Usinggrey-levelanddistanceinformation formedialsurfacerepresentationofvolumeimages StinaSvensson,IngelaNystr¨ om CentreforImageAnalysis L¨ agerhyddsv¨ agen17,75237Uppsala,SWEDEN stina@cb.uu.se, ingela@cb.uu.se CarloArcelli,GabriellaSannitidiBaja IstitutodiCibernetica,CNR ViaCampiFlegrei34,80078Pozzuoli,Napoli,ITALY car@imagm.cib.na.cnr.it, gsdb@imagm.cib.na.cnr.it Abstract A medial surface representation of a grey-level volume im- age is computed. The foreground is reduced to a sub- set topologically equivalent to the initial foreground and mainly consisting of surfaces centred within regions hav- inglocally higher intensities, here, regarded as more infor- mative. This result is obtained by combining distance in- formation with grey-level information. A surface skeleton is first computed, where excessive shortening is prevented by a regularity condition defined on the distance transform. The structure of the surface skeleton is then simplified by re- moving some peripheral surfaces, so obtaining the desired medial surface representation. 1.Introduction Thenumberofimagingdevicesgenerating3D(volume)im- agesandtheapplicationsutilizingtheseimagesareincreas- ing.A3Dimageisgenerallygrey-levelandhardtotrans- formintoabi-levelimagewithoutlossofimportantinfor- mation. Thispaperpresentsashaperepresentation,where thegrey-leveldistributionoftheimageisinfocus. Volumeimagescontainlargeamountsofdata,butthein- formationrelevantforshapeanalysisisactuallycarriedbya limitednumberofvoxels.Thus,thereisaninterestforrep- resentationschemeswithreduceddimensionality,e.g.,the skeleton. Skeletonization of bi-level 2D images has been widelyinvestigated.Forgrey-level2Dimages,skeletoniza- tionhasbeenfacedthoroughlyonlyduringthelastdecade, [1,2,3,7]. Forbi-level3Dimages,whereallforeground voxelshavethesamegrey-leveland,hence,thesamerele- vance,anumberofalgorithmsareavailableproducingthe desiredresult:theskeletonpreservesthetopologicalprop- ertiesoftheforegroundand,insomecases,allowsitsrecon- struction. Forgrey-level3Dimages,wheretheforeground ischaracterizedbyseveralgrey-levels,thecontributionsare few,[6,9].Inthiscase,representingtheforegroundinterms ofentitiesoflowerdimensionality,surfacesandcurves,is not a straightforward task, as the relevant information is not evenly distributed. Here, we refer to image domains where the relevant information is gathering in correspon- dencewiththeforegroundsubsetswithlocallyhigherinten- sities,sothatsurfacesandcurvesshouldbefoundmainly therein. This is the case, e.g., for MRA (Magnetic Reso- nance Angiography) images, where the foreground is the bloodvessels,whicharecharacterizedbyhighintensities. Weoutlineamethodtoreducetheforegroundofagrey- level 3D image to a medial surface representation. This representationistopologicallyequivalenttotheinitialfore- groundandismainlyconstitutedbysurfaces(andcurves) centredwithinregionshavinglocallyhigherintensities.Our medialsurfacerepresentationisobtainedviaaprocessthat wecall3Dgrey-skeletonization. Thesetresultingfromit, the grey-skeleton,isprocessedtomaintainthemostsignif- icant surfaces (and curves), originating the desired grey- medialsurfacerepresentation(grey-MSR).Ourdefinitionof agrey-skeleton(and,hence,ofagrey-MSR)ofa3Dimage descendsfromthenotionsoftheskeletonofagrey-level2D image,[2],andtheskeletonofabi-level3Dimage,[11]. 2.Notionsandnotations Weconsideragrey-levelvolumeimage .Anyvoxel in has26neighboursinthe setofvoxelscentred on :6sharingaface,12sharinganedge,and8sharing 1051-4651/02 $17.00 (c) 2002 IEEE