303 Hue that is invariant to brightness and gamma Graham Finlayson and Gerald Schaefer School of Information Systems, University of East Anglia Norwich NR4 7TJ, United Kingdom graham,gerald @sys.uea.ac.uk Abstract Hue provides a useful and intuitive cue that is used in a variety of com- puter vision applications. Hue is an attractive feature as it captures intrinsic information about the colour of objects or surfaces in a scene. Moreover, hue is invariant to confounding factors such as illumination brightness. However hue is not stable to all of the types of confounding factors that one might rea- sonably encounter. Specifically, the RGBs captured in images are sometimes raised to the power gamma. This is done for two reasons. First, to make the images suitable for display (since monitors have an intrinsic non-linearity). Second, applying a gamma is the simplest way to change the contrast in images. It has also been observed that digital cameras often apply a scene dependent gamma type function (which is unknown to the user). In this paper we show that a simple photometric ratio in log RGB space cancels both brightness and gamma. Furthermore, some simple manipulation reveals that the brightness/gamma invariant can usefully be interpreted as a hue in a log opponent colour space. We carried out indexing experiments to evaluate the usefulness of the derived hue correlate. In situations where gamma is held fixed, the new hue supports recognition equal to conventional definitions. In situations where gamma varies the new correlate supports better indexing. The new hue is also found to predict some psychophysical data quite accurately. 1 Introduction According to the International Commission on Illumination (CIE), hue is the attribute of a visual sensation according to which an area appears to be similar to one of the perceived colours, red, yellow, green and blue, or a combination of two of them [5]. In more practical terms, hue is the ’name’ of a colour. It is also the property of colour that people find is easiest to use. Computer vision, in trying to mimic human’s abilities, has found hue to be useful in various applications. These include [14] where a colour segmentation algorithm based on hue only is introduced. [12] presents a hue based approach to suppress the effects of cloud shadows for remote sensing applications. It has been shown that (assuming the light source of a scene is white) hue does not change in the presence of specularities [8]. Colour transformations like HSV and HLS that convert image RGB values to a hue based representation [17] allow not only for a more intuitive description of colour but can also BMVC 2001 doi:10.5244/C.15.32
Hueprovidesa usefulandintuitive cuethat is usedin a varietyof com-putervision applications.Hue is anattractive featureasit capturesintrinsicinformationaboutthecolourof objectsor surfacesin ascene.Moreover, hueis invariantto confoundingfactorssuchasillumination brightness.Howeverhueis notstableto all of thetypesof confoundingfactorsthatonemight rea-sonablyencounter. Specifically, theRGBscapturedin imagesaresometimesraisedto thepower gamma.This is donefor two reasons.First, to make theimagessuitablefor display(sincemonitorshave an intrinsic non-linearity).Second,applying a gammais the simplestway to changethe contrastinimages. It hasalsobeenobserved that digital camerasoften apply a scenedependentgammatypefunction(which is unknown to theuser).
In this paperwe show thata simplephotometricratio in log RGB spacecancelsbothbrightnessandgamma.Furthermore,somesimplemanipulationrevealsthat the brightness/gammainvariantcanusefullybe interpretedasahue in a log opponentcolour space. We carriedout indexing experimentsto evaluatethe usefulnessof the derived huecorrelate. In situationswheregammais heldfixed,thenew huesupportsrecognitionequalto conventionaldefinitions. In situationswheregammavariesthe new correlatesupportsbetterindexing. Thenew hueis alsofoundto predictsomepsychophysicaldataquiteaccurately.
1 Introduction
According to the InternationalCommissionon Illumination (CIE), hue is the attributeof a visual sensation according to which an area appears to be similar to one of theperceived colours, red, yellow, green and blue, or a combination of two of them [5]. Inmorepracticalterms,hueis the ’name’ of a colour. It is alsothepropertyof colour thatpeoplefind is easiestto use.
Computervision, in trying to mimic human’s abilities,hasfoundhueto beusefulinvariousapplications.Theseinclude [14] wherea colour segmentationalgorithmbasedon hueonly is introduced. [12] presentsa huebasedapproachto suppressthe effectsof cloudshadows for remotesensingapplications.It hasbeenshown that (assumingthelight sourceof a sceneis white) huedoesnot changein thepresenceof specularities[8].ColourtransformationslikeHSV andHLS thatconvertimageRGBvaluesto ahuebasedrepresentation[17] allow not only for a moreintuitive descriptionof colourbut canalso
Remarkably, the humanvision systemcan ascribefairly constanthuesto surfacesviewedin differentvisualcontexts. Looking at themathematicaldefinitionsof hueusedin computervision it is easyto show that CV hue is invariant to brightness. Shadedsurfacesor surfacesviewedunderdifferentpowersof illuminationhavethesameintrinsichue.But we find thatotherconfoundingfactorsdo not cancelout.
A gammadifferentfrom 1 impliesthat thereexistsa power functionrelationshipbe-tweensceneintensitiesandpixel values[15]. Sodevice responsesdenotedas ��������� �will becomepixel RGBsdescribedas ������������������ . It is oftenwronglyassumedin com-putervision that ����� or that � might be turnedoff andthat thedefault restingstateis����� . Yet, our practicalexperiencehasshown that this is rarely the case. Indeed,ithasbeenfoundthatsomelow enddigital camerasapplya gammathatdependson scenecontent[6].
Nonunity gammais neededbecausethecoloursthataredisplayedonascreenarenotalinearfunctionof theRGBssentto themonitor. Rather, thereexistsapowerfunction(orgamma)relationshipbetweentheincomingvoltageandthedisplayedintensity. A linearimagedisplayedon screenwill look too darkandlackcontrast.This is becausemidtonesgetattenuatedby thegammafunction in comparisonto darkandlight pixel values[15].To compensatefor this, imagesareusuallystoredin a way thatreversestheeffect of themonitor. This canbe achievedby applyinga gammafunction with the reciprocalvalueof themonitorgammaasexponent.Usuallythis normalizationtakesplacedirectly at thestageof imageacquisition,i.e. in the device. It shouldalsobe notedthat, asdifferentmonitorshave differentgammas(e.g.the ”standards”for PCandMacintoshare2.2 and1.8 respectively) imageswith different � valuesarea consequence.Anotherreasonforapplyinganonunity gammais to changethecontrastof animagee.g.asapreprocessingstepprior to othertaskssuchassegmentation.
In this paperwe look at huein the context of changingbrightnessandcontrast.Ascommonhuedescriptorsare invariantonly to brightness,we areseekinga descriptionof huethat remainsconstantafter a changein brightnessand/orcontrast(eitherdevicerelatedor throughpost-processing).GivenanRGB andpossiblebrightnessandgammadependenciesweshow how somesimplemanipulationin log RGBspacecancancelbothfactors. Moreover, the manipulationmight usefully be interpretedas a hue correlate.Specificallywe show that if hueis definedastheanglebetweentwo log opponentcolorcoordinates(a red-greenandayellow-bluecoordinate)thenhueis brightnessandgammaindependent.This definition of hue naturally falls out of the algebrainvolved in can-cellingbrightnessandgamma.Yet,thealgebraleadsto adefinitionthatmesheswell withdefinitionsusedin colourscience[4].
To testtheutility of thegammainvariancewe scanneda datasetof 27 designimagesusingtwo differentgammasettings: ����� and �����! "� . We show that correspondinghueimagesasobtainedfrom theHSV colourmodeldo indeeddiffer dueto thedifferentgammasettings.However, imagesbasedon our newly definedhuespacelook very simi-lar. To quantitativelyassesshuestability, weperformedcolourindexing [20] experiments.Is it possible,usinghuecontentalone,to matchimagesacrossthetwo differentscanningsettings?Wefoundthatthiswasthecasefor ournew huecorrelatebut thatHSV andHLS
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failed(aswemight expect).Of coursethis is a very simpleexperimentwhich is really only useful to show that
the derivedinvariantis fairly stableto gammachanges.However, we wishedto look toits generalapplicability even in situationswherea varying gammais not a problem. Ina secondexperimentwe indexedinto a largesetof (around4000)imagesandfoundthatthehuedescriptoralonesupportedgoodperformance.Moreover, our new huecorrelatedeliveredsimilar performanceto conventionaldescriptors.
In a final experimentwe wonderedwhetherour new huedescriptorhasrelevancetoour own visualsystem.We foundthat thederivedcorrelatecanpredicttheconstanthuelinesderivedin psychophysicalexperimentmoreaccuratelythantheHSV colourspace.
Beforeproceedingwe point out to the readerthat brightnessandgammainvariancewill not renderhueappropriateto all imagingsituations. If the colour of the light thatilluminatesthescenechanges,sodothecoloursin thesceneasrecordedby adevicesuchasa digital camera[7]. In termsof huethis manifestsitself asa global shift of objecthuestowardsthecolourof thelight source.This is truefor our new huedefinitionasit isfor HLS andHSV. Henceforthwe will assumethat thecolourof theilluminant hasbeendiscountedfrom images.
The restof the paperis organisedasfollows: Section2 briefly explainsthe processof imageformation,definesconventionalhuebasedcolourspacesandshows thathueinthesecolourmodelschangeswith a changein contrast.Section3 introducesour log huespace.Section4 describestheexperimentswe performedto demonstratethevalidity andusefulnessof thenewly definedhue.Section5 concludesthepaper.
2 Background
2.1 Image Formation
A lineardevicecapturescolour, or R, G andB, accordingto:# $&%(' �*)+�,�.- �*)+�0/21 ��)��43!5768��)9�;:<�>=?��:��@� �A:<�>B�: (1)
where : is wavelength,# $(%(' is a 3-vectorof sensorresponses(RGB pixel values),6DC isthesurfacereflectanceat location ) , = thespectralpowerdistributionof theillumination,and � is the 3-vector of sensitivity functionsof the device. Integration is performedover the visible spectrumE . The light reflectedat ) is proportionalto 6DC4�A:<�>=?��:�� , itsmagnitudeis determinedby the dot product - C?/�1 C where - C is the unit vector in thedirectionof thelight source,and 1 C is theunit vectorcorrespondingto thesurfacenormalat ) . In thestrictestsenseEquation(1) only describestheresponseof Lambertian(matte)reflectances.But, in practiceit is a tolerablygoodmodelfor mostsurfaces(eventhosethathavesomehighlight component).
Equation(1) is thestartingpoint for mostcolourbasedalgorithmsusedin computervision. Yet, in practice(outsidethedomainof computervision) linearcameraresponseis not the norm. Rather, cameraresponseis the linear RGB responseraisedto some �(gamma)power: # �*)��F�G��H # $&%I' �*)+�>� � (2)
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wherethe scalar H modelsthe interactionof surfaceand illumination normalsand theintensityof the light source. To simplify notationstill further, let us denotethe linearRGBresponses(Equation(1)) with �����J��0 � . Equation(2) canbethenwrittenas# ��)��,�K�>��HJ�L� � �M��HN�O� � �F��HJ�� � � (3)
Therearetwo reasonsfor non linear cameraresponses.First, colour monitorshavea non linear transferfunction: PC monitorsapply a power of 2.2 to the signals(RGBs)driving thedisplay. It follows that in orderto achieve a true(physicallyaccurate)coloursignal,RGBsmustberaisedto thepowerof �P�G�RQS�! "� . Monitorstiedto Applecomputersapplyapowerof 1.8prior to display. Theimplicationof this is thatcamerascalibratedtoPCsandApplesrequiredifferentgammasettings.
Thesecondreasonfor a non-unitygammais to changethecontrastof animage.Ap-plying a gammalarger than1 tendsto compressthe signal rangein the bright areaofimagesbut to bring out detail in thedarker regions. Converselya gammaof lessthan1bringsout detail in bright areasbut compressesthesignalin darker imageregions. To afirst approximationmostimagesfrom unknown sources(e.g. imagesdownloadedfromthe Internet)canbe consideredto be linear after an appropriate(but unknown) gammacorrection.Contrastadjustmentsarealsomadeasa simpleform of dynamicrangecom-pression(mappingthelargerphysicalrange(16 to 20 bit) of intensitiesto the8-bit rangeof typical cameras).Experimentshave shown thatsomecameraswill adjustcontrastin ascenedependentwaywithout userintervention[6].
While appropriatebrightnessandgammaadjustmentsmight be made(to achieve alinearimage)in acalibratedlabenvironment,this is not in generalpossible.It is howeverreasonableto askwhethersomepropertyof colour(whichis definedby thethreenumbersR, G andB) might beindependentof thetwo confoundingfactors ��HF�@�T� .2.2 Hue based colour models
The simplestsinglenumberusedto definecolour is ’hue’. Hue correlatesto the colournamewe might useto classifya surface(red,green,pink etc). Huemight becalculatedusingany of the colourspaces:HSV, HLS andIHS [17]. Indeed,all areusedin imageprocessingand computervision. Based,on perceptualstudiesof how we seecolour,eachof thesespacescodesRGB by three’perceptual’correlates:hue, saturationandbrightness.Brightnesscorrelatesto magnitude:white is brighter thangrey. Saturationmeasuresthepurity of colour:awhitishpink is moredesaturatedthanasaturatedred(yetboththesemayhave thesamebrightnessandhue).
To increaseefficiency severalsimplerdefinitionsweredeveloped[17]. However, they arealsobasedon Equation(4) andgivenumericalresultsthatdiffer only slightly.
We now want to inspectwhateffect changesin brightnessandcontrast,asmodelledby Equation(3) have on hueasdefinedabove. For that we substitutethe RGBsfrom
We seeimmediatelythatit is possibleto cancelthe H termsleadingtoU �.V2X[Z \^] _ "`baI��� � cd� � �Tef��� � cd � �ihj ��� � cd� � �2��� � cd� � �Jek��� � cg � �2��� � cd � � (6)
Thatis, huedoesnotchangewith achangein brightness.ThiswaswhatwemightexpectgiventheideathatHSV, HLS andIHS separateout brightness.However, we seethatthe� exponentdoesnot cancel. Thus,huedependson the imagegammaandwill changewhen � is altered.
3 Brightness and gamma invariant hue
For imagesfrom an unknown source(like thosefound on the web) the imagegammais alsoanunknown. Furthermoreit is quitepossiblethat two imagesof thesamescenewill be capturedwith a differentgamma.This might be dueto eitherthe imagesbeingcapturedfor differenttargetsystems(e.g.thegammafor a PCis 2.2, for Macintosh1.8),or applicationof a different gammato enhancethe contrastof the image. This latterenhancementmaybeautomaticallyappliedby thecamera.As shown in the lastsection,while hueis independentof brightnessit dependson gamma.
It turnsout that it is quitestraightforward to derive a singlescalarvaluefrom an R,G andB measurementthat cancelsboth brightnessandgamma.From observingEqua-tion (3) we seethatapplyinga log transformto RGBsremovesthe � s from theexponentandturnstheminto multiplicativescalars.At thesametime thebrightnessH becomesanadditiveratherthana multiplicativeterm:
Takingdifferencesof colourchannelsallowsusto removethebrightnesstermsv �>�*��oIXSp+��H0�9eq�ro(X[p����L�>�0c��w�roIXSp+��H0�9eq�roIXSp+���O�>��w��oIXSp���H0�Jeq�roIXSp<���L�>�9eW�w�7o(X[p<��H0�Jeq�roIXSp+���O���0cd�4�w�roIXSp+��H0�9eq��oIXSp��� ���yx �v �ro(X[p����L�Ncz�7o(X[p<���O��7o(X[p<���L�9eq�roIXSp����O�Dcq�R��o(X[p<���� x (8)
Wenotethatthewaywedefinetheabovedifferencesdescribescoordinatesin anopponentcolourrepresentation[1]. They aresimilar to theopponentcolouraxesusedby thehumanvisualsystem[11] andsohaveperceptualrelevance.
Figure1: Exampleof a designimagescannedusingtwo differentgammasettings: ����S _ on theleft, and �|�f�! "� on theright.
So,theabove singlescalaris independentof brightnessandgammaandmight beanappropriatefunction for usein computervision. However, comparedto the ideaof hue(red,green,blueetc),this log-differenceratiodoesnot seemsointuitive.
An alternative to removing the gammaterm throughratios is to calculatethe angleof the vectorfrom Equation(8) with respectto the ) -axis, i.e. we calculatethe inversetangentof theratio in Equation(9)U ��}�~��T\^] o(X[p<�����Dc{oIXSp����O�oIXSp����L�9e�o(X[p<���O��cd�Do(X[p4���� (10)
In color science(e.g. in the CIELab space[4]), hue is definedasan anglein a red-greenandblue-yellow coordinatespace.Herewe have shown that thesimpleststrategyfor removing brightnessandgammadependency from RGB measurementsresultsin ananalogoushuecorrelate.Hueis thatpartof animagesignalwhich is invariantto changesin brightnessandgamma.
4 Experimental Results
To evaluateour new huedefinition, we createda small imagedatabaseof 27 colourfuldesigns,eachscannedin twice with differentgammasettingsof thescanner. In thefirstcasethedirectsensorresponsesweresaved,i.e.nogammawasappliedresultingin linearimagesascommonlyusedin computervision applications.The designswerescannedfor a secondtime usinga gammaof 2.2. An exampleimagepair is shown in Figure1.The differencesareobviouswith the linear imageappearingmuchdarker andwith lesscontrast.From Equation(6) we expectthe huesfrom correspondingregionsof the twoimagesto differ due to a changein imagegamma. To illustrate this we convertedtheoriginal RGB imagesinto theHSV colourspace,fixedbrightness(value)andsaturationover the whole image,and transformedthem back to RGB. The resulting imagesareshown in Figure 2. The differencein imagecolours is againquite evident. We thenperformedthesameprocedurefor ournew log huespace,i.e. convert theimagesinto huebasedrepresentation,fix saturationandbrightness,andconvert thembackto RGB. Theresultfor theimagepair from Figure1 is givenin Figure3. Clearly, asexpected,thetwoimageslook muchcloserto eachotherthanis thecasefor theHSV basedimages.Here
we have a visual confirmationof the brightnessandgammainvarianceof the new huecorrelate.
To betterquantify huestability, we performedcolour indexing [20] experimentsontheabove dataset.For this we dividedthe54 imagesinto two halves,accordingto theirgammasettings.Onehalf wasassignedmodelimages,i.e. thoseimageswearesearchingthrough,andtheotherhalf queryimages,i.e. theimagesthatareusedasinputfor asearch.We transformedall theimagesinto huebasedrepresentations,boththeconventionalonefrom Equation(4) andthelog basedhuefrom Equation10. Wetakeonly theresultinghueanglesandgeneratea16-binhistogramby quantisingthepossiblehuerangeinto discreteintervals. For eachqueryimagea matchingscoreto eachof themodelsis calculatedastheintersectionof thecorrespondingtwo histograms.(Histogramintersectionestablishestheoverlapof two histograms[20].) Theretrievedimagesarethensortedin orderof theirmatchingscore.
Theresultsof this experimentarelisted in Table1. They aregivenin termsof aver-agematchpercentile,thepercentageof thecorrectimagesretrievedin 1st,2nd,and3rdrank,andtheworst rank in which a correspondingimagewasretrieved. Averagematchpercentileis a standardmeasureusedin the colour indexing literature[20]. A matchpercentileof e.g.99 informsus that thecorrectimagewasretrievedin thetop 1% of allmodelimagesin thedatabase.FromTable1 we seethatimagegammaindeedinfluencesthematchingperformancebasedonconventionalhuedefinition.Theachievedmatchper-centile is only about95, moreover the recognitionrate (i.e. the percentageof 1st rankretrievals)is only slightly over50(only half of theimagesbeingcorrectlyidentified),andtheworstrankin which thecorrectimagewasretrievedis 8. For a small imagedatabase
Table1: Resultsof thecolourindexing experimenton animagedatabaseof 27 colourfuldesignscannedwith two differentgammasetting.
suchastheoneusedin theexperiment,this is clearlynot goodenough.In contrast,if weturn our attentionto theresultsobtainedfrom thelog huedefinition,we seeimmediatelythat herethe performanceis very good. The averagematchpercentileis 99.72whichcorrespondsto all correctimagesretrievedin 1stplaceexceptfor two thatrank2nd.
The above experimentillustratesthat commonvaluesof gammaimpacton conven-tionaldefinitionsof hueto theextentthatindexing performancedeteriorates.In a secondexperimentwe wantedto evaluatethegeneralutility of thenew definition. Doesthenewhuecorrelatecaptureintrinsicallyusefulinformation?Canit beusedasanalternateto hueasdefinedin HSV (HLS or IHS)?Wetookalargeimagedatabasecomprising4100imagetriplets(this imagesetis similar to theonedescribedin [3]). Eachtriplet consistsof oneoriginal image,takenfrom theCorelPhotostock,andtwo croppedversionswhere �RQ�� oftheimagewasremovedeitherhorizontallyor vertically. Clippingtheleft andright sideofimagessimulatesportrait image.Clipping top andbottomsimulatespanoramiccapture.Wepointout to readersthatthisclippingis exactlywhathappensin theAPSphotographicsystem(a full resolutionimageis alwayscapturedbut panoramicandportraitprintscanbemadethroughclipping).
Again, we performedimageretrieval on this dataset.The original imagesmake upthe modelset,while the croppedimagesarethe queryimages.As above, we quantisedhueinto 16 and8 valuesandindexedonly on these.Theresultsthatwe obtainedprovedto be excellent. The averagematchpercentileover the whole dataset(i.e. 8200queryimages,4100modelimages)is 99.80for the16 bin and99.22for the8 bin histograms,and is comparableto the performanceachieved by indexing on conventionalHSV hue(99.95and99.73percentilerespectively). This shows that hueaswe have definedit inEquation(10) providesa powerful cuefor objectrecognition. Not only that. Hue alsoallows for a compactrepresentationof colourcontent.Theamountof compressionthatwasachieved here- an imagedescribedby 16 or 8 numbersonly - is similar to othermethodsintroducedin theliterature[3, 18].
Thoughour angulardefinitionof hueis similar in spirit to thoseusedin colorscience(which aredesignedto modelperceptualresponse),we wishedto examinethis relation-shipin moredetail. In Figure4 we have plottedlinesof constanthuein thecolourspacedefinedby theopponentlog colouraxesfrom Equation8. Thedatafor this plot is takenfrom from [10] andwasderivedthroughpsychophysicalexperiment.Thelinesthuscon-nect points humanobservers judgedto have the samehue. We can seethat, with theexceptionof onehuelocusin the blue region, all the lines arefairly straightandhencecorrespondwell with thehumanvisualsystem.In fact,our newly derivedhuespaceis inbetteragreementwith psychophysicaldatathanconventionalhuespaces.This is demon-stratedin Figure5 wherethesamehuelinesasin Figure4 areplottedin thehue-saturationplaneof theHSV colourspace.Here,clearlythelinesappearmorecurved.
We have demonstratedthathue,asconventionallydefined,is not a stablecuewhenthegammaof imageschanges.To overcomethis we have derived a new definition of huethat is invariantto imagegammaandbrightness.Invarianceis achievedthrougha trans-form to a 2-dimensionalcolour log opponentcoordinatesystem. With respectto polarcoordinates,hueis theangleof opponentcolours.
Experimentsdemonstratethat this hue definition indeedoutperformsclassicalhuespaces(HLS, HSV and IHS) when the imagegammais not held fixed. Moreover, itworksaswell asconventionaldefinitionswhengammadoesnot vary. Experimentsalsodemonstratethat the new hue correlateappearsto be more perceptuallyrelevant thanconventionalmeasuresusedin computervision.
Acknowledgements
Thiswork wasfundedby EPSRCgrantGR/L60852.
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