西安文理學院本科畢業設計（論文）第1頁附錄原文：ProbingpictorialrelieffromexperimentaldesigntosurfacereconstructionAbstract:Theperceptionofpictonalsurfaceshasbeenstudiedquantitativelyformorethan20years.Dutingthistime,the“gaugefiguremethod”hasbeenshowntobeafastandintuitivemethodtoquantifypictorialrelief.Inthismethod,observershavetoadjusttheattitudeofagaugefiguresuchthatitappearstolieflatonasurfaceinpictorialspace.Althoughthemethodhasreceivedsubstantialattentionintheliteratureandhasbecomeincreasinglypopular,aclear,step-by-stepdescriptionhasnotbeenpublishedyet.Inthisarticle,adetaileddescriptionofthemethodisprovided:stimulusandsamplepreparation,performingtheexperiment,andreconstructinga3-Dsurfacefromtheexperimentaldata.Furthermore,software(writteninPsychToolbox)basedonthisdescriptionisprovidedinanonlinesupplement.Thisreportservesthreepurposes:First,itfacilitatesexperimenterswhowanttousethegaugefiguretaskbuthavebeenunabletodesignit,duetothelackofinformationintheliterature.Second,thedetaileddescriptioncanfacilitatethedesignofsoftwareforvariousotherplatforms,possiblyWeb-based.Third,themethoddescribedinthisarticleisextendedtoobjectswithholesandinnercontours.Thisclassofobjectshavenotyetbeeninvestigatedwiththegaugefiguretask.Keywords:Depthperception.Pictorialspace.3DshapeIntroductionAlmost20yearsago,Koenderink,vanDoorn,andKappers(1992)publishedakeystudyonquantifyingtheperceived3-Dstructureofapictorialsurface.Theirexperientaltaskwastoadjusttheattitudeofagaugefigureprobe.Thegaugefigureconsistsofacirclewitharodthatsticksoutperpendicularlyfromthemiddle.Observersareinstructedtomanipulatethe3-Dorientationofthisprobesuchthatthediskappearstolieflatonthepictorialsurface,whiletherodconsequentlysticksoutinthenormaldirection.Sincethen,numerousresearchershaveusedthisparadigmtostudyvisualperceptionor3-Dshape.Yetthecommunityofscientistsusingthismethodhasbeenlimitedtothosewhounderstandtheunderlyingmathematicsandareabletoexperimentallyimplementthismethod.Detaileddocumentationhasneverbeenpublished西安文理學院本科畢業設計（論文）第2頁inacompletefashion.Thisarticlewillexplainindetailallstepsoftheprocedure.Furthermore,softwarewrittenforPsychToolbox(Brainard,1997；Pelli,1997)ismadeavailablethatcoversallofthesestepsandshouldleadtoaneasilyusableprocedure,bymeansofwhichanyuserofPsychToolboxcanconductgaugefigureexperiments.TheprocedureforrunninganexperimentisvisualizedinFig.1.Eachofthestepscanbedescribedasfollows.ContourselectionAfterselectingastimulusimage,theexperimenterneedstoselectwhichpartofthepictorialsurfaceistobeusedfortheexperiment.TriangulationWithinthecontour,measurementsamplesneedtobedefined.Thisisdoneusingatriangulationgrid.ExperimentAfteritissetup,theexperimentcanbeconducted.Thegaugefigureprobeshouldberenderedinthepicture,andtheobservershouldbeabletomanipulateitsattitude.Fig.1Illustrationofthefourproceduralsteps3-DreconstructionOnthebasisoftheobserverssettings,the3-Dsurfacecanbereconstructed.Thesedataarethefinalresult；furtheranalysiswilldependonthespecificresearchquestion,andshouldthusbedesignedbytheexperimenter.Thesefourstepswillnowbeexplainedindetail.Contourselection:First,animageisneeded.Someshapeshouldbevisible,preferablyasmoothone.Inpreviousresearch,onlyanoutercontourwasdefined.Themethodpresentedherealsoallowsfordefiningaholeandinnercontours.ThesethreetypesofcontoursarevisualizedinFig.2.Theexperimentercandefinethecontourmanuallybyselectingcontoursamplepointsthatformapolygonthatapproximatestheactualcontour.Thedistancebetweenthecontoursamplepointscanhaveapproximatelythesamesizeasthetriangulationfaces.Asamplingofcontourpoints,asshownbythereddotsinFig.3,isthussufficientlydetailed.Theoutputofthecontourprocedureconsistsofthreesetsofcoordinates,fortheouter,inner,andholecontours,whichcanbewritteninn-by-2arrays.Apointonthecontourcanbewrittenascjxj；yj,whereqdefinesthecontourtypebythelettero,h,oriforouter,hole,orcontours,thelastelement(say,nandm,respectively)Triangulation:西安文理學院本科畢業設計（論文）第3頁Basedonthecontourdata,thetriangulationcanbedefined.Tothisend,atriangulargridisusedthatinprinciplecoversthewholescreen.However,onlypointswithintheoutercontourthatarenotwithintheholecontourshouldbeusedanddisplayed(atthisstage,innercontoursareneglected).Thisrequiresanalgorithmtotestwhetherapointisbetweentheouterandholecontours.Contour-enclosedpointsfilteringAscanbeseeninFig.3,asimplerulecanbedefinedtoassesswhetherapointpiiswithintheclosedcontours:Whenahorizontallineisdrawninthepositivexdirection,itintersectsanumberoftimeswiththeclosedcontour.Ifthisnumberisodd,piiswithintheclosedcontours.Thus,thenumberofintersectionsneedstobecalculated.First,weneedtoselectcontourpointpairswhosecoordinatesenclosethey-coordinateofthepoint.InFig.3,thesepairsareci,ci+1andcj,cj+1.Nowwecandefinestraightlinesthroughthesepointpairs.Astraightlinethroughtwosubsequentcontourpointsci=(xi,yi)andci+1=(xi+1,yi+1)canbedefinedasy=ax+b,witha=(yi+1yi)/(xi+1xi)andb=yiaxi.Fig.2Definitionofthethreetypesofcontours西安文理學院本科畢業設計（論文）第4頁Fig.3VisualizationofthealgorithmthattestwhetherapointiswithintheclosedcontoursWhenthisprocedureisperformedforallpoints,wegetoneintersectionforp1(odd,andthusthispointisinsidetheclosedcontours),twointersectionsforp2(outside),andsoforth.Testingwhetherapointiswithintheclosedcontoursiscomputationallylaborious.Therefore,theproceduremayincludeaninitialselectionofthetriangulationpositionsthatarewithintherectangledefinedbythewidthandheightoftheoutercontour,asisshownbytheouterdottedlineinFig.3.AdjustingthetriangulationgridsizeandpositionItcanbeusefulfortheexperimentertoadjustthegridsizeandpositionofthetriangulationinrealtime.Thiscanbedoneusingtheproceduresdescribedabove,whicharealsoimplementedinthesupplementalsoftware.Inthesoftware,thepositioncanbeadjustedwiththemouseandgridsizebythearrowkeys,asisillustratedinFig.4a,butothertypesofimplementationsmaybeequallyuserfriendly.CalculatingfacesandbarycentresandperformingfinalpointfilteringUptonow,onlypointsthatspanthetriangulargridhavebeenused,withoutexplicitfacenumbering.However,thereconstructionalgorithmrequiresexplicitinformationaboutthevertexnumbersthatconsti-tutethetriangles.Eachface(triangle)isdefinedbythreevertices,soadefinitionofallfacescomprisesanm-by-3matrix,withasetofthreenumbersineachrowthatrefertothevertices.Notethatthenumberoffacesdoesnotequalthenumberofvertices.Thefacescanbecalculatedwithabrute-forcemethod,whichiswhythisalgorithmisnotusedduringthereal-timeadjustmentofgridsizeandlocation.Havingdefinedtheindividualtriangles,wecancalculatethebarycentresofthefaces,whicharetheactualsamplepointswherethegaugefigurewillberendered.Lastly,trianglescrossingtheinnercontoursneedtobefiltered.Tothisend,alineintersectionalgorithmisneeded.Thebasicquestionis,dot