . . . . . . . . . 13
2.3 Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Ordinary Differential Equations . . . . . . . . . . . . . . . . 29
2.5 Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Partial Differential Equations . . . . . . . . . . . . . . . . . . 36
2.7 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . 39
2.8 Fourier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.9 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3 Scanning Techniques and Image Processing 57
3.1 Scanning Techniques . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.5 Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Fundamentals to Geometric Modeling and Meshing 99
4.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2 Geometric Objects and Transformations . . . . . . . . . . . . 108
4.3 Curves and Surfaces . . . . . . . . . . . . . . . . . . . . . . . 117
4.4 Spline-Based Modeling . . . . . . . . . . . . . . . . . . . . . 123
4.5 Isocontouring and Visualization . . . . . . . . . . . . . . . . 144
v
vi Contents
5 Image-Based Triangular and Tetrahedral Meshing 155
5.1 A Review of Unstructured Triangular and Tetrahedral Mesh
Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.2 Octree-Based Triangular and Tetrahedral Mesh Generation
from Images . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
5.3 Resolving Topology Ambiguities . . . . . . . . . . . . . . . . 174
5.4 Quality Improvement . . . . . . . . . . . . . . . . . . . . . . 179
6 Image-Based Quadrilateral and Hexahedral Meshing 193
6.1 AReviewofUnstructuredQuadrilateralandHexahedralMesh
Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
6.2 Octree-Based Quadrilateral and Hexahedral Mesh Generation
from Images . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.3 Sharp Feature Preservation for CAD Assemblies . . . . . . . 207
6.4 Octree vs. RD-Tree Based Adaptive Hexahedral Meshing . . 212
6.5 Quality Improvement . . . . . . . . . . . . . . . . . . . . . . 216
7 Volumetric T-Spline Modeling 229
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.2 ConvertingUnstructuredQuadrilateralandHexahedralMeshes
to T-Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
7.3 Polycube-Based Parametric Mapping Methods . . . . . . . . 248
7.4 Eigenfunction-Based Surface Parameterization . . . . . . . . 269
7.5 Truncated Hierarchical Catmull−Clark Subdivision Modeling 273
7.6 Weighted T-Spline and Trimmed Surfaces . . . . . . . . . . . 277
7.7 Incorporating T-Splines into Commercial Software . . . . . . 283
8 Finite Element and Isogeometric Analysis Applications 287
8.1 Introduction to Finite Element Method and Its New
Developments . . . . . . . . . . . . . . . . . . . . . . . . . . 288
8.2 Multiscale Biomolecular Modeling . . . . . . . . . . . . . . . 292
8.3 Patient-Specific Geometric Modeling for Cardiovascular
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
8.4 Applications in Material Sciences . . . . . . . . . . . . . . . 299
Bibliography 305
Preface
With finite element method (FEM) and scanning technology seeing increased
useincyberinfrastructure-revolutionizedresearchareassuchascomputational
scienceandengineering,thereisanemergingneedforqualitymeshgeneration
from scanned images to enable the analysis, understanding and prediction of
complex physical phenomena. It is well known that FEM is currently well de-
veloped and efficient, but mesh generation for complex geometries still takes
80% of the total analysis time and is the major obstacle to reducing the total
computationtime.High-fidelitygeometricmodelingforsuchsophisticateddo-
mainsiscriticalforalotofcyber-enabledinnovativeapplications.Asanewly
emerging interdisciplinary research area, Geometric Modeling and Mesh Gen-
eration from Scanned Images aims to integrate image processing, geometric
modelingand mesh generationwith FEM tosolve problems incomputational
biology, medicine, materials sciences and engineering.
Thisbook,thefirstforsuchaninterdisciplinarytopic,isbasedonacourse
“ComputationalBiomodeling&Visualization”thatItaughtatCarnegieMel-
lon University over the past eight years and also some of our latest research.
It aims at introducing the fundamentals of medical imaging, image process-
ing, computational geometry, mesh generation, visualization and finite ele-
ment analysis; and also to expose readers to novel and advanced applications
in computational biology, medicine, material sciences and other engineering
fields. The principal audience includes senior undergraduate students, gradu-
ate students and researchers in mechanical engineering, biomedical engineer-
ing, material sciences and other engineering departments. This book can be
useddirectlyforteaching,researchandasaprofessionalreference.Itcanalso
be useful to more general researchers in related industry companies, medical
centers, government laboratories and other research institutions.
The subject integrates mechanical engineering, biomedical engineering,
computer science and mathematics together. The covered topics include
biomedical/materialimaging,imageprocessing,geometricmodelingandvisu-
alization, finite element method and biomedical and engineering applications.
This book starts with an introduction of pipelines from imaging to mesh-
ing and simulation as well as advances and challenges in this area (Chapter
1), followed by a review of numerical methods used in various modules of
the pipelines (Chapter 2). Chapter 3 introduces several important scanning
techniques, including computational tomography (CT), magnetic resonance
imaging (MRI), nuclear medicine, ultrasound and cryo-electronic microscopy
vii
viii Preface
(cryo-EM),aswellastechniquesusedtoscanpolycrystallinematerialssuchas
electron backscatter diffraction (EBSD) and high energy X-rays. In addition,
this chapter also talks about some basic operators in image processing such
as contrast enhancement, filtering, segmentation and registration. In Chapter
4, fundamentals of geometric modeling and computer graphics are first intro-
duced, followed by geometric objects and transformations, as well as curves
and surfaces. Since isocontouring is important for medical image visualiza-
tion, we introduce two isocontouring methods in detail: marching cubes and
dual contouring. The following two chapters (Chapters 5 and 6) talk about
various triangular/tetrahedral and quadrilateral/hexahedral mesh generation
techniques.Thesemethodsarealsoextendedtomeshgenerationformultiple-
materialdomains,resolvingtopologyambiguitiesandwithguaranteedquality.
Afterthat,Chapter7discussesvolumetricT-splinemodelingforisogeometric
analysis (IGA). Finally, Chapter 8 introduces FEM and its three new devel-
opments such as IGA, extended FEM (XFEM) and immersed FEM (IFEM);
overviews the broad application areas; and explains how the above topics (or
chapters) are used in various applications through several real projects.
This book touches on many related topics and has many unique features
compared to other books, including
• Being the first textbook for this new and interdisciplinary area;
• Coveringalltherelatedtopicsfromimagetosimulationandapplication;
• Integrating mechanical engineering, biomedical engineering, computer
science and mathematics together;
• Being a textbook suitable for both senior undergraduate students and
graduatestudentsinmechanicalengineering,biomedicalengineeringand
material sciences;
• The latest state-of-the-art techniques; and
• For each topic, discussions of the latest research advances, challenges
and related applications.
These unique features can be beneficial to many people working on various
interdisciplinary research areas.
This book introduces our latest research projects. Therefore, I thank my
formerandcurrentstudentsfortheirgreateffortinourresearchprojects,and
also their help in generating pictures for this book: Joshua Chen, Kangkang
Hu, Arjun Kumar, Yicong Lai, Xinghua Liang, Tao Liao, Lei Liu, Aishwarya
Pawar,JinQian,WenyanWang,XiaodongWei;visitingPhDstudentsYueJia
and Juelin Leng; as well as many collaborators who have made contributions:
Drs. Chandrajit L. Bajaj, Yuri Bazilevs, Lei Dong, Andrew B. Geltmacher,
Shaolie S. Hossain, Thomas J.R. Hughes, Pete M. Kekenes-Huskey, Trond
Kvamsdal, Shawn Litster, Wing Kam Liu, Jim Lua, Andrew McCammon,
Preface ix
Andrew McCulloch, Timon Rabczuk, Michael A. Scott, Thomas W. Seder-
berg,KenjiShimadaandGuoliangXu.OurprojectsweresupportedbyONR-
PECASE, NSF-CAREER, ONR-YIP, ONR, NRL, NAVAIR, AFOSR, NSF-
MRSEC, NIH-UCSD Subaward, SINTEF in Norway, UPMC-HTI, Winters
Foundation, Berkman Faculty Development Foundation and Chinese NSF.
Their support is greatly appreciated.
Chapter2waswrittenbasedonmylecturenotesfromtwoteachingcourses
on numerical methods (one at the graduate level and the other one at the
undergraduatelevel).IthankmycolleaguesProfessorsAlanJ.H.McGaughey
and Metin Sitti who kindly shared their lecture notes with me. Their help
is greatly appreciated! I also thank my course teaching assistants, Xinghua
Liang, Tao Liao, Kangkang Hu and Onder Erin, for organizing the solution
manual for all the homework and project assignments.
Jessica Zhang
Pittsburgh, USA