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西安文理学院本科毕业设计(论文)第1页附录原文ProbingpictorialrelieffromexperimentaldesigntosurfacereconstructionAbstractTheperceptionofpictonalsurfaceshasbeenstudiedquantitativelyformorethan20years.Dutingthistime,thegaugefiguremethodhasbeenshowntobeafastandintuitivemethodtoquantifypictorialrelief.Inthismethod,observershavetoadjusttheattitudeofagaugefiguresuchthatitappearstolieflatonasurfaceinpictorialspace.Althoughthemethodhasreceivedsubstantialattentionintheliteratureandhasbecomeincreasinglypopular,aclear,stepbystepdescriptionhasnotbeenpublishedyet.Inthisarticle,adetaileddescriptionofthemethodisprovidedstimulusandsamplepreparation,performingtheexperiment,andreconstructinga3Dsurfacefromtheexperimentaldata.Furthermore,softwarewritteninPsychToolboxbasedonthisdescriptionisprovidedinanonlinesupplement.ThisreportservesthreepurposesFirst,itfacilitatesexperimenterswhowanttousethegaugefiguretaskbuthavebeenunabletodesignit,duetothelackofinformationintheliterature.Second,thedetaileddescriptioncanfacilitatethedesignofsoftwareforvariousotherplatforms,possiblyWebbased.Third,themethoddescribedinthisarticleisextendedtoobjectswithholesandinnercontours.Thisclassofobjectshavenotyetbeeninvestigatedwiththegaugefiguretask.KeywordsDepthperception.Pictorialspace.3DshapeIntroductionAlmost20yearsago,Koenderink,vanDoorn,andKappers1992publishedakeystudyonquantifyingtheperceived3Dstructureofapictorialsurface.Theirexperientaltaskwastoadjusttheattitudeofagaugefigureprobe.Thegaugefigureconsistsofacirclewitharodthatsticksoutperpendicularlyfromthemiddle.Observersareinstructedtomanipulatethe3Dorientationofthisprobesuchthatthediskappearstolieflatonthepictorialsurface,whiletherodconsequentlysticksoutinthenormaldirection.Sincethen,numerousresearchershaveusedthisparadigmtostudyvisualperceptionor3Dshape.Yetthecommunityofscientistsusingthismethodhasbeenlimitedtothosewhounderstandtheunderlyingmathematicsandareabletoexperimentallyimplementthismethod.Detaileddocumentationhasneverbeenpublished西安文理学院本科毕业设计(论文)第2页inacompletefashion.Thisarticlewillexplainindetailallstepsoftheprocedure.Furthermore,softwarewrittenforPsychToolboxBrainard,1997Pelli,1997ismadeavailablethatcoversallofthesestepsandshouldleadtoaneasilyusableprocedure,bymeansofwhichanyuserofPsychToolboxcanconductgaugefigureexperiments.TheprocedureforrunninganexperimentisvisualizedinFig.1.Eachofthestepscanbedescribedasfollows.ContourselectionAfterselectingastimulusimage,theexperimenterneedstoselectwhichpartofthepictorialsurfaceistobeusedfortheexperiment.TriangulationWithinthecontour,measurementsamplesneedtobedefined.Thisisdoneusingatriangulationgrid.ExperimentAfteritissetup,theexperimentcanbeconducted.Thegaugefigureprobeshouldberenderedinthepicture,andtheobservershouldbeabletomanipulateitsattitude.Fig.1Illustrationofthefourproceduralsteps3DreconstructionOnthebasisoftheobserverssettings,the3Dsurfacecanbereconstructed.Thesedataarethefinalresultfurtheranalysiswilldependonthespecificresearchquestion,andshouldthusbedesignedbytheexperimenter.Thesefourstepswillnowbeexplainedindetail.ContourselectionFirst,animageisneeded.Someshapeshouldbevisible,preferablyasmoothone.Inpreviousresearch,onlyanoutercontourwasdefined.Themethodpresentedherealsoallowsfordefiningaholeandinnercontours.ThesethreetypesofcontoursarevisualizedinFig.2.Theexperimentercandefinethecontourmanuallybyselectingcontoursamplepointsthatformapolygonthatapproximatestheactualcontour.Thedistancebetweenthecontoursamplepointscanhaveapproximatelythesamesizeasthetriangulationfaces.Asamplingofcontourpoints,asshownbythereddotsinFig.3,isthussufficientlydetailed.Theoutputofthecontourprocedureconsistsofthreesetsofcoordinates,fortheouter,inner,andholecontours,whichcanbewritteninnby2arrays.Apointonthecontourcanbewrittenascj¼xjyj,whereqdefinesthecontourtypebythelettero,h,oriforouter,hole,orcontours,thelastelementsay,nandm,respectivelyTriangulation西安文理学院本科毕业设计(论文)第3页Basedonthecontourdata,thetriangulationcanbedefined.Tothisend,atriangulargridisusedthatinprinciplecoversthewholescreen.However,onlypointswithintheoutercontourthatarenotwithintheholecontourshouldbeusedanddisplayedatthisstage,innercontoursareneglected.Thisrequiresanalgorithmtotestwhetherapointisbetweentheouterandholecontours.ContourenclosedpointsfilteringAscanbeseeninFig.3,asimplerulecanbedefinedtoassesswhetherapointpiiswithintheclosedcontoursWhenahorizontallineisdrawninthepositivexdirection,itintersectsanumberoftimeswiththeclosedcontour.Ifthisnumberisodd,piiswithintheclosedcontours.Thus,thenumberofintersectionsneedstobecalculated.First,weneedtoselectcontourpointpairswhosecoordinatesenclosetheycoordinateofthepoint.InFig.3,thesepairsare{ci,ci1}and{cj,cj1}.Nowwecandefinestraightlinesthroughthesepointpairs.Astraightlinethroughtwosubsequentcontourpointscixi,yiandci1xi1,yi1canbedefinedasyaxb,withayi1–yi/xi1–xiandbyi–axi.Fig.2Definitionofthethreetypesofcontours西安文理学院本科毕业设计(论文)第4页Fig.3VisualizationofthealgorithmthattestwhetherapointiswithintheclosedcontoursWhenthisprocedureisperformedforallpoints,wegetoneintersectionforp1odd,andthusthispointisinsidetheclosedcontours,twointersectionsforp2outside,andsoforth.Testingwhetherapointiswithintheclosedcontoursiscomputationallylaborious.Therefore,theproceduremayincludeaninitialselectionofthetriangulationpositionsthatarewithintherectangledefinedbythewidthandheightoftheoutercontour,asisshownbytheouterdottedlineinFig.3.AdjustingthetriangulationgridsizeandpositionItcanbeusefulfortheexperimentertoadjustthegridsizeandpositionofthetriangulationinrealtime.Thiscanbedoneusingtheproceduresdescribedabove,whicharealsoimplementedinthesupplementalsoftware.Inthesoftware,thepositioncanbeadjustedwiththemouseandgridsizebythearrowkeys,asisillustratedinFig.4a,butothertypesofimplementationsmaybeequallyuserfriendly.CalculatingfacesandbarycentresandperformingfinalpointfilteringUptonow,onlypointsthatspanthetriangulargridhavebeenused,withoutexplicitfacenumbering.However,thereconstructionalgorithmrequiresexplicitinformationaboutthevertexnumbersthatconstitutethetriangles.Eachfacetriangleisdefinedbythreevertices,soadefinitionofallfacescomprisesanmby3matrix,withasetofthreenumbersineachrowthatrefertothevertices.Notethatthenumberoffacesdoesnotequalthenumberofvertices.Thefacescanbecalculatedwithabruteforcemethod,whichiswhythisalgorithmisnotusedduringtherealtimeadjustmentofgridsizeandlocation.Havingdefinedtheindividualtriangles,wecancalculatethebarycentresofthefaces,whicharetheactualsamplepointswherethegaugefigurewillberendered.Lastly,trianglescrossingtheinnercontoursneedtobefiltered.Tothisend,alineintersectionalgorithmisneeded.Thebasicquestionis,dothelinesbetweentwopointpairs{p1,p2}and{p3,p4},asshowninFig.5,coincideThiscansimplybecalculatedbyparameterizingvectorsthroughtheselinesv12ttp2–p1p1andv34ssp4–p3p3.When0t1,v12tliesbetweenp1andp2,andtheequivalentholdsfortheparameters.Theintersectionparameterscanbefoundbysolvingv12tv34s.Ifbothintersectionparametersarebetweenzeroandone,thelinesintersect.AscanbeseeninFig.4,itcanhappenthatatrianglelinecrossesthehole,whichisunwanted.Toovercomethisproblem,theholecontourshouldbeincludedinthelastfilteringprocedure.Whentheexperimenterissatisfiedwiththetriangulationparameters,thepointsvertices,faces,andbarycentresshouldbesaved.Ascreenshotofthefinalresultfromthesupplementalsoftwareisalsoexported,forlaterreferenceseeFig.4b.
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