Surface Extraction and Flattening for Anatomical Visualization

135 Pages·2007·3.79 MB·English

Surface Extraction and Flattening for
Anatomical Visualization
Thèse n° 3575 (2006)
PRESENTEE A LA FACULTE INFORMATIQUE & COMMUNICATIONS
ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
POUR L’OBTENTION DU GRADE DE DOCTEUR ES SCIENCES
PAR
LAURENT SAROUL
Ingénieur en électronique CPE-Lyon, DEA de Traitement de l’Image, Université de
Saint-Etienne, France de nationalité française
Prof. W. Gerstner, président du jury
Prof. R.D. Hersch, directeur de thèse
Prof. Eduard Gröller, rapporteur
Dr. Jean Marie Becker, rapporteur
Dr. Ronan Boulic, rapporteur
Lausanne, EPFL
2006
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Table of Contents
Table of Contents...................................................................................................3
Acknowledgements ...............................................................................................7
Abstract..................................................................................................................9
Résumé ................................................................................................................11
Notations..............................................................................................................13
1 Introduction.......................................................................................................15
1.1 Preface.........................................................................................................................................15
1.2 Previous research on visualization of volume images................................................................15
1.3 Contents of this work..................................................................................................................18
1.4 The Visible Human dataset.........................................................................................................20
2 Fundamental notions on curves, surfaces and differential geometry...............21
2.1 Curves.........................................................................................................................................21
2.2 Parametric surfaces.....................................................................................................................22
2.3 Geodesic and normal curvature of a surface curve.....................................................................23
2.3.1 Definitions..........................................................................................................................................23
2.3.2 Calculation of principal curvatures.....................................................................................................26
3 Curved surface extraction for exploring anatomic structures..........................27
3.1 Previous work on curved surface extraction...............................................................................27
3.2 Ruled surface extraction from 3D volume images......................................................................28
3.2.1 Specification and extraction of a ruled surface...................................................................................28
3.2.2 Flattening of a ruled surface for visualization....................................................................................31
3.3 Free-form surface extraction from 3D volume images...............................................................33
3.3.1 Specification and extraction of free-form surfaces.............................................................................33
3.3.3 Visualizing free-form textured surfaces using a flattened view..........................................................37
3.4 Interactive specification of surfaces............................................................................................38
3.5 Exploration of anatomic structures with surfaces and 3D models..............................................40
3.6 Conclusion..................................................................................................................................42
4 Introduction to surface flattening.....................................................................43
4.1 Introduction.................................................................................................................................43
4.2 Surface parameterization concept...............................................................................................44
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4.2.1 Mapping definition.............................................................................................................................44
4.2.2 Isometric, conformal, harmonic and equiareal mappings...................................................................44
4.2.3 Definitions of surface parameterization, surface flattening and texture mapping...............................45
4.2.4 Cartographic projections....................................................................................................................48
4.3 Previous work on surface parameterization................................................................................49
4.4 Bennis et. al. Algorithm and Geodesic Curvature preservation..................................................51
4.4.1 Outline of the approach......................................................................................................................51
4.4.2 Curve flattening with arc length and geodesic curvature preservation...............................................52
4.4.3 Bennis et. al. Algorithm......................................................................................................................53
4.6 Conclusion..................................................................................................................................55
5 Distance preserving flattening of surface sections: parallel planes and radial
planes flattening...................................................................................................57
5.1 Introduction.................................................................................................................................57
5.2 Parallel planes flattening.............................................................................................................58
5.3 Radial planes flattening...............................................................................................................60
5.4 Evaluation of the flattening methods by distortion measurements.............................................62
5.5 Interactive Flattening..................................................................................................................69
5.6 Carrying out measurements along flattened surfaces..................................................................72
5.7 Conclusion..................................................................................................................................74
6 Optimal parallel planes flattening ....................................................................77
6.1 Introduction.................................................................................................................................77
6.2 Optimal plane orientation minimizing the geodesic curvature...................................................78
6.3 Minimizing the overall geodesic curvature by principal component analysis............................80
6.4 Optimal parallel planes flattening of curved surfaces.................................................................82
6.4.1 Distortions of optimally flattened surfaces.........................................................................................82
6.4.2 Comparison with Bennis et. al. surface flattening..............................................................................87
6.4.3 Computation times..............................................................................................................................90
6.5 Flattening of anatomical surfaces...............................................................................................90
6.6 Conclusion..................................................................................................................................94
7 Integration of surface extraction and flattening into the Visible Human server
project..................................................................................................................95
7.1 Introduction.................................................................................................................................95
7.2 The Visible Human Server project..............................................................................................96
7.2.1 Previous works...................................................................................................................................96
7.2.2 History................................................................................................................................................96
7.2.3 Visible Human server framework.......................................................................................................98
7.3 Surface texture extraction.........................................................................................................100
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7.3.1 Basic principles.................................................................................................................................100
7.3.2 Slice extraction.................................................................................................................................101
7.3.3 Ruled surface texture extraction.......................................................................................................102
7.3.4 Curved surface texture extraction.....................................................................................................103
7.4 Java applet functionalities.........................................................................................................106
7.4.1 Curved surface flattening..................................................................................................................106
7.4.2 Interactive rotation of the distance-preservation orientation............................................................107
7.4.3 Specification of a region of interest for parallel planes flattening....................................................108
7.4.4 Measurements on flattened surfaces.................................................................................................109
7.5 Conclusion................................................................................................................................109
8 Conclusion......................................................................................................111
Appendices ........................................................................................................115
A. Cubic spline interpolation..........................................................................................................115
B. Glossary of medical terms..........................................................................................................117
C. Java applet user interface...........................................................................................................120
References..........................................................................................................129
Biography ..........................................................................................................135
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Acknowledgements
First of all, I would like to thank Professor Roger David Hersch for giving me the opportunity
to complete this work at the Peripheral Systems Laboratory (LSP) of the EPFL under his
direction. His continuous guidance, his interesting remarks and advice helped me to reach the
objectives of this work.
I also would like to thank Oscar Figueiredo from CPE-Lyon (France) which helped me to
carry out this research.
I would like to give special thanks to Jean-Marie Becker from CPE-Lyon for his precious help
for solving several mathematical problems encountered during this work, to Sebastian
Gerlach who helped me in the development of the software presented in this work, to Isaac
Amidror who helped me to improve the English of this thesis, and to all the persons who
contributed to the project, especially Prof. J.P. Hornung and Dr B. Riederer, from the
University of Lausanne, faculty of medicine and Lionel Micol, student from the University of
Lausanne, faculty of medicine.
I also would like to thank all the LSP staff, especially Sylvain Chosson and Fabienne Allaire.
Finally, special thanks to my family and friends, for their help and support during these years.
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Abstract
In the last years, three-dimensional (3D) medical imaging techniques have taken an
increasing importance in patient care and medical research. Volume images provide medical
specialists with a direct access to the interior of a patient’s body and reduce the need for
invasive exploration. The use of volume imaging modalities such as X-ray CT, PET or MRI
has therefore become essential for medical diagnosis and surgical planning.
Computer visualization techniques such as extraction of planar slices of arbitrary
orientation (Multiplanar Reprojection), surface rendering of anatomic structures, and volume
rendering provide medical users with the tools for exploiting 3D volume images.
Surface or respectively volume rendering provides information about the 3D geometry
and 3D context of the structures of interest but does not allow to directly visualize original
intensities, respectively colors located within the 3D structures. In addition, surface rendering
requires the segmentation of the volume data and volume rendering often requires a
classification of the volume image pixels. In contrast, the extraction of planar sections
provides interactivity, requires no pre-processing and the original intensity, respectively color
of each slice element may be directly inspected. However, it does not allow the visualization
of curved anatomic structures within a single slice. In this thesis, we propose to overcome this
limitation by generalizing the concept of planar section to the extraction of curved
cross-sections.
In the first part, we focus on the interactive extraction of curved surfaces from volume
images. Unlike planar slices, curved cross-sections may follow the trajectory of tubular
structures such as the Aorta or follow structures with an irregular shape such as the Pelvis. In
the second part of this work, we focus on the visualization of curved surfaces. We would like
to offer the possibility of carrying out distance measurements along a structure of interest both
for medical applications and for anatomical studies. Orthogonal or perspective projection of
curved surfaces induces angular and metric distortions as well as surface overlapping. In order
to enable measurements, we propose to use surface flattening methods, which preserve
distances along specific orientations and minimize distortions around a focus point. Flattening
of curved cross-sections enables inspecting spatially complex relationship between anatomic
structures and their neighbourhood. They also allow the visualization of a curved anatomic
structure within a single planar view and therefore to precisely inspect the original intensity,
respectively color at each surface point. Thanks to a multi-resolution approach, surfaces are
flattened at interactive rates, allowing users to displace the focus point during the
visualization of the flattened surface. We also propose a new efficient method for computing a
flattened surface minimizing global distortions and still preserving distances along one
orientation.
Surface extraction and flattening techniques are integrated into an interactive
visualization Java applet. This Java applet enables anyone to precisely and interactively
inspect the Visible Human anatomy. Besides medical visualization, the presented methods
may also be useful for creating new interesting views of anatomic structures for didactic
purposes.
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Keywords: medical visualization, anatomic structures, texture extraction, curved sections,
free-form surfaces, surface flattening, differential geometry.
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