Geometric Methods in Bio-Medical Image Processing

2002
ISBN: 978-3-540-43216-6
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 147 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 407 g

Reihe: Mathematics and Visualization

showcleverapplicationsinvesseldetectionin3Dmedicaldata. Finally,in Chapter7,A. Sarti,K. Mikula,F. Sgallari,andC. Lamberti,describean- linearmodelfor?lteringtimevarying3Dmedicaldataandshowimpressive resultsinbothultrasoundandechoimages. IoweadebtofgratitudetoClaudioLambertiandAlessandroSartifor invitingmetoBologna,andlogisticalsupportfortheconference. Ithank thecontributingauthorsfortheirenthusiasmand?exibility,theSpringer mathematicseditorMartinPetersforhisoptimismandpatience,andJ. A. Sethianforhisunfailingsupport,goodhumor,andguidancethroughthe years. Berkeley,California R. Malladi October,2001 Contents 1 FastMethodsforShapeExtractioninMedicaland BiomedicalImaging. 1 R. Malladi,J. A. Sethian 1. 1Introduction. 1 1. 2TheFastMarchingMethod. 3 1. 3ShapeRecoveryfromMedicalImages. 6 1. 4Results. 10 References. 13 2 AGeometricModelforImageAnalysisinCytology. 19 C. OrtizdeSolorzano,R. Malladi,S. J. Lockett 2. 1Introduction. 19 2. 2GeometricModelforImageAnalysis. 20 2. 3SegmentationofNuclei. 22 2. 4SegmentationofNucleiandCellsUsingMembrane-RelatedProtein Markers. 31 2. 5Conclusions. 37 References. 38 3 LevelSetModelsforAnalysisof2Dand3D EchocardiographicData. 43 A. Sarti,C. Lamberti,R. Malladi 3. 1Introduction. 43 3. 2TheGeometricEvolutionEquation. 45 3. 3TheShock-TypeFiltering. 46 3. 4ShapeExtraction. 49 3. 52DEchocardiography. 52 3. 62D+timeEchocardiography. 53 3. 73DEchocardiography. 56 3. 83D+timeEchocardiography. 58 3. 9Conclusions. 59 References. 61 4 ActiveContourandSegmentationModelsusing GeometricPDE’sforMedicalImaging. 63 T. F. Chan,L. A. Vese 4. 1Introduction. 63 4. 2DescriptionoftheModels. 64 4. 3ApplicationstoBio-MedicalImages. 68 4. 4ConcludingRemarks. 68 References. 70 VIII Contents 5 SphericalFlatteningoftheCortexSurface. 77 A. Elad(Elbaz),R. Kimmel 5. 1Introduction. 77 5. 2FastMarchingMethodonTriangulatedDomains. 80 5. 3Multi-DimensionalScaling. 80 5. 4CortexUnfolding. 84 5. 5Conclusions. 86 References. 86 6 GroupingConnectedComponentsusingMinimalPath Techniques. 91 T. Deschamps,L. D. Cohen 6. 1Introduction. 91 6. 2MinimalPathsin2Dand3D. 93 6. 3FindingContoursfromaSetofConnectedComponentsR. 96 k 6. 4FindingaSetofPathsina3DImage. 102 6. 5Conclusion. 103 References. 104 7 NonlinearMultiscaleAnalysisModelsforFilteringof 3D+TimeBiomedicalImages. 107 A. Sarti,K. Mikula,F. Sgallari,C.

Zielgruppe

Research

Autoren/Hrsg.

Malladi, Ravikanth

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Biowissenschaften Biowissenschaften
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizinische Fachgebiete Bildgebende Verfahren, Nuklearmedizin, Strahlentherapie Radiologie, Bildgebende Verfahren
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Klinische und Innere Medizin Innere Medizin
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker

Inhaltsverzeichnis

1 Fast Methods for Shape Extraction in Medical and Biomedical Imaging.- 1.1 Introduction.- 1.2 The Fast Marching Method.- 1.3 Shape Recovery from Medical Images.- 1.4 Results.- References.- 2 A Geometric Model for Image Analysis in Cytology.- 2.1 Introduction.- 2.2 Geometric Model for Image Analysis.- 2.3 Segmentation of Nuclei.- 2.4 Segmentation of Nuclei and Cells Using Membrane-Related Protein Markers.- 2.5 Conclusions.- References.- 3 Level Set Models for Analysis of 2D and 3D Echocardiographic Data.- 3.1 Introduction.- 3.2 The Geometric Evolution Equation.- 3.3 The Shock-Type Filtering.- 3.4 Shape Extraction.- 3.5 2D Echocardiography.- 3.6 2D + time Echocardiography.- 3.7 3D Echocardiography.- 3.8 3D + time Echocardiography.- 3.9 Conclusions.- References.- 4 Active Contour and Segmentation Models using Geometric PDE’s for Medical Imaging.- 4.1 Introduction.- 4.2 Description of the Models.- 4.3 Applications to Bio-Medical Images.- 4.4 Concluding Remarks.- References.- 5 Spherical Flattening of the Cortex Surface.- 5.1 Introduction.- 5.2 Fast Marching Method on Triangulated Domains.- 5.3 Multi-Dimensional Scaling.- 5.4 Cortex Unfolding.- 5.5 Conclusions.- References.- 6 Grouping Connected Components using Minimal Path Techniques.- 6.1 Introduction.- 6.2 Minimal Paths in 2D and 3D.- 6.3 Finding Contours from a Set of Connected Components Rk.- 6.4 Finding a Set of Paths in a 3D Image.- 6.5 Conclusion.- References.- 7 Nonlinear Multiscale Analysis Models for Filtering of 3D + Time Biomedical Images.- 7.1 Introduction.- 7.2 Nonlinear Diffusion Equations for Processing of 2D and 3D Still*Images.- 7.3 Space-Time Filtering Nonlinear Diffusion Equations.- 7.4 Numerical Algorithm.- 7.5 Discussion on Numerical Experiments.- 7.6 Preconditioning and Solving of Linear Systems.-References.- Appendix. Color Plates.