Topology Simplification Algorithm for the Segmentation of Medical Scans
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Magnetic Resonance Imaging, Computed Tomography, and other image modalities areroutinely used to visualize a particular structure in the patient's body. The classificationof the image region corresponding to this structure is called segmentation. For... Lire la suite
Magnetic Resonance Imaging, Computed Tomography, and other image modalities are
routinely used to visualize a particular structure in the patient's body. The classification
of the image region corresponding to this structure is called segmentation.
Magnetic Resonance Imaging, Computed Tomography, and other image modalities are routinely used to visualize a particular structure in the patient's body. The classification of the image region corresponding to this structure is called segmentation. For applications in Neuroscience, it is important for the segmentation of a brain scan to represent the boundary of the brain as a single folded sheet. However the segmentation of the brain generally exhibits many erroneous holes. Consequently we have developed an algorithm for automatically removing holes in segmented medical scans while preserving the accuracy of the image. Upon concepts of Discrete Topology, we correct the holes based on the smallest modification to the image. First we detect each hole with a front propagation and a Reeb graph. Then we search for a number of loops around the hole on the isosurface of the image. Finally we select the loop that minimizes the modification to the image and correct the hole in the image. At each step we limit the size of the data in memory. With these contributions our algorithm removes every hole in the image with high accuracy and low complexity even for images that do not fit into the main memory. To help doctors and scientists to obtain segmentations without holes, we make our software publicly available.
routinely used to visualize a particular structure in the patient's body. The classification
of the image region corresponding to this structure is called segmentation.
Magnetic Resonance Imaging, Computed Tomography, and other image modalities are routinely used to visualize a particular structure in the patient's body. The classification of the image region corresponding to this structure is called segmentation. For applications in Neuroscience, it is important for the segmentation of a brain scan to represent the boundary of the brain as a single folded sheet. However the segmentation of the brain generally exhibits many erroneous holes. Consequently we have developed an algorithm for automatically removing holes in segmented medical scans while preserving the accuracy of the image. Upon concepts of Discrete Topology, we correct the holes based on the smallest modification to the image. First we detect each hole with a front propagation and a Reeb graph. Then we search for a number of loops around the hole on the isosurface of the image. Finally we select the loop that minimizes the modification to the image and correct the hole in the image. At each step we limit the size of the data in memory. With these contributions our algorithm removes every hole in the image with high accuracy and low complexity even for images that do not fit into the main memory. To help doctors and scientists to obtain segmentations without holes, we make our software publicly available.
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Spécifications
- Éditeur
- Presses universitaires de Louvain
- Partie du titre
-
Numéro 24
- Auteur
- Sylvain Jaume,
- Collection
- Thèses de l'École polytechnique de Louvain
- Langue
- anglais
- Catégorie (éditeur)
- Sciences appliquées > Informatique > Réseaux et télécommunication
- Catégorie (éditeur)
- Sciences appliquées > Electricité
- Catégorie (éditeur)
- Sciences appliquées
- BISAC Subject Heading
- TEC000000 TECHNOLOGY & ENGINEERING
- Code publique Onix
- 06 Professionnel et académique
- CLIL (Version 2013-2019 )
- 3069 TECHNIQUES ET SCIENCES APPLIQUEES
- Date de première publication du titre
- 2004
- Subject Scheme Identifier Code
- Classification thématique Thema: Technologie, ingénierie et agriculture, procédés industriels
- Type d'ouvrage
- Thèse
Livre broché
- Date de publication
- 01 janvier 2004
- ISBN-13
- 978-2-93034-447-8
- Ampleur
- Nombre de pages de contenu principal : 120
- Format
- 16 x 24 x 0,7 cm
- Poids
- 208 grammes
- Prix
- 22,00 €
- ONIX XML
- Version 2.1, Version 3
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Sommaire
Abstract . . . . . . . . . . . . . . . . . . . . 1
1 Introduction . . . . . . . . . . . . . . . . . . . . 3
1.1 Imaging modalities . . . . . . . . . . . . . . . . . . . . 3
1.2 Representation of the medical scan . . . . . . . . . . . . . . . . . . . . 4
1.3 Visualization of the scan . . . . . . . . . . . . . . . . . . . . 5
1.3.1 Reviewing planar cuts . . . . . . . . . . . . . . . . . . 5
1.3.2 Volume rendering . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Surface rendering . . . . . . . . . . . . . . . . . . . . 9
1.4 Limitations of medical scans . . . . . . . . . . . . . . . . . . . . 9
1.4.1 Resolution of the scanner . . . . . . . . . . . . . . . . . . . . 10
1.4.2 Acquisition time . . . . . . . . . . . . . . . . . . . . 10
1.4.3 Movement of the patient . . . . . . . . . . . . . . . . . . . . 10
1.4.4 Artifacts due to metal objects . . . . . . . . . . . . . . . . . . . . 10
1.4.5 Radiation doses . . . . . . . . . . . . . . . . . . . . 11
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . 12
2 Neuroscience Applications . . . . . . . . . . . . . . . . . . . .13
2.1 Brain structures . . . . . . . . . . . . . . . . . . . .13
2.2 Anatomical and functional brain imaging . . . . . . . . . . . . . . . . . . . . 14
2.3 Segmentation . . . . . . . . . . . . . . . . . . . .15
2.4 Holes in the segmentation . . . . . . . . . . . . . . . . . . . . 17
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . 21
3 Theory of Topology . . . . . . . . . . . . . . . . . . . . 23
3.1 Continuous Topology . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Definition . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Non-separating loops . . . . . . . . . . . . . . . . . . . . 24
3.2 Discrete representation of a volume and a surface . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Volume representation . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Surface representation . . . . . . . . . . . . . . . . . . . . 26
3.2.3 Holes in the volume and in the surface . . . . . . . . . . . . . . . . . . . . 27
3.3 Discrete Topology . . . . . . . . . . . . . . . . . . . . 27
3.3.1 Euler characteristic . . . . . . . . . . . . . . . . . . . . 27
3.3.2 Reeb graphs . . . . . . . . . . . . . . . . . . . . 29
3.4 Definitions . . . . . . . . . . . . . . . . . . . . 36
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . 38
4 Related Work . . . . . . . . . . . . . . . . . . . . 39
4.1 Topologically constrained models . . . . . . . . . . . . . . .39
4.1.1 Surface model . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.2 Volume model . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.3 Limitations of topologically constrained models . . . 41
4.2 Correction of the image . . . . . . . . . . . . . . . . . . . . . . 41
4.2.1 Correction of a surface . . . . . . . . . . . . . . . . . . 41
4.2.2 Correction of the volume . . . . . . . . . . . . . . . . 42
4.2.3 Decomposition into components . . . . . . . . . . . . 42
4.2.4 Methods based on a Reeb graph . . . . . . . . . . . . 43
4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 Topology Detection . . . . . . . . . . . . . . . . . . . . .47
5.1 Overview of the algorithm . . . . . . . . . . . . . . . . . 47
5.1.1 Entire algorithm . . . . . . . . . . . . . . . . . . . . . 48
5.1.2 Hole detection . . . . . . . . . . . . . . . . . . . . . . . 48
5.2 Exploration of the image . . . . . . . . . . . . . . . . . 49
5.2.1 Wavefront over the image . . . . . . . . . . . . . . . . 49
5.2.2 Detection of holes in the wavefront . . . . . . . . 50
5.2.3 Illustration of the wavefront . . . . . . . . . . . . . . . 51
5.3 Modified Reeb graph . . . . . . . . . . . . . . . . . . . . . . . 53
5.4 Memory requirements in O(n 2 ) . . . . . . . . . . . . . .54
5.4.1 Wavefront propagation . . . . . . . . . . . . . . . . . 54
5.4.2 Graph construction . . . . . . . . . . . . . . . . . . . . 55
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6 Topology Localization . . . . . . . . . . . . . . . . . . . . .57
6.1 Principle of hole localization . . . . . . . . . . . . . . . . . . . 57
6.2 Localization of a hole detected in the graph . . . . . . . 58
6.3 Localization of a hole inside a ribbon . . . . . . . . . . . . 60
6.4 Localization of a cross loop . . . . . . . . . . . . . . . . . . . 62
6.5 Shortest path algorithm . . . . . . . . . . . . . . . . . . . . . 63
6.5.1 Improved accuracy . . . . . . . . . . . . . . . . . . . . 63
6.5.2 Reduced complexity . . . . . . . . . . . . . . . . . . . 64
6.6 Closing the loop . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.7 Reducing the complexity . . . . . . . . . . . . . . . . . . . 66
6.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7 Topology Simplification . . . . . . . . . . . . . . . . . . . . .69
7.1 Structure of the algorithm . . . . . . . . . . . . . . . . . . . . 69
7.2 Principle of hole removal . . . . . . . . . . . . . . . . . . . . . 69
7.3 Filling or emptying the loop . . . . . . . . . . . . . . . . . . . 72
7.3.1 Signed areas of contours . . . . . . . . . . . . . . . . . 72
7.3.2 Reeb loop and cross loop . . . . . . . . . . . . . . . . 72
7.4 Rasterization inside the loop . . . . . . . . . . . . . . . . 73
7.4.1 Rasterization along lines . . . . . . . . . . . . . . . . . 74
7.4.2 Comparison with other methods . . . . . . . . . . . . 74
7.5 Loop selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.6 Correction of gray scale images . . . . . . . . . . . . 76
7.6.1 Updating the graph . . . . . . . . . . . . . . . . . . . 77
7.6.2 Avoiding the halting problem . . . . . . . . . . .78
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8 Results 81 8.1 Goal of the experiment . . . . . . . . 81
8.2 Input and output of the algorithm . . . . . . . . . . . . . . . 82
8.3 Visualization of the output image . . . . . . . . . . . . . . . . 83
8.4 Visualization of the modified voxels . . . . . . . . . . . . . . 85
8.4.1 Differences in the volume . . . . . . . . . . . . . . . . 85
8.4.2 Differences on a plane . . . . . . . . . . . . . . . . . . 85
8.5 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.5.1 Number of modified voxels . . . . . . . . . . . . . . . 87
8.5.2 Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.5.3 Size of the corrections . . . . . . . . . . . . . . . . . . 88
8.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.6.1 Assessment of the method . . . . . . . . . . . . . . . . 90
8.6.2 Further experiments . . . . . . . . . . . . . . . . . . . 91
8.6.3 Comparison procedure . . . . . . . . . . . . . . . . . . 91
8.6.4 Selection of the best loop . . . . . . . . . . . . . . . . . 92
8.6.5 Other criteria for the hole removal . . . . . . . . . . . 92
8.6.6 Dependence on the direction of propagation . . . . . . . . . . 93
8.6.7 Correction of large holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8.6.8 Interactive topology simplification . . . . . . . . . . . . . . . . . . . . 94
8.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
9 Conclusions and Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . 97
9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
9.2 Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.2.1 Improved segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
9.2.2 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
9.2.3 Morphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.2.4 Shape Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104
9.2.5 Data compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107