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Mathematics - Computational Science & Engineering | Geometric Methods in Bio-Medical Image Processing

Geometric Methods in Bio-Medical Image Processing

Malladi, Ravikanth (Ed.)

2002, VIII, 147 p.

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Itgivesmegreatpleasuretoeditthisbook. Thegenesisofthisbookgoes backtotheconferenceheldattheUniversityofBolognainJune1999,on collaborativeworkbetweentheUniversityofCaliforniaatBerkeleyandthe UniversityofBologna. Theoriginalideawastoinvitesomespeakersatthe conferencetosubmitarticlestothebook. Thescopeofthebookwaslater- hancedand,inthepresentform,itisacompilationofsomeoftherecentwork usinggeometricpartialdi?erentialequationsandthelevelsetmethodology inmedicalandbiomedicalimageanalysis. Thesynopsisofthebookisasfollows:Inthe?rstchapter,R. Malladi andJ. A. Sethianpointtotheoriginsoftheuseoflevelsetmethodsand geometricPDEsforsegmentation,andpresentfastmethodsforshapes- mentationinbothmedicalandbiomedicalimageapplications. InChapter 2,C. OrtizdeSolorzano,R. Malladi,andS. J. Lockettdescribeabodyof workthatwasdoneoverthepastcoupleofyearsattheLawrenceBerkeley NationalLaboratoryonapplicationsoflevelsetmethodsinthestudyand understandingofconfocalmicroscopeimagery. TheworkinChapter3byA. Sarti,C. Lamberti,andR. Malladiaddressestheproblemofunderstanding di?culttimevaryingechocardiographicimagery. Thisworkpresentsvarious levelsetmodelsthataredesignedto?tavarietyofimagingsituations,i. e. timevarying2D,3D,andtimevarying3D. InChapter4,L. VeseandT. F. Chanpresentasegmentationmodelwithoutedgesandalsoshowextensions totheMumford-Shahmodel. Thismodelisparticularlypowerfulincertain applicationswhencomparisonsbetweennormalandabnormalsubjectsis- quired. Next,inChapter5,A. EladandR. Kimmelusethefastmarching methodontriangulateddomaintobuildatechniquetounfoldthecortexand mapitontoasphere. Thistechniqueismotivatedinpartbynewadvances infMRIbasedneuroimaging. InChapter6,T. DeschampsandL. D. Cohen presentaminimalpathbasedmethodofgroupingconnectedcomponentsand 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.

Content Level » Research

Keywords » Biomedical Images - Diffusion - Ultrasound Imagery - algorithm - calculus - computed tomography (CT) - echocardiography - filtering - image analysis - image processing - life sciences - medical imaging - methodology - protein - ultrasound

Related subjects » Biomedical Sciences - Computational Science & Engineering - Radiology

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