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1、StatisticalTomographyofMicroscopicLifeAviadLevis,YoavY.Schechner,RonenTalmonViterbiFacultyofElectricalEngineeringTechnion-IsraelInstituteofTechnology,Haifa,Israelaviad.levis@gmail.com;yoav@ee.technion.ac.il;ronen@ee.technion.ac.ilAbstractWeachievetomographyof3Dvolumetricn
2、aturalob-jects,whereeachprojected2Dimagecorrespondstoadifferentspecimen.Eachspecimenhasunknownrandom3Dorientation,location,andscale.Thisimagingsce-narioisrelevanttomicroscopicandmesoscopicorgan-isms,aerosolsandhydrosolsviewednaturallybyamicro-scope.In-classscalevariationi
3、nhibitspriorsingle-particlereconstructionmethods.Wethusgeneralizetomographicrecoverytoaccountforalldegreesoffreedomofasimilar-itytransformation.Thisenablesgeometricself-calibrationinimagingoftransparentobjects.Wemakethecomputa-tionalloadmanageableandreachgoodqualityrecons
4、truc-tioninashorttime.Thisenablesextractionofstatisticsthatareimportantforascientificstudyofspecimenpopu-lations,specificallysizedistributionparameters.Weapplythemethodtostudyofplankton.1.IntroductionTheenvironmentisteemingwithmicroscopicandmeso-Figure1.Arandomsetofmovingor
5、ganismsatdifferentorienta-scopicobjects,whosestudybothstructurallyandasapopu-tionsandscalesisimagedusingasubmergedmicroscope.Statisti-lationiscentraltoscience[39].Examplesincludeaerosols,caltomographicreconstructionyieldsself-calibratedestimationofhydrosols,andsmallorgani
6、smswhichhavewidevarietiesthe3Ddensitymap,alongwiththeunknownorientationandscaleofclasses.Itispossibletotakesamplestoalabandmeasureofeachsample.Estimationofthepopulation’ssize-distributionistheir3Dstatistics,whiletheyarefewandsitstill.However,thusenabled,jointlywith3Drecov
7、ery(3D-POP).Microscope3Dsuchanapproachhasdrawbacks.Inalab,organismsdomodelcourtesyofJaffeLab.notbehaveasinnature.Tominimizebiasingnature,in-situmicroscopesareused,asillustratedinFig.1.There,andhigh-temporalresolutionin2D[1,15],while3Dimagingofalsoinmanylabstudies,specimen
8、sdonotsitstill.Hencefixatedplanktonisdoneinthelaboratory[22,27].eachimageisofadifferentspecimenat
