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. . . . . . . . . . . . . . . . . . . . . . .
Industry Reviews
From the reviews: R. Malladi (ed.) Geometric Methods in Bio-Medical Image Processing "This is an excellent monograph on geometric methods in biomedical image processing. I strongly recommend this book to visualization experts in mathematics, computer science and bio-medical applications and to research students on above topics."--JOURNAL OF COMPUTATIONAL METHODS IN APPLIED MATHEMATICS "This book is based on the conference held at the University of Bologna at June 1999. ! The book gives a good review on some of the traditional applications in medical imagery (CT, MR, Ultrasound). ! This is an excellent monograph on geometric methods in biomedical image processing. I strongly recommend this book to visualization experts in mathematics, computer science and bio-medical applications and to research students on the above topics." (T. E. Simos, Journal of Computational Methods in Sciences and Engineering, Vol. 3 (2), 2003)
