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Volume 107, Number 3, May–June 2002Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 107, 247–259 (2002)]

The Role of Rendering in the CompetenceProject in Measurement Science for Optical

Reflection and Scattering

Volume 107 Number 3 May–June 2002

Harold B. Westlund andGary W. Meyer

Department of Computer andInformation Science,University of Oregon,Eugene, Oregon 97403

and

Fern Y. Hunt

National Institute of Standards andTechnology,Gaithersburg, MD 20899-8910

[email protected]

[email protected]

[email protected]

Computer rendering is used to simulatethe appearance of lighted objects forapplications in architectural design, foranimation and simulation in the enter-tainment industry, and for display anddesign in the automobile industry. Rapidadvances in computer graphics technologysuggest that in the near future it will bepossible to produce photorealistic images ofcoated surfaces from scattering data.This could enable the identification ofimportant parameters in the coatingsmanufacturing process that lead to desirableappearance, and to the design of virtualsurfaces by visualizing prospective coatingformulations once their optical propertiesare known. Here we report the results ofour work to produce visually and radio-metrically accurate renderings of selectedappearance attributes of sample coatedsurfaces. It required changes in the render-

ing programs, which in general are notdesigned to accept high quality optical andmaterial measurements, and changes inthe optical measurement protocols. Anoutcome of this research is that somecurrent ASTM standards can be replaced orenhanced by computer based standardsof appearance.

Key words: BRDF; computer rendering;gloss, reflectance.

Accepted: May 15, 2002

Available online: http://www.nist.gov/jres

1. Introduction and Background

The durability and attractiveness of paint and relatedpolymer coatings are crucial to the marketability andperformance of manufactured products from virtuallyevery industrial sector: automobiles, computer screens,buildings and home appliances to name a few. As ad-vances in material science and technology enhance ourability to manufacture coatings with novel and attractivevisual effects, customer expectations for these productshave increased. Thus maintaining the consistency andpredictability of surface coating performance in thisenvironment will require that companies have the abilityto predict appearance at the coatings formulation

level—the level most under the manufacturer’s control.Progress in material characterization and optical metrol-ogy are the foundation for achieving this capability, butrapid advances in information technology suggest that itwill be possible in the near future to use the results ofoptical and material measurements to render the appear-ance of painted surfaces from which the measurementswere taken. Computer graphic rendering is used tosimulate the appearance of lighted objects for designapplications in architecture, for animation and simula-tion in the entertainment industry, and for display anddesign in the automobile industry.

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In the future, rendering could be used to predict theappearance of a surface from the optical properties ofthe coating, permitting the development of tools that canbe used firstly to identify important parameters in theformulation process and secondly to allow designers tovisualize the appearance of a proposed coating. Theability to view a virtual end stage product will eventu-ally lead to a computer graphics based standard forappearance. In this report we will describe some firststeps toward this goal. The work reported here was partof an effort arising from a competency project entitled“Measurement Science for Optical Reflectance andScattering” involving four laboratories at NIST: theBuilding and Fire Research Laboratory, the InformationTechnology Laboratory, the Manufacturing EngineeringLaboratory, and the Physics Laboratory. The project wasinitiated in response to recommendations by industry[1] and the Council of Optical Radiation Measurements[2]. Its purpose was to apply the technical advances inmaterial science, optical metrology, light scatteringmodeling and computer graphic rendering to developmore accurate methods of modeling and predicting theappearance of coatings and coated objects.

1.1 The Physical and QuantitativeCharacterization of Appearance

When we use the term “appearance” we are referringto a complex of attributes determined by the interactionsof light with a surface. These include but are not limitedto gloss, glitter, color and fluorescence. We will notdiscuss the human psychophysics involved in theperception of these characteristics, although renderingprograms do take these considerations into account andinvestigation of their effects is an active area of research[3]. When you look at an object, say a tabletop in alighted room lit by a single lightsource which forsimplicity we assume has a single wavelength, theamount of light that reaches your eye from the table canbe derived from a function whose values are the fractionof light incident on the surface that is scattered in thedirection of your line of sight. This function is known asthe bi-directional reflectance distribution function(BRDF). Each surface has a BRDF that quantitativelysummarizes its light scattering characteristics. It is anassumption in our research that knowledge of the BRDFis essential to successful representation of surfaceappearance. This assumption was strongly supported ina number of meetings between NIST members of thecompetency project and researchers from industry andacademia concerned with appearance including NISTWorkshops held in 1996 and 2000 and at SIGGRAPHmeetings in 1997 and 1999.

1.2 Rendering

In order to realize the overall purposes of the projectthat we mentioned at the beginning, we set the goal ofproducing visually and radiometrically accurate render-ings of selected aspects of the appearance of complexsurfaces; seeking to provide a proven path from materialmeasurement and characterization to object rendering.At this point, it would be helpful to answer the question,just what is rendering? It is the process of producing asynthetic image using a computer. To do this, certaininput parameters are required. If the scene is a confer-ence room for example, a geometric description of theobjects in the room (furniture, light sources, carpeting,windows, etc.) must be provided. Second, there needs tobe a description of the light sources, their location andradiometric properties. Third, the light scatteringproperties of an object in the room must be described.Thus we must have the BRDF of the object or BRTDFif light is also transmitted. Finally an observation view-point must be specified that defines the plane fromwhich the image will be viewed. These parameters areused in an integral equation which describes therelationship between the amount of light incident to asurface in every direction and at a given point, and theamount of light reflected or emitted from the surface ina given direction at that point.

Lr(�r, �r; � ; x, y, z ) = ��i

�Li (�i, �i; � ; x, y, z )

cos(�i)d�i+emittance (1)

where � = � (�i, �i; �r, �r; � ) is the BRDF of a surfaceat the incident direction �i, �i and reflected direction�r, �r, and � is the wavelength of the incident lightwhich we assume remains the same when reflected.Li (�i, �i; � ; x, y, z ) is the radiance of incoming light at(x,y,z ) travelling in the direction given by �i, �i.Lr(�r, �r; � ; x, y, z ) is similarly defined for light in anoutgoing direction from (x, y, z ) [4]. The units ofradiance are W/m2sr where sr (steradians) are solidangle units [5]. The radiance of light incident at a point(x, y, z ) can be related to the outgoing radiance at thesame point so that the integral equation can be writtenas an equation for a single unknown radiance function L[4]. A large part of the work done by the renderingprogram is the computation of a numerical solution ofthis equation, providing the radiance for each point inthe scene that is visible to the observer or detector. Avisual representation of the solution in a geometricdescription of the scene is the basis for the syntheticimage. Global illumination methods [4] compute thecontribution to the radiance at a point coming from

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direct illumination (i.e., incident light coming directlyfrom light sources) and the contribution from indirectillumination, that is light that has been scattered andreflected off other surfaces in the scene before reachingthe point. Physics based methods attempt to accuratelydescribe the propagation of light and its interaction withmaterials in the scene, often using results from the fieldsof radiative heat transfer and illumination engineering.Diffraction, polarization and other effects that dependon the wave-like nature of light are taken into account tosome extent, but computations are based primarily ongeometric optics. Approximations to the BRDF used inthese rendering programs have been developed largelyin isolation from the BRDF measurement and modelingcommunity. Because the major rendering applicationshave come from the entertainment industry, speed hasbeen more important than physical accuracy. Our firsttask, therefore, was to build an interface from the highprecision BRDF measurements and models to formssuitable for input to a rendering program. As a startingpoint we used the program Radiance discussed in thenext section. The result was an enhanced renderingprogram called iBRDF (see Sec. 4)—a significant steptowards achieving project goals.

1.3 Radiance and NIST Measurements

Radiance is a publicly available and widely usedrendering program which is physically accurate andwhich uses global illumination methods [6]. We workedwith its author, Gregory Ward, to determine require-ments for the interface and with Michael Metzler, whowrote the modeling and data fitting code for the NEFDS[7] database that we will discuss later. We soughtto answer the question, what kind of BRDF data isneeded for rendering? Like many rendering programs,Radiance uses Monte Carlo methods to evaluate theintegral on the right hand side of the radiance equation.In order to assess the contribution of light from pointsin the scene to light reaching the observer, many valuesof the BRDF of the surface containing the contributingpoint must be used, particularly when light coming fromdiffuse interreflections is computed. To meet this need,one might consider exhaustive measurements. Howeverfor diffuse materials these are unnecessary and specularmaterials would require extensive sampling that wouldbe too time consuming and difficult to be feasible. Ourapproach—a mixture of modelling and measurementswas tailored to the appearance attributes and materialsunder study with the aim of balancing physical accuracyand computational efficiency. Two materials arediscussed here. Black glass samples with a clear epoxycoating and metal panels painted with metallic paint.Gloss was studied in the black glass samples and gloss,

haze, and color were investigated in the metallic paintedpanels. In the case of black glass, a reflection modelbased on the geometric ray approximation of lightpropagation and on surface topographical measurementsproduced a BRDF of adequate accuracy. Large numbersof BRDF values could be generated easily and were usedas input for iBRDF. A modified Beard-Maxwell model[8] was used for the painted panels. Parameters for themodel were determined from reflectance measurementsusing a protocol like that employed in the NEFDSdatabase.

1.4 Evaluation and Comparison

Rendering simulates a human observer looking at areal scene by converting reflectance and spectralcharacteristics into perceptual characteristics. Whatmetrics can be used to evaluate how well a conversionmethod works especially in comparison with othermethods? Since visual inspection is an irreducible partof any comparison, a rigorous quantitative metric mustinclude an adequate model of human perception andpsychophysics. Since the considerations leading to sucha model were beyond our scope we were forced to relyon visual comparison of an object and its renderedimage combined with a comparison of radiance mea-surements of the object and image. This was done forobjects in a light box illuminated by light sources ofknown radiometric characteristics. The results of thisstudy can be found in [9].

In the next section we describe the leading BRDFmodels used in rendering and a tool specially developedfor visualizing them—the Oregon BRDF Library. Adescription of iBRDF is at the beginning of Sec. 4 andis followed by a description of its use in rendering theappearance of the black glass samples and paintedpanels. ASTM standards can be tied to the parameters ofBRDF rendering models. This is discussed in Sec. 4.2.A discussion of the implications of these results forcomputer based appearance standards can be found inthe concluding section.

2. Oregon BRDF Library

The appearance of an object is determined by theinteraction of light with the object surface; the widevariation in the appearance of objects that we see can belinked to the variation in the light-surface interaction.This light-surface interaction is generalized by thebidirectional reflectance distribution function, BRDF,and has been studied extensively in many fields ofresearch. The Oregon BRDF Library, part of mastersthesis work reported in [10] (OBL) is a compilation of

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a wide range of BRDF functions constructed over theprevious 30 years in the fields of physics and computergraphics. OBL offers a uniform, object oriented inter-face in C++ to this collection of BRDF functions, and isflexible enough to incorporate future BRDF models.

Each BRDF included in OBL is based on the following definition. The BRDF of a surface, � , is the ratio ofdirectionally exitant radiance to directionally incidentirradiance at a particular wavelength:

� (�i; �r; � ) =dLr(�i; �r; � )

dEi (�i; � )(2)

where the subscripts i and r denote incident and re-flected respectively, � = � , � is the direction of lightpropagation, � is the wavelength of light, L is radiance,and E is irradiance [5]. The geometry used by the BRDFis shown in Fig. 1. OBL includes quite a diversity ofBRDFs. They range from the simple to the complex andinclude both analytical and empirical models.

One of the most common and by far simplest BRDFprovided by OBL is the one proposed by Lambert [11].This is the BRDF of constant value (having constantradiance in all directions) which describes the reflectionproperties of a diffuse surface. Other more complexdiffuse BRDF models are also included in OBL. Min-naert proposed a generalization of the LambertianBRDF in order to describe the reflection properties ofthe moon [12]. Ideal diffuse reflector microfacets wereused by Oren and Nayar to derive a physics based BRDFfor diffuse surfaces [13]. These three diffuse OBLBRDF models (shown in Fig. 2) range widely in boththeir complexity and generality.

The wavelength dependency of the BRDF has beencaptured with varying success by different BRDF mod-els which are included in OBL as well. Cook and Tor-rance described a physics based BRDF model whichcan capture much of the spectral dependency of rough-ened metals [14]. Lafortune et al. approximated themeasured BRDF of materials using a summation of aseries of cosine lobes [15]. Although an approximation,their model provided a simple means of capturing muchof the detail of the BRDF, including color dependency.Sample BRDF lobes from these two OBL models at asingle wavelength are shown in Fig. 3.

Several BRDF models included in OBL have alsobeen developed to capture the shininess of materials.Phong proposed a cosine function raised to a power toapproximate this type of surface [16]. Ward fit a Gaus-sian based function to measured data, and included theability to model anisotropic effects [17]. He et al.derived a physics based BRDF for shiny surfaces whichincorporates Fresnel reflectance and wave optics [18].Examples of the BRDF models are shown in Fig. 4.

The Oregon BRDF Library which includes the aboveBRDF models and more has been used as the BRDFinterface for a BRDF visualization system. A secondtool was also created to determine the correspondencebetween the BRDF models of OBL and standard ap-pearance scales. These tools have been used to providethe BRDF values for realistic image synthesis.Fig. 1. Light reflection geometry.

Fig. 2. Diffuse BRDF models: Lambert, Minnaert and Oren-Nayar.

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3. NEFDS

The Beard-Maxwell model [8] is another physicsbased BRDF model, but one whose parameters arespecified with empirical measurements. The model isespecially important because there is a governmentdatabase of surface reflection parameters, the Noncon-ventional Exploitation Factors Data System [19](NEFDS), that utilizes a modified form of the Beard-Maxwell model, the NEF Beard-Maxwell (NEF-BM)model. Additional surface reflection parameters for thedatabase can be determined because a measurementprotocol, using existing radiometric instruments, hasbeen specified [7].

3.1 Beard-Maxwell Reflection Model

The Beard-Maxwell model presented by Maxwell etal. [8] is built on the assumption that the material sur-face is a three dimensional terrain of micro-facets ofvarying orientation. In this model, reflected light is theresult of only two physical occurrences. Light is re-flected off one of the micro-facets (first surface reflec-tance) and light is scattered out of the surface afterhaving first entered the sub-surface medium (volumetricreflectance).

First surface reflection causes light to be reflected inthe specular direction (i.e., mirror reflection) off eachindividual micro-facet as determined by the micro-facet’s normal rather than the macro-surface normal.Therefore the distribution of the first surface reflectanceis determined by the distribution of the micro-facet nor-mals which in turn is driven by the density function� (� ), the relative density of micro-facet normals (persteradian) in vector direction � . Maxwell et al. calcu-lated the first surface reflectance to be

�fs(�i, �r) =R (� )� (H)

4cos�icos�rSO (3)

where H is the half angle vector, � is the bistatic angle(i.e., the angle between either the incident or reflecteddirection and the half angle vector), R (� ) is the Fresnelreflectance, and SO is a shadowing and obscurationterm. Figure 5 is a diagram of the geometry used by theBeard-Maxwell model.

Fig. 3. Spectrally variant BRDF models: Cook-Torrance and Lafortune (shown at� = 550 nm).

Fig. 4. Three BRDFs used to model first-surface reflection: Phong, Ward, and He .

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Rather than attempting to measure � of Eq. (3)directly, Maxwell et al. replaced it with the measuredzero-bistatic (� = 0) first surface reflectance at the halfangle, �fs(H, H ). SO = 1 when � = 0, so Eq. (3) can berewritten as

� (H ) =4�fs(H, H )cos2 �H

R (0)(4)

This is simplified further by their assumption that thesurface is isotropic. In that case to generate reflectancevalues for all incident and reflected directions, �fs(H, H )need only be sampled at the angles 0�H

2

and the

azimuthal angle �H = 0.Light reflected from the first surface is assumed to

maintain its original polarization (i.e., incident and re-flected light are of like polarization) while any lightreflected through volumetric scattering is assumed to betotally depolarized. In this way, separation of the firstsurface reflectance from the volumetric reflectance caneasily be performed by measuring the polarization ofreflected light. A few additional, well defined measure-ments are used to determine other model parameters,such as the surface index of refraction and the shadow-ing and obscuration parameters.

3.2 Database System

At the heart of NEFDS is a database system contain-ing the BRDFs of over four hundred materials. The

materials in the database fall into 12 different cate-gories: asphalt, brick, camouflage, composite, concrete,fabric, water, metal, paint, rubber, soil and wood. Thisdatabase which can be accessed either through the inter-active XWindows program NefMenu, or by using com-mand line control, allows the user to query for BRDFvalues of materials or material groups at ranges of wave-lengths for any given geometry.

The variation of material BRDFs available throughNEFDS can be seen in Fig. 6, which shows the BRDFsof cement and lumber. Notice the significant differencein geometry that can be characterized by the modifiedBeard-Maxwell reflection model. This strength (theability to capture a wide variety of BRDF distributions)coupled with the systematic method of measurementmakes for a very powerful tool.

Although the number of materials is large and thevariety is wide, the selection is limited by two keyconditions. One requirement for the inclusion of amaterial in the database is that the BRDF of the materialmust be well represented by the NEF-BM BRDF model.For example, the BRDF should not be characterized bystrong surface anisotropy since the NEF-BM BRDFmodel only works with isotropic data. There are in factsome materials included in the NEFDS which areanisotropic. To represent anisotropic material using theNEF-BM model, the material’s BRDF is averaged toisotropy.

The second condition is a result of the main applica-tion of NEFDS—materials were selected to be part ofthe database based on their relevance to the field ofremote sensing. These materials are mostly objectswhich would be viewed from a remote sensor, such asa satellite. However, the well defined measurementprotocol lends to the future inclusion of other materials.

A potential limitation of the NEFDS is that themodified Beard-Maxwell equation used with NEFDSresults in inaccuracy at grazing angles. Light incident atgrazing angles will result in more energy reflected thanwas incident. In the application to remote sensing this isnot relevant since measurements are performed farenough away from grazing, but it might be relevant inthe application to computer graphics. In practice, theinaccuracy usually has not resulted in noticeableartifacts, primarily because of the foreshortening ofincident energy which also occurs at grazing angles.However, this is an important point to keep in mind.

Fig. 5. Beard-Maxwell BRDF model geometry.

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4. iBRDF

The BRDF models represented in the previous twosections can capture subtle differences in surface lightreflection. However most shaders, the algorithmicimplementation of the reflection model, are not able torepresent the BRDF at this level of generality. In orderto use these BRDFs in generating synthetic imagesrequires a shader capable of capturing the detail whichis available in the BRDFs. A new shader, called iBRDF,has been developed which accurately simulates thisdetail through its ability to utilize any arbitrary BRDFfunction.

4.1 Alias Method

iBRDF was implemented within the RadianceLighting Simulation and Rendering System (Radiance)[6, 20, 21] to generate synthetic images. Radiance is asuite of programs built around an advanced distributedraytracer designed for realistic image synthesis. Itwas selected because it is a physically-based renderingsystem designed to accurately model the light behaviorof a scene using physical units [21]. Using such a systemcomplements the validity of the results obtained by thephysics based BRDFs within OBL and those generatedfrom NEFDS. Additionally, the source code to Radianceis publicly available [6] and the program is currently inwide use, aiding future work.

Radiance is a distributed ray tracer which utilizesMonte Carlo importance sampling to solve Eq. (1),termed the rendering equation in computer graphics[22]. The rendering equation specifies the reflectedradiance in direction �r from the values of the surface’sBRDF and the incident irradiance, integrated over allincident directions. As mentioned earlier the solution ofthis integral often is the most computationally expensivetask of a rendering program. For this reason the solution

to this integral is often found through the use of MonteCarlo integration.

We have developed an efficient method of perform-ing this Monte Carlo integration. Instead of casting raysin a uniform distribution about the hemisphere andweighting the returned value by the reflectance, the raydistribution itself is weighted by the reflectance. Thiscan be done in a straightforward manner when theBRDF is composed of invertible functions such asGaussians. When the BRDF is represented discretely,either by taking measurements over the hemisphere orby sampling a non-invertible functional form, anothermethod must be used to generate random variates forMonte Carlo integration. This can be accomplished byfirst subtracting the smallest hemisphere that fits withinthe BRDF data. This removes the diffuse or uniformlyvarying portion of the BRDF and leaves only the highlydirectional specular part. The alias selection method[23] can be employed to create random variates fromthese remaining specular reflectances

Radiance was designed with built-in support ofarbitrary BRDFs, but only for computing the directcontribution of the dominant light sources. In Radiance,the dominant light sources are handled separately toreduce the variance introduced in the Monte Carloevaluation of Eq. (1). Figure 7 (top) which uses thebuilt-in BRDF shader, shows the direct reflection of thesix light sources correctly, but there is no reflection atall of the indirect illumination from the surroundingcheckered floor. Performing uniform sampling of theBRDF begins to capture this indirect contribution fromthe floor as seen in Fig. 7 (middle) , but the reflectedimage of the floor contains excessive noise. The bestresults are obtained with the importance sampling ofiBRDF in Fig. 7 (bottom). The reflection of the floor isaccurately captured in the four spheres of this imageusing the same number of samples as the middle image.

Fig. 6. BRDFs of cement (left) and bare construction lumber (right) obtained from NEFDS.

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4.2 Application of iBRDF

4.2.1 Coated Epoxy

iBRDF was used to render reflectance data comingfrom samples of black glass covered with a layer of clearepoxy. In this simple first case, the surface was isotropicand a pre-specified degree of surface roughness wasobtained by appropriate fabrication conditions. We wereinterested in seeing how well differences in the renderedimages of samples with different roughnesses displayedthe gloss differences in the samples. Black glassminimized the effect of subsurface reflection andtransmission, and the index of refraction of the epoxyand the glass were approximately equal. Details onsample preparation, reflectance modeling, and measure-

ment can be found in [24]. The reflectance modelingmakes use of surface topography measurements—anapproach that is new in the rendering field. The reflec-tion model known as the ray method, is based on theassumption that incident light is specularly reflected bythe local tangent plane on the surface. Measurements oflocal surface height were made using scanning whitelight interferometry by researchers in the Manufactur-ing Engineering Laboratory (MEL) who then used theseheights to construct the normals to local tangent planesneeded to compute the scattering directions. The BRDFwas computed by simulating the uniform illuminationof the surface for various incident directions, and count-ing the number of scattered rays that reach detectorsdistributed over a hemisphere of scattering directions.

Fig. 7. Four spheres of increasing glossiness rendered using three different methods. Top—Radiance’sbuilt-in arbitrary BRDF shader incorrectly ignores the contribution from indirect illumination. Middle—Uniform Monte Carlo sampling (160 samples per pixel) results in an image filled with sampling noise.Bottom—Monte Carlo importance sampling with iBRDF (160 samples per pixel) correctly renders image.

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Comparisons between the results of this calculationand optical measurements of the sample and comparisonwith a more rigorous scattering model showed thatthe ray method furnished a good approximation to theBRDF. The method is also computationally efficientso a sufficient number of incident and scatteringdirections could be quickly generated and used asinput for iBRDF. Figure 8 shows two black glass tiles.The tile on the left has rms roughness of approximately0.2 �m while the tile on the right has approximateroughness of 0.8 �m. The images were consistentwith visual inspection of the tiles. The study demon-strated that gloss loss due to surface roughening couldin fact be predicted by the rendering. This work isreported in [25].

4.2.2 NEFDS

As discussed in Sec. 3, not only does NEFDS offerhundreds of pre-existing materials, it also allows newmaterials to be added. Using the methods of measure-ment referred to in that section, two surfaces paintedwith gray metallic paint were fit to the NEF-BM model.The surfaces were fabricated by automotive coatingprocesses and were measured at NIST [9]. The paintswere mixed so that one had mostly coarse metallicflakes while the other was dominated by fine metallicflakes. The paint with a greater number of fine flakeshad a larger diffuse component due to more edgescattering. This is easily captured by the NEF-BMmodel and iBRDF as can be seen in the rendered imageof Fig. 9.

4.2.3 ASTM Standards

While it is important to be able to accurately depictthe full BRDF of a material, there is also much merit in

the ability to characterize a material with appearanceattributes such as gloss or haze. To this end, peopleconducting research in appearance have sought todevelop and standardize a number of simple measure-ments and corresponding measuring devices whicheasily and objectively quantify the reflection propertiesof a surface. The result is a number of one-dimensionalscales of appearance, such as gloss and haze, andinexpensive appearance measurement devices, such asglossmeters.

The standard specular gloss measurement defined bythe American Society for Testing and Materials (ASTM)in ASTM method D523 measures the magnitude of lightreflected in a small solid angle about the speculardirection [26]. ASTM method E430 specifies that hazeis a measure of the fraction of light reflected in anoff-specular direction to that reflected in the speculardirection [27]. These well defined measurementsresult in a single numerical value describing particularappearance attributes of the measured surface. Ananalogous calculation may be performed on theBRDF of a surface through computer simulation of themeasurement protocol. In this way, a simulated gloss-meter or hazemeter can be used to determine the glossor haze of any arbitrary BRDF.

A computer program was developed which appliesthe measurement protocol of standardized appearancetools to BRDFs in order to simulate their results[28]. This new virtual light meter is essentially acustomized integration tool, using numerical quadratureof the specified BRDF model over an adaptively

Fig. 9. Simulation of coarse and fine metallic paint on vases.

Fig. 8. Rendering from reflectance data generated using the Raymethod and a surface topographical map of coated epoxy sampleswith rms roughness values 201 nm (left) and 805 nm (right).

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subdivided source and receptor aperture (Fig. 10) tocompute the final standard appearance value. In additionto being able to calculate the current standards, thevirtual light meter can be customized for other measure-ments. The customizable parameters include the sizeand locations of the source and receptor apertures,the specular angle, the surface orientation, and thereflection model.

The reflected flux passing through the receptoraperture is directly responsible for the standard glossand haze values. Integration of this flux begins by firstsubdividing the source aperture. For each sampledpoint on the source aperture, the receptor aperture isadaptively subdivided. Subdivision of the receptor aper-ture continues until either the discretely computed fluxapproaches some stable value or a maximum subdivi-sion depth is reached. Figure 10 is an example of theflux passing through the receptor aperture resulting

from a single subdivided source element. After the fluxdue to this source element is computed, the process isrepeated for the other source elements. Adaptivesubdivision of the source continues until either theflux approaches some stable value or a maximumsubdivision depth is reached.

This program was used with surface reflection prop-erties defined by the Ward reflection model [17] inorder to develop a correspondence between the modelparameters and the standard 20� gloss values. Using thiscorrespondence, an image of tiles with decreasing glosswas generated (Fig. 11). These tiles, with modelparameters selected to produce 20� gloss values of80, 60, 40, and 20, create a close correspondencebetween appearance and gloss value. In a similar fash-ion, the correspondence between 2� standard haze andthe Ward model was determined and used to render fourtiles of increasing haze (Fig. 12). The BRDF model

Fig. 10. Left—Subdivision of light meter apertures using the 60� specular gloss specifications [26]. Thesource and receptor apertures are oriented in directions �i and �r, 60� down from the surface normal, N ,in the plane of incidence. Right—Flux passing through receptor aperture due to one source aperturesubdivision. Aperture sizes are not to scale.

Fig. 11. Tiles with measured 20� specular gloss values 80, 60, 40, and 20.

Fig. 12. Tiles with measured 2� haze values 10, 60, 110, and 160.

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roughness parameter values were chosen so as toproduce 2� haze values for these tiles of 10, 60, 110, and160. The 20� gloss of the four haze tiles was maintainedat 100 by scaling the specular coefficient.

4.2.4 Metallic Paint

A more recent appearance measurement, currently inthe standardization process [29], is that used to charac-terize metallic paints and plastics. These metallicsurfaces contain small platelets of metal usuallyaccompanied by colored particles or dyes in thesubstrate. The platelets are oriented nearly parallel to thesurface so as to create a strongly directional reflection.This directionally reflected light changes color as itpasses through the colored substrate.

The method proposed for standardization specifiesmeasurement of the tristimulus values at three angles:near specular, far from specular and one more angle inbetween. Interpolation of these three measuredvalues has been found to accurately characterize theappearance of metallic surfaces. A BRDF can then begenerated from the interpolated tristimulus values andused with iBRDF to render synthetic images of objectsmodeled with metallic paint.

Figure 13 is an image of three vases modeled usingtristimulus data measured from actual metallic paintsamples and rendered using iBRDF. These vasesdemonstrate the sub-surface characteristic of metallicpaint but not the usual glossiness attributed withmetallic automobile finish. Combining the gonio-apparent sub-surface reflection with a first-surface

BRDF leads to a more realistic image as can be seen inFig. 14. The first-surface BRDF was chosen so that the20� gloss values are 10 for the left shell and 60 for theright.

5. Conclusion

In this work we reported the results of our efforts tocreate visually and radiometrically accurate renderingsof the appearance of gloss in coated epoxy samples(with controlled roughness), gloss and haze in paintedmetallic panels, and color in painted metallic panels.These investigations help build a path from the materialproperties of coatings to a visually accurate representa-tion of their appearance. To achieve this we had to linkBRDF measurement and modelling on the one hand,and computer graphic rendering on the other. We startedwith a publicly available program Radiance that had abuilt-in reflectance model that is accurate for so-calledGaussian surfaces that are well described by Gaussianstatistics. Its major drawback was that it could not acceptmeasurement data as input and could not handle non-Gaussian surfaces. The enhanced rendering programiBRDF constructed by Westlund and Meyer,does accept arbitrary input because it performs Monte-Carlo inversion for arbitrary distributions and thereforeremoves the restriction to the kind of BRDFs used inRadiance. We found that rendering required BRDFmodels where a large number of values could be pro-duced with computational efficiency. Our approach tomeasurement and modelling was designed to achievethe balance between this need and physical accuracy.

Fig. 14. Two automotive shells with 20� specular gloss of 10 and 60.

Fig. 13. Three vases with metallic paint but no clear coat.

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iBRDF was used to render images of coated blackglass samples from reflectance data. Using a reflectancemodel based on the distribution of normals to localtangent planes on the surface, a BRDF was constructedfrom surface topographical measurements. In thepainted metallic panel case a modified Beard-Maxwellreflectance model was used. This model is physicallybased but has terms and parameters that can be deter-mined by a measurement protocol as was used in theNEFDS database. M. Nadal of the Physics Laboratoryperformed the measurements on the panels.

ASTM gloss measurement standards are linked to thevisual evaluation of gloss. Rendering is a potentiallyimportant tool in developing such standards or couldbecome a procedure cited in new gloss standards. Thework described in Sec. 4.2.3 is a first step along thisline. Rendering materials under an ASTM standardprocedure will enable the systematic study of thevariation of the appearance of standard materialswith distance between object and viewer or degree ofillumination. Moreover this work shows how compari-sons can be made between different rendering programsso that a computer graphic based gloss standard can bedefined independently of the program used. We alsonote that programs rendering a set of objects withdefined gloss standards can be compared, thus givingrise to a possible standard for rendering programs.

An important outcome of our work has been thedemonstration that satisfactory rendering of manycolored objects can be done with just a few measure-ments. This was seen in the rendering of metallicpainted shells using iBRDF.

The BRDF has played an essential role in our studyof appearance but progress in capturing complex visualeffects will have to go beyond this function. The glitter-ing micro-appearance of metallic paint so evident whenone approaches a newer automobile is an effect thatinvolves scales that are too small to be described byBRDF and depends on human binocular vision as well.Image texture is an extremely important attribute and ittoo falls outside the range of BRDF description. Wehave also neglected the effects of paint application inour modeling. Nevertheless, the rapid developmentsin computer graphics—where the turn around timebetween theoretical formulation and practical applica-tion is so short—make significant progress on theseproblems in the near future an exciting and likelypossibility.

Acknowledgments

We would like to thank Dr. Egon Marx andDr. Theodore Vorburger of the ManufacturingEngineering Laboratory for their work on modeling

and surface topography measurements of the coatedepoxy tiles. We would also like to thank Peter Walkerfor his work on many of the BRDF tools and the BRDFvisualization images. Finally, the authors would liketo acknowledge and thank Maria Nadal of the OpticalTechnology Division of the Physics Laboratory forperforming the BRDF measurements and for hercooperation and collaboration in creating a measure-ment protocol for rendering applications.

6. References

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[2] CORM Sixth Report, Pressing Problems and Projected NationalNeeds in Optical Radiation Measurements, 1995.

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[7] For more information about NEFDS contact Eric Stenberg,[email protected].

[8] J. R. Maxwell, J. Beard, S. Weiner, and D. Ladd. Bidirectionalreflectance model validation and utilization, Technical ReportAFAL–TR–73–303, Environmental Research Institute ofMichigan (ERIM), October 1973.

[9] M. Nadal, L. P. Sung, F. Hunt, H. Westlund, and G. Meyer,Rendering the geometrical aspects of appearance of metallic-flake pigmented coatings from reflectance measurements, inpreparation 2001.

[10] Peter Andrew Walker, A visualization system for bidirectionalreflectance distribution functions, Master’s thesis, University ofOregon, 1999.

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[12] M. Minnaert, Light and Color in the Open Air, Dover (1954).[13] Michael Oren and Shree K. Nayar, Generalization of lambert’s

reflectance model, Proceedings of SIGGRAPH 94, July 1994,ISBN 0-89791-667-0, Orlando, Florida.

[14] Robert L. Cook and Kenneth E. Torrance, A reflectance modelfor computer graphics, ACM Trans. Graphics, 1, 7-24 (1982).

[15] Eric P. F. Lafortune, Sing-Choong Foo, Kenneth E. Torrance,and Donald P. Greenberg, Non-linear approximation of reflec-tance functions in Proceedings of SIGGRAPH 97, AddisonWesley, August 1997, pp. 117-126.

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[17] Gregory J. Ward, Measuring and modeling anisotropic reflec-tion, Computer Graphics Proceedings of SIGGRAPH 92 26(2),265-272 (1992).

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[18] Xiao D. He, Kenneth E. Torrance, Francois X. Sillion, and Don-ald P. Greenberg, A comprehensive physical model for lightreflection, Computer Graphics Proceedings of SIGGRAPH 91,25(4), 175-186 (1991).

[19] Nonconventional Exploitation Factors (NEF) Modeling, ORD257-96, August 1996.

[20] Greg Ward Larson and Rob Shakespeare, Rendering withRadiance. The Art and Science of Lighting Visualization,Morgan Kaufmann Publishers, Inc., San Francisco (1998).

[21] Gregory J. Ward, The radiance lighting simulation and renderingsystem, in Computer Graphics, Annual Conference Series, ACMSIGGRAPH (1994) pp. 459-472.

[22] James T. Kajiya. The rendering equation, in Computer Graphics,Annual Conference Series, ACM SIGGRAPH (1986) pp. 143-150.

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[24] M. E. McKnight, M. Nadal E. Marx, T. V. Vorburger, and M. A.Galler, Measurements and predictions of light scattering by clearepoxy coatings, Appl. Opt., 40(13), 2159-2168 (2001).

[25] F. Y. Hunt, E. Marx, G. W. Meyer, T. V. Vorburger, P. A. Walker,and H. B. Westlund, A first step towards photorealistic renderingof coated surfaces and computer based standards of appearance,J. W. Martin and D. R. Bauer, eds., Service Life Methodologyand Metrology, Oxford University Press (2001).

[26] ASTM D 523-89, Standard Test Method for Specular Gloss,Volume 06.01 of Annual Book of ASTM Standards (1999). SeeRef. [30].

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[28] Harold B. Westlund and Gary W. Meyer Applying appearancestandards to light reflection models, in Computer Graphics,Annual Conference Series, ACM SIGGRAPH (2001).

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[30] Annual Book of ASTM Standards, Volume 06.01, AmericanSociety for Testing and Materials, Philadelphia, PA (1999).

About the authors: Harold B. Westlund is a graphicsresearch programmer at Radical Entertainment inVancouver, Canada. His main interest is developing andincorporating advanced lighting algorithms in realtime computer games. Gary W. Meyer is an AssociateProfessor in the Department of Computer Scienceand Engineering at the University of Minnesota. Hisresearch interests include the synthesis of color incomputer graphic pictures, perceptual issues related tosynthetic image generation, and color reproduction andcolor selection for the human computer interface. FernY. Hunt is a mathematician in the Mathematical andComputational Sciences Division of the InformationTechnology Laboratory. She is interested in the applica-tions of probability modeling and Monte Carlo methodsto material science. The National Institute of Standardsand Technology is an agency of the TechnologyAdministration, U.S. Department of Commerce.

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