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..SensingcolorwiththeTAOSTCS230TheTAOSTCS230isasmall,highlyintegratedcolorsensingdevicepackagedinaclearplastic8-pinSOIC.Itreports,asanalogfrequency,theamountofshortwave<blue>,mediumwave<green>,longwave<red>,andwideband<white>opticalpowerincidentontothedevice.Itcanbeusedinavarietyofcolorsensingapplications.Detailsofthedevicecanbefoundinitsdatasheet.ThiswhitepaperdetailstheconceptsandcalculationsinvolvedincolorsensingusingtheTCS230.WewillusetheColorCheckerchartasanopticalstimulustoworkthroughanumericalexampleofcolorsensing.Thechart,depictedinFigure1,ismanufacturedanddistributedbyGretagMacbeth.Thechartmeasuresapproximately13inchesby9inches<330mmby230mm>;itcontains24coloredpatchesarrangedina6by4array.Figures2through5overleafshowthespectralreflectanceofthepatchesineachofthefourrowsofthechart–thatis,thefractionofincidentlightthatisreflected<withrespecttoanidealdiffusereflector>,asafunctionofwavelengthfrom350nmto750nm.Figure1TheColorCheckercontains18coloredpatchesanda6-stepgrayseries.Figure2ColorCheckerspectra,toprow.Figure3ColorCheckerspectra,secondrow.Figure4ColorCheckerspectra,thirdrow.Figure5ColorCheckerspectra,bottomrow<neutralseries>Figure6Conesensitivitiesofconephotoreceptorsareshown.Theshortwave-sensitivephotoreceptorsaremuchlesssensitivethantheothertwotypes.Theresponsesofthemediumwaveandlongwavephotoreceptorshaveagreatdealofoverlap.Visionisnotsensitivetotheprecisewavelengthofthestimulus:Whatattersisopticalpowerintegratedundereachresponsecurve.IntroductiontocolorvisionPhotoreceptorcellscalledconesintheretinaareresponsibleforhumancolorvision.Therearethreetypesofconecells,sensitivetolongwave,mediumwave,andshortwaveradiationwithintheelectro-magneticspectrumbetweenabout400nmand700nm.Becausetheconesensitivitiesareveryroughlyinthepartsofthespectrumthatappearred,green,andblue,colorscientistsdenotethecelltypesasρ,γ,and,theGreeklettersforr,g,andb.<TodenotethesensorsR,G,andBwouldwronglysuggestaclosercorrespondence.>EstimatesofthespectralresponseoftheconetypesaregraphedinFigure6above.Lightinthephysicalworldcanbecharacterizedbyspectralpowerdistributions<SPDs>.Coloredobjectscanbecharacterizedbyspectralreflectancecurves,suchasthoseoftheColorChecker.However,visionisinsensitivetotheexactwavelengthofastimulus:Accordingtothemoderntheoryofcolorscience,allthatmattersistheintegralofopticalpowerunderneatheachresponsecurve.Thatthereareexactlythreetypesofconecellsleadstothepropertyoftrichromaticity:Threecomponentsarenecessaryandsufficienttocharacterizecolor.Somepeoplemightusethephrase"colorassensedbytheeye,"butIcon-siderthatqualifiertoberedundantatbest,andmisleadingatworst:Colorisdefinedbyvision,sothereisnoneedtousethequalifyingphrase"assensedbytheeye,"ortousetheadjectivevisiblewhenreferringtocolor.OverviewofCIEColorimetryThespectralresponsesoftheconecellsthatIgraphedinFigure6wereunavailabletoresearchersinthe1920s.Researchersatthetimeusedpsychophysicalexperiments,suchasthefamouscolormatchingexperiment,toteaseoutthedata.TheCIEistheinternationalbodyresponsibleforcolorstandards.In1931,thatorganizationadoptedthecolormatchingfunctionsdenotedx<λ>,y<λ>,andz<λ>,graphedinFigure7.Figure7CIE1931,2°color-matchingfunctions.Acamerawith3sensorsmusthavethesespectralresponsecurves,orlinearcombinationsofthem,inordertocaptureallcolors.However,practicalconsiderationsmakethisdifficult.Theseanalysisfunctionsarenotcomparabletospectralpowerdistributions!WeightingaphysicalSPDundereachofthesethreecurves<thatis,formingthewavelength-by-wavelengthproduct>,andsummingtheresults,formsatripleofthreenumbers,denotedX,Y,andZ.Incontinuousmathematics,threeintegralsneedtobecomputed;indiscretemath,amatrixproductissufficient.TheX,Y,andZtristim-ulusvaluescharacterizecolor.Theyarelinear-lightquantities,propor-tionaltoopticalpower,thatincorporatethewavelengthsensitivityofhumanvision.TheYvalueisluminance,whichisordinarilyexpressedinunitsofcandelapermetersquared<cd·m-2>.Ifyouaremeasuringreflectance,thereflectedtristimulusvaluesdependuponthespectralcharacteristicsoftheilluminant,andtheiramplitudesscalewiththepoweroftheillumination.Relativeluminanceistheratioofreflectedluminancetotheluminanceoftheillumination;itisalsoknownastheluminancefactor.Figure8SPDsofvariousilluminantsaregraphedhere.IlluminantA,showninorange,isrepresentativeoftungstenlightsources;itisdeficientinshortwavepower,andmaycauseerrorsinsensingbluecolors.ThebluelinegraphstheSPDofaNichiawhiteLED.Thereisapeakintheblueportionofthespectrum:Uncorrected,thesensorwouldreportexcessivebluevalues.TheotherfourlinesrepresentCIEstandardilluminantsC,D50,D55,andD65.Inmanyapplications,tristimulussignals<includingluminance>scalewiththeillumination,andareotherwiseuninterestinginthemselves.Whatismoreinterestingistheratiosamongthem,whichcharacterizecolordisregardingluminance.TheCIEhasstandardizedtheprojectivetransformationofEquation1,inthemargin,totransform[X,Y,Z]valuesintoapairof[x,y]chromaticitycoordinatesthatrepresentcolordisregardingluminance.Thesecoordinatesaresuitableforplottingintwodimensionsonachromaticitydiagram.x=y=Eq1ChromaticitycoordinatesIlluminationAnonemissiveobjectmustbeilluminatedinordertobevisible.TheSPDreflectedfromanilluminatedobjectisthewavelength-by-wave-lengthproductoftheilluminant’sSPDandthespectralreflectanceoftheobject.Beforelightreachestheeye,theinteractionamonglightsourcesandmaterialstakesplaceinthespectraldomain,notinthedomainoftrichromaticity.Toaccuratelymodeltheseinteractionsrequiresspectralcomputations.WhenapplyingtheTCS230,attentionmustbepaidtothespectralcontentoftheilluminationandtopoten-tialinteractionbetweentheilluminationandthesamplestobesensed.Generally,thelessspikythespectra,thebetter.Figure8graphsseveralilluminants.Yourapplicationmayinvolvesensingcolor,inwhichcasetheprecedingdescriptionapplies.However,someapplicationsoftheTCS230involvenotsomuchestimatingcolorasseenbytheeyebutrathersensingphysicalparametersassociatedwithopticalpowerinthevisiblerange.Insuchapplications,toapproximatethevisualresponsemaynotbethebestapproach:Itmaybemoreeffectivetotakeamoredirectapproachtoestimatingtheparametersoftheunderlyingphysicalprocess.TheColorCheckerEquippedwithknowledgeofhowspectraarerelatedtocolors,theplottingofchromaticitycoordinates,andthedependenceofcolorsuponillumination,wecanreturntotheColorChecker.GretagMac-bethdoesn’tpublishorguaranteethespectralcompositionofthepatchesoftheColorChecker.However,nominalCIE[X,Y,Z]valuesarepublished.ThepatchesinthebottomrowoftheColorCheckercontainneutralcolors;thenumericnotationsinthelegendsofFigure5reflectonetenthofthelightness<L*>valuesofthosepatches.Thespectragraphedonpages2and3representthephysicalwave-length-by-wavelengthreflectanceofthepatches.Thesespectralreflec-tanceshavebeenmeasuredbycolormeasurementinstrumentcalledaspectrophotometer.Ifyouhadaccesstoalightsourcehavingperfectlyevendistributionofpoweracrossthevisiblespectrum,thenthereflectancecurvesgraphedherecouldsimplybescaledtorepre-sentthereflectanceinyourapplication.Practicallightsourcesdonothaveperfectlyevenspectraldistributions,socompensationisneces-sary:Youmustcomputethewavelength-by-wavelengthproductoftheilluminant’sSPDwiththespectralreflectanceofthechart.WewillfirstcalculatetheCIE[X,Y,Z]valuesfromthechart.<ThesevaluesshouldagreewiththefiguresprovidedbyGretag.>Thenwewillcalculatethe[R,G,B]valuesthatwillbedetectedbyaTCS230.TocalculateCIE[X,Y,Z],wetakethe31×3matrixrepresentingthecolormatchingfunctions<CMFs>oftheCIEStandardObserver,andperformamatrixproductwith31spectralresponsevaluesascorrectedforillumination.Thisproducesthe[X,Y,Z]tristimulusvalues.Whenchromaticitycoordinates[x,y]arecomputedfrom[X,Y,Z]throughtheprojectivetransforminEquation1,thenplotted,thechromaticitydiagraminFigure9results.Thehorseshoe-shapedfigure,closedatthebottom,containsallcolors:Everynon-negativespectraldistributionproducesan[x,y]pairthatplotswithinthisregion.Thelightly-shadedtriangleshowstheregioncontainingallcolorsthatcanbeproducedbyanadditiveRGBsystemusingsRGB<Rec.709>primarycolors.Thisregiontypifiesvideoanddesktopcomputing<sRGB>.ThepointsplottedinFigure9arethecolorsoftheColorChecker.Whiteandgrayvaluesareclusterednearthecenterofthechart.Figure9CoordinatesofColorCheckerpatchesaregraphedontheCIE[x,y]chromaticitydiagram.Thehorseshoeenclosesallcolors;thetriangleenclosesthecolorsthatcanberepresentedinvideo<Rec.709>andindesktopcomputing<sRGB>.TheTCS230Figure10showstheresponsesofthefourchannelsoftheTCS230.Theblackcurveshowstheresponseoftheunfilteredsensorelements.Thered,green,andbluecurvesshowtheresponsesofthelongwave-sensitive,mediumwave-sensitive,andshortwave-sensitiveelementsrespectively.AsImentionedonpage5,theCIEmodelofcolorvisioninvolvesinte-gratinganSPDundertheX<λ>,Y<λ>,andZ<λ>colormatchingfunc-tions<graphedinFigure7>,producingX,Y,andZvalues.TousetheTCS230toestimatecolorweperformananalogouscalculation,butusingtheTCS230sensitivityfunctionsinsteadoftheCIECMFs:WeintegratetheSPDundertheTCS230’ssensitivitycurves,andproduceR,G,andBvalues.ThedeviceR,G,andBvalueswilldependuponseveralfactors:thespectralcontentoftheilluminant,thespectralreflectanceofthesample,thespectralattenuationofanyinterveningopticalcomponents<suchasthelens>,andfinally,thespectralresponsefunctionsoftheTCS230.Thevariousspectralphenomenaaremodelledbycomputingwavelength-by-wavelengthproducts.Figure10TCS230spectralsensitivitiesaregraphedhere.Thered,green,andbluechannelsaregraphedinthecorrespondingcolors;thegraylinereflectsthesensitivityoftheclear<unfiltered>channel.BecausetheseresponsesaredifferentfromtheCIEstandardobserver,thevaluesreportedbytheTCS230arenotcolorimetric.However,suitablesignalprocessingyieldscolorinformationthatissufficientlyaccurateformanyindustrialapplications.OwingtothefactthattheTCS230issensitivetoinfraredlight<havingwavelengthsabove700nm>,andthefactthatmostlightsourcesproducepowerintheinfraredregion,typicalapplicationsincludeanIRcutfilterinfrontoftheTCS230.Figure11overleafshowstheresponseofatypicalIRcutfilter.ToformamoreaccurateestimateofcolorrequiresprocessingtherawTCS230R,G,andBvaluesthroughalinear3×3matrixwhosecoeffi-cientsareoptimizedwithrespecttothespectrumoftheilluminant,thespectralresponseofinterveningopticalcomponents,andtheresponsecurvesoftheTCS230.Thedataprocessingoperationcanberepresentedinmatrixformasfollows:x=M?tEq2Thesymboltrepresentsathree-elementvectorcontainingthedevicevaluescapturedfromacolorpatch.Mrepresentsthe3×3colorcorrectionmatrixthatwewillapplytothesevaluesthroughmatrixmultiplication,denotedbythe?symbol.Thesymbolxrepresentstheresultingvectorofestimated[X,Y,Z]values.Wecanusematrixnotationtosymbolizeprocessingasetofthreecolorpatchesatonce,byarrangingthethreesetsofdevicevaluesintosuccessivecolumnsofa3×3matrixT.SuccessiverowsofTcontainred,green,andbluedatarespectively.UponmatrixmultiplicationbyM,thecolumnsoftheresultingmatrixXcontainXYZvaluesofthesuccessivesamples;therowsofXcontainX,Y,andZvaluesrespec-tively.Oneequationexpressesthemappingofthreepatchesatonce:X=M?TEq3GivenamatrixTwhosecolumnscontainthreesetsofdevicesamples,andamatrixXcontainingthecorrespondingsetofthreeidealXYZtriples,thereisauniquematrixMthatmapsfromTtoX.ItisfoundbycomputingthematrixinverseofT,thencomputingthematrixproduct<bypremultiplication>withX:M=X?T-1Theresulting3×3colorcorrectionmatrixMexactlymapstheeachofthechosenthreesetsofdevicevaluestothecorrespondingsetoftris-timulusvalues.Itisnotnecessarytoinvertmatricesatthetimeofsensing!ThematrixMcanbecomputedinadvance,baseduponthesamplesthatareexpectedtobepresentedtothesensorintheintendedapplication.Toprocessthreedevicevaluesuponsensingasample,allthatisnecessaryiscomputationofthematrixproductofEquation3.Acolorcorrectionmatrixthatproducesgoodresultsacrossmorethanthreesamplescanbecomputedthroughanumericaloptimizationprocedure.Whenthisisdone,noparticularsampleislikelytomapexactlytoitsidealtristimulusset,butalinearmatrixcanbeconstructedthatminimizestheerroracrossarangeofsamples<wheretheerrorismeasuredinaleast-squaressense>.ThecolorcorrectionoperationisstillaccomplishedexactlyasinEquation2.基于TAOS公司的TCS230的顏色感應(yīng)TAOS公司的TCS230是一個小的、高度集成、8引腳、SOIC封裝的色彩傳感裝置。它以模擬頻率的方式輸出短波〔藍(lán)色、中波〔綠色、長波〔紅色、寬帶〔白光功率的事件數(shù)量。它可用于各種色彩感應(yīng)應(yīng)用領(lǐng)域。該設(shè)備的詳細(xì)資料中可以找到它的數(shù)據(jù)表。本白皮書詳細(xì)介紹了色彩感應(yīng)的概念和使用TCS230參與計(jì)算。我們將使用一個光學(xué)刺激方案的ColorChecker圖表工作,通過檢測的色彩數(shù)值例子。下圖,在圖1所示,是由GretagMacbeth生產(chǎn)和分配。圖表長約13英寸,9英寸〔330毫米×230毫米,它包含了64陣列安排24色斑。到5背面圖2顯示了在圖表的每一行四個補(bǔ)丁的光譜反射-即入射光被反射的那部分〔相對于一個理想的漫反射作為波長從350功能,納米到750納米。圖1ColorChecker色補(bǔ)丁包含18個和6步灰色系列圖2ColorChecker譜,第一行圖3ColorChecker譜,第二排圖4ColorChecker光譜,第三行圖5ColorChecker譜,底排〔中性系列圖6錐錐光感受器敏感性所示。短波敏感的感光細(xì)胞遠(yuǎn)遠(yuǎn)低于其他兩種類型的敏感。中波和長波的感光細(xì)胞的反應(yīng)有很大的重疊。視覺是不敏感,準(zhǔn)確的刺激波長:什么是光功率下atters每個響應(yīng)曲線綜合。色覺簡介所謂感光細(xì)胞在視網(wǎng)膜視錐細(xì)胞是人類色彩視覺負(fù)責(zé)。內(nèi)有電磁頻譜三種類型的視錐細(xì)胞,敏感的長波,中波,短波輻射及約400納米之間和700納米。由于錐敏感性在頻譜的部分出現(xiàn)紅色,綠色和藍(lán)色的很粗糙,色彩科學(xué)家記為ρ,γ,以及希臘字母為R,G細(xì)胞的類型,和b〔為了表示對傳感器的R,G,和B將錯誤建議更密切的對應(yīng)關(guān)系。的圓錐體的譜反應(yīng)的估計(jì)是在上面繪制圖6。在物理世界的光,其特征是光譜功率分布〔結(jié)構(gòu)化產(chǎn)品說明。彩色對象,其特征是反射光譜曲線,如在的ColorChecker的。然而,視覺不敏感,對刺激精確波長:根據(jù)現(xiàn)代色彩科學(xué)理論,最重要的事情是在每個響應(yīng)曲線光功率積分。這恰有三種視錐細(xì)胞類型導(dǎo)致trichromaticity財(cái)產(chǎn):三個組成部分是必要的和足夠的特征顏色。有些人可能會用"感覺到的顏色的眼睛,"但我了CON-Sider的限定詞是多余的,充其量,誤導(dǎo)在最壞的情況:色彩是由視覺定義,所以沒有必要使用合格的短語"因?yàn)楦杏X到的眼睛,"或使用的形容詞時可見指顏色。概述Cie的比色法錐細(xì)胞,我在圖6繪制光譜反應(yīng)無法在20世紀(jì)20年代的研究人員。當(dāng)時的研究人員使用,如著名的配色實(shí)驗(yàn)心理實(shí)驗(yàn),以梳理出的數(shù)據(jù)。在CIE是國際機(jī)構(gòu),顏色標(biāo)準(zhǔn)。In1931,該組織通過了顏色匹配函數(shù)記×〔λ和Y〔λ和z〔λ,在圖7繪制。圖7Cie公司1931年2°色彩匹配功能。一個3傳感器的相機(jī)必須具備以下的光譜響應(yīng)曲線,或它們的線性組合,以捕捉所有的顏色。然而,實(shí)際的考慮作出這一困難。這些分析功能比不上光譜功率分布!加權(quán)根據(jù)這三個曲線每個物理社民黨〔即,形成了波長的波長產(chǎn)品,總結(jié)的結(jié)果,形成了三個數(shù)字三倍,記在連續(xù)數(shù)學(xué)的X,Y和Z,三積分需要計(jì)算,在離散數(shù)學(xué),矩陣產(chǎn)品就足夠了。在X,Y和Ztristim-汗國值特征的顏色。它們是線性光量,正比于光學(xué)力量,即納入人類視覺波長的敏感性。Y值是亮度,這是通常在每平方米坎德拉〔光碟?米-2為單位表示。如果你是測量反射率,反射的三刺激值取決于對光源的光譜特性,其幅度與規(guī)模的照明電源。相對亮度的反射亮度的照明亮度的比值,它也被稱為亮度因素。圖8是繪制各種光源結(jié)構(gòu)化產(chǎn)品說明這里。A光源,以橙色顯示,鎢光源是代表,它是在短波力量不足,可能會導(dǎo)致感應(yīng)藍(lán)色的錯誤。藍(lán)線圖的社民黨的日亞白光LED。有一個光譜的藍(lán)色部分高峰:裸時,傳感器會舉報過度藍(lán)色值。另外四線代表Cie的?,D50的,D55和D65的標(biāo)準(zhǔn)光源。在許多應(yīng)用中,三刺激信號〔包括亮度與照明規(guī)模,并應(yīng)在其他無趣自己。什么是更有趣的是它們之間的比例,所特有的顏色無視亮度。在CIE有標(biāo)準(zhǔn)化的公式1中的保證金射影變換,將其轉(zhuǎn)化為一對[的X,Y和Z]值[的x,y]表示顏色的色度坐標(biāo)無視亮度。這些坐標(biāo)在二維色度圖上繪制合適。x=y=公式1色度坐標(biāo)照明一個nonemissive對象必須是為了照明可見。社民黨從一照物體反射的波長是按波長的光源產(chǎn)品的社民黨和對象的光譜反射率。光線到達(dá)之前光源和材料之間的眼睛,相互作用發(fā)生在譜域的地方,不是在trichromaticity域。為了準(zhǔn)確地需要這些相互作用的光譜模型計(jì)算。當(dāng)應(yīng)用TCS230,必須注意對光照光譜內(nèi)容和電位-TiAl金屬間的照明和樣品被覺察的互動。一般來說,越尖的光譜,就越好。圖8圖數(shù)光源。您的應(yīng)用程序可能涉及敏感的顏色,在這種情況下,前面的說明適用。然而,一些應(yīng)用涉及TCS230沒有這么多的眼睛所看到的,而是傳感在可見光范圍內(nèi)光功率相關(guān)的物理參數(shù)估計(jì)的顏色。在這種應(yīng)用中,近似的視覺反應(yīng)可能不是最好的方法:它可能是更有效地采取更直接的方法來估計(jì)底層物理過程的參數(shù)。色彩檢查如何光譜與顏色相關(guān)的知識裝備,繪制色度坐標(biāo),對照明色彩的依賴,我們可以返回的ColorChecker。GretagMac-Beth沒公布或保證的ColorChecker補(bǔ)丁的光譜成分。然而,標(biāo)稱Cie的[的X,Y和Z]值被公布。在底行的ColorChecker補(bǔ)丁包含中性色,在圖5中的神話傳說中的數(shù)字符號反映十分之一的亮度〔長*值的這些補(bǔ)丁。光譜繪制2和第3頁上表示物理波長由波長的反射率的補(bǔ)丁。這些光譜反射已測色儀測量tances稱為分光光度計(jì)。如果你有機(jī)會訪問光源具有完全的權(quán)力分配,甚至在整個可見光譜,反射率曲線則繪制在這里可以簡單地?cái)U(kuò)展到repre,發(fā)送應(yīng)用程序中的反射率。實(shí)踐沒有光源的光譜分布十分均勻,因此補(bǔ)償neces-薩利:你必須計(jì)算與圖表的光譜反射的光源的波長社民黨按波長的產(chǎn)品。我們將首先從圖表計(jì)算在CIE[的X,Y和Z]值?!策@些值應(yīng)同意Gretag提供的數(shù)字。然后我們將計(jì)算[的R,G,B]的,將由一TCS230檢測值。為了計(jì)算Cie公司[的X,Y和Z],我們把31×3矩陣代表職能的配色在CIE標(biāo)準(zhǔn)觀察者〔CMFs,并執(zhí)行一個有31個光譜響應(yīng)矩陣產(chǎn)品價值為照明糾正。這將產(chǎn)生的[x,Y,Z軸]三刺激值。當(dāng)色度坐標(biāo),通過投影[的x,y]是來自[的X,Y和Z]變換計(jì)算公式1,然后繪制,結(jié)果如圖9色度圖。馬蹄狀的人物,在底部封閉,包含所有的顏色:每個非負(fù)的光譜分布產(chǎn)生[的x,y]對本地區(qū)范圍內(nèi)的陰謀。擁有輕成蔭的三角顯示包含所有的地區(qū),可

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