Models and algorithms for image-based analysis of microstructures [Elektronische Ressource] / Oliver Wirjadi

Oliver Wirjadi

Description

Models and Algorithms for Image-Based Analysisof MicrostructuresDipl.-Inform. Oliver WirjadiVom Fachbereich Informatik der Technischen Universit at Kaiserslauternzur Verleihung des akademischen Grades Doktor der Naturwissenschaften(Dr. rer. nat.) genehmigte Dissertation.Dekan: Prof. Dr. Karsten BernsVorsitzender der Promotionskommission: Prof. Dr.-Ing. Jens SchmittBerichterstatter: Prof. Dr. Thomas BreuelProf. Dr.-Ing. Andreas K onigTag der wissenschaftlichen Aussprache: 13.02.2009(D 386)AbstractModern digital imaging technologies, such as digital microscopy or micro-computed tomography,deliver such large amounts of 2D and 3D-image data that manual processing becomes infeasible.This leads to a need for robust, exible and automatic image analysis tools in areas such as histol-ogy or materials science, where microstructures are being investigated (e.g. cells, ber systems).General-purpose image processing methods can be used to analyze such microstructures. Thesemethods usually rely on segmentation, i.e., a separation of areas of interest in digital images. Asimage segmentation algorithms rarely adapt well to changes in the imaging system or to di erentanalysis problems, there is a demand for solutions that can easily be modi ed to analyze di erentmicrostructures, and that are more accurate than existing ones.

Sujets

• Informatik
• Gesundheit

Informations

• Publié par: technische_universitat_kaiserslautern
• Publié le: 01 janvier 2009
• Nombre de lectures: 14
• Langue: English
• Poids de l'ouvrage: 10 Mo

Extrait

Models and Algorithms for Image-Based Analysis
of Microstructures
Dipl.-Inform. Oliver Wirjadi
Vom Fachbereich Informatik der Technischen Universit at Kaiserslautern
zur Verleihung des akademischen Grades Doktor der Naturwissenschaften
(Dr. rer. nat.) genehmigte Dissertation.
Dekan: Prof. Dr. Karsten Berns
Vorsitzender der Promotionskommission: Prof. Dr.-Ing. Jens Schmitt
Berichterstatter: Prof. Dr. Thomas Breuel
Prof. Dr.-Ing. Andreas K onig
Tag der wissenschaftlichen Aussprache: 13.02.2009
(D 386)Abstract
Modern digital imaging technologies, such as digital microscopy or micro-computed tomography,
deliver such large amounts of 2D and 3D-image data that manual processing becomes infeasible.
This leads to a need for robust, exible and automatic image analysis tools in areas such as histol-
ogy or materials science, where microstructures are being investigated (e.g. cells, ber systems).
General-purpose image processing methods can be used to analyze such microstructures. These
methods usually rely on segmentation, i.e., a separation of areas of interest in digital images. As
image segmentation algorithms rarely adapt well to changes in the imaging system or to di erent
analysis problems, there is a demand for solutions that can easily be modi ed to analyzet
microstructures, and that are more accurate than existing ones. To address these challenges, this
thesis contributes a novel statistical model for objects in images and novel algorithms for the
image-based analysis of microstructures.
The rst contribution is a novel statistical model for the locations of objects (e.g. tumor cells) in
images. This model is fully trainable and can therefore be easily adapted to many di erent image
analysis tasks, which is demonstrated by examples from histology and materials science. Using
algorithms for tting this statistical model to images results in a method for locating multiple
objects in images that is more accurate and more robust to noise and background clutter than
standard methods. On simulated data at high noise levels (peak signal-to-noise ratio below 10
dB), thisd achieves detection rates up to 10% above those of a watershed-based alternative
algorithm.
While objects like tumor cells can be described well by their coordinates in the plane, the
analysis of ber systems in composite materials, for instance, requires a fully three dimensional
treatment. Therefore, the second contribution of this thesis is a novel algorithm to determine
the local ber orientation in micro-tomographic reconstructions of ber-reinforced polymers and
other brous materials. Using simulated data, it will be demonstrated that the local orientations
obtained from this novel method are more robust to noise and ber overlap than those computed
using an established alternative gradient-based algorithm, both in 2D and 3D. The property of
robustness to noise of the proposed algorithm can be explained by the fact that a low-pass lter is
used to detect local orientations. But even in the absence of noise, depending on ber curvature
and density, the average local 3D-orientation estimate can be about 9 more accurate compared
to that alternative gradient-based method.
Implementations of that novel orientation estimation method require repeated image ltering
using anisotropic Gaussian convolution lters. These lter operations, which other authors have
used for adaptive image smoothing, are computationally expensive when using standard imple-
mentations. Therefore, the third contribution of this thesis is a novel optimal non-orthogonal
separation of the anisotropic Gaussian convolution kernel. This result generalizes a previous one
reported elsewhere, and allows for e cient implementations of the corresponding convolution oper-
ation in any dimension. In 2D and 3D, these implementations achieve an average performance gain
by factors of 3.8 and 3.5, respectively, compared to a fast Fourier transform-based implementation.
The contributions made by this thesis represent improvements over state-of-the-art methods,
especially in the 2D-analysis of cells in histological resections, and in the 2D and 3D-analysis of
brous materials.Contents
1 Introduction 1
2 Object Localization 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 The proposed model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Classi ers used as image models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Point processes as object models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Model-based multiple object localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 Fiber Orientation 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Gaussian orientation space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Sampling on the hemisphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 Computation and interpretation of the orientation tensor. . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.5 Fiber models for evaluating the proposed method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Separation of Anisotropic Gaussian Filters 71
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Separating the Gaussian convolution integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 An optimal symmetric factorization of . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4 Separable anisotropic Gaussian lters in image processing . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.5 Discrete implementations of the separated lter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 Discussion 97
A Training of Convolutional Neural Networks 99
A.1 Backpropagation training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
A.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
B Source Code of Control Methods 103
B.1 Isodata Thresholding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
B.2 Watershed Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
iiiiv CONTENTS
C Points on the Upper Hemisphere 107
C.1 Modi cations for the hemisphere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
C.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
D Factorization and Parameterization of 113
3D.1 Explicit symmetric factorization of Cholesky type in R . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
t 3D.2 Parameterization of VDV inR using polar coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
E Curriculum Vitae 117List of Abbreviations
AUC Area under the curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
CRF Conditional random eld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
DT-MRI Di usion tensor magnetic resonance imaging . .