Presses universitaires de Louvain onixsuitesupport@onixsuite.com 20260611T0728Z eng

COM.ONIXSUITE.9782930344478 03 01 Presses universitaires de Louvain 02 2930344474 03 9782930344478 15 9782930344478 02 01 00 BC 01 9.45 in 02 6.30 in 03 0.71 in 08 7.33 oz 01 24 cm 02 16 cm 03 0.71 cm 08 208 gr BE 10 02 24 01 02 Thèses de l'Université catholique de Louvain (UCL) 03 Thèses de l'École polytechnique de Louvain 01 01 Numéro 24 Topology Simplification Algorithm for the Segmentation of Medical Scans 1 A01 01 Onixsuite Contributor ID 5644 Sylvain Jaume Jaume, Sylvain Sylvain Jaume 1 01 eng 00 120 03 10 TEC000000 24 INTERNET Réseaux et télécommunication 24 INTERNET Electricité 24 INTERNET Sciences appliquées 29 2012 3069 TECHNIQUES ET SCIENCES APPLIQUEES 93 T 01 06 03 00 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. 02 00 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... 03 00 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. 02 00 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... 04 00 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 01 00 03 02 01 D502 02 188 03 123 06 e97190b455020dbb9100b641e4708606 07 9934 https://pul.uclouvain.be/resources/titles/29303100661440/images/6e96be832cf8bc6b35a956e8fb66c76a/THUMBNAIL/9782930344478.jpg 17 20160216T0949Z 06 3052405007518 Presses universitaires de Louvain 01 01 Dilicom PULOUVAIN 06 3052405007518 Presses universitaires de Louvain Louvain-la-Neuve BE 04 01 20040101 11 20040101 01 WORLD 02 01 GCOI 29303100661440 WORLD 00 03 06 3012405004818 CIACO - DUC 01 2 20 1 02 00 02 02 STD 02 22.00 01 R 6.00 20.75 1.25 EUR BE FR 00 02 06 3019000200508 Librairie Wallonie-Bruxelles 33 www.librairiewb.com/ http://www.librairiewb.com/ 01 2 20 1 04 00 02 02 STD 02 22.00 01 R 5.50 20.85 1.15 EUR