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-RelatedPr
