Image-based bidirectional reflectance distributionfunction measurement

Stephen R. Marschner, Stephen H. Westin, Eric P. F. Lafortune, andKenneth E. Torrance

We present a new image-based process for measuring a surface’s bidirectional reflectance rapidly,completely, and accurately. Requiring only two cameras, a light source, and a test sample of knownshape, our method generates densely spaced samples covering a large domain of illumination andreflection directions. We verified our measurements both by tests of internal consistency and by com-parison against measurements made with a gonioreflectometer. The resulting data show accuracyrivaling that of custom-built dedicated instruments. © 2000 Optical Society of America

OCIS codes: 290.5820, 120.5820, 160.4760, 290.5880, 110.2960.

1. Introduction

One of the major goals of computer graphics is tosynthesize realistic images of scenes modeled in acomputer. To create such a realistic image, a com-plete model or description of reflectance is needed foreach reflective surface in the scene. In optics termi-nology, the complete bidirectional reflectance distri-bution function ~BRDF! described by Nicodemus etal.1 is needed. In contrast to many optical inspec-tion and surface metrology applications, computerrendering requires BRDF information over the com-plete scattering hemisphere for any incident direc-tion, including wavelength-dependent informationfor color. Computer graphics has long been aware ofthe BRDF literature, beginning with Blinn’s2 adap-tation of the work of Torrance and Sparrow,3 butphysically based models are still used only occasion-ally, both because of their complexity and becauseparameters are not readily available. Renderingfrom measured BRDF data is also possible,4 but evenrarer because the necessary BRDF data are notwidely available.

When this research was undertaken, S. R. Marschner, S. H.Westin ~shw5@cornell.edu!, E. P. F. Lafortune, and K. E. Torrance~ket1@cornell.edu! were with the Program of Computer Graphics,Cornell University, 580 Rhodes Hall, Ithaca, New York 14853-3801. S. R. Marschner ~stevemar@microsoft.com! is now with Mi-crosoft Research, One Microsoft Way, Redmond, Washington98052-6399. E. P. F. Lafortune ~Eric.Lafortune@luciad.com! isnow with Luciad, Parijsstraat 74, Leuven B-3000 Belgium.

Received 7 October 1999.0003-6935y00y162592-09$15.00y0© 2000 Optical Society of America

2592 APPLIED OPTICS y Vol. 39, No. 16 y 1 June 2000

Several researchers have built BRDF measure-ment instruments specifically for computer graphics.Some have used custom-made equipment; othershave measured only a small part of the hemisphere tosupply data for fitting the parameters of a simpleBRDF model. None has stressed absolute accuracy,instead aiming for visually plausible reflectances.

In this paper we present a system that measuresreflectance quickly, completely, and without specialequipment. The method works by our taking a se-ries of photographs of a curved object. Each imagecaptures light reflected from many differently ori-ented parts of the surface, and with the knowledge ofthe sample shape and the light source position thephotographs can be analyzed to determine the sam-ple’s BRDF. By using a curved test sample and animaging detector, we eliminate the mechanismneeded to position the detector in a traditional go-nioreflectometer; and by using automated photo-grammetry to measure the source position, weeliminate the precise source positioning mechanism.Although the apparatus is simple and the measure-ment is rapid, the technique provides millions of ac-curate samples that cover the full hemisphere toangles near grazing.

2. Prior Research

The BRDF is measured traditionally with a goniore-flectometer, positioning a source and detector withrespect to a flat sample. Four degrees of rotationalfreedom are needed, because, apart from wavelength,the BRDF is a function of four variables: two for theillumination direction and two for the reflection di-rection. For isotropic surfaces—those whose BRDF

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is invariant under rotation about the surfacenormal—the BRDF has just three angular variables,requiring three geometric degrees of freedom. Inthis paper we concentrate on this important class ofmaterials.

We denote the incident and exitant directions by~ui, fi! and ~ue, fe!, with u measuring elevation ~u 5 0at the surface normal! and f measuring azimuth.An isotropic BRDF depends only on the difference inazimuth, Df 5 fe 2 fi, so the variables ui, ue, and Dfsuffice in the isotropic case.

In a classical setup,5,6 the three or four angularimensions are handled by specialized mechanismshat position a light source and a detector at variousirections from a flat sample of the material to beeasured. The final dimension, that of wavelength,

s handled either with a broadband spectroradiom-ter that measures the entire spectrum at once or byultiple measurements varying the wavelength of aarrow-band source or detector. Because three,our, or five dimensions must be sampled sequen-ially, the measurement of reflectance functions cane time-consuming, even with modern computer con-rols. Moving the motor stages and measuring theeflected light can take several seconds, and, becauseeasurements are taken point by point, even a

parse sampling of the incident and exitant hemi-pheres can take several hours.The advent of good two-dimensional ~2-D! image

sensor arrays, such as CCD’s, offers the opportunityto reduce dimensionality in angle rather than inwavelength. The sensor array can measure a 2-Drange of angles simultaneously, leaving one or twodimensions of angle and one dimension of wavelengthto be sampled by sequential measurements.

Several such instruments have been developed tomeasure scattering for optical inspection and metrol-ogy purposes. They typically simplify BRDF mea-surement by any ~or several! of the followingrestrictions: covering a subset of the scatteringhemisphere, using a single incident direction, or mea-suring at a single wavelength. Breault Research’sOmniScatR device7 uses fiber optics to collect multi-ple points on the hemisphere and direct them to aCCD array. It covers a 44° cone of the scatteringhemisphere in one measurement. Hatab et al.8 andMcNeil and Wilson9 built a device that uses a hemi-spherical screen to capture scattered laser light; thisscreen is imaged onto a CCD array. Davis and Raw-lings10 at Boeing have recently patented a device us-ing an ellipsoidal mirror to gather a large part of thescattering hemisphere onto a CCD sensor.

Computer graphics, however, demands both fullhemispherical BRDF information and complete cov-erage of the visible spectrum. Exhaustive measure-ment of the entire hemispheres of the BRDF isrequired because image synthesis algorithms mustevaluate the BRDF in arbitrary directions. The vis-ible wavelength spectrum must be covered for correctcolor reproduction. On the other hand, accuracywithin a few percent is quite acceptable, only visible

wavelengths are of interest, and coarse wavelengthresolution is often sufficient.

Computer graphics practitioners need completedata, but usually lack the resources of an opticalmeasurement laboratory. It is important to use rel-atively nonspecialized equipment in a relatively sim-ple procedure. Because of these demands,researchers in computer graphics have developedtechniques and instruments specifically to acquirethe data needed.

Ward4 used a curved mirror to gather light scat-tered from a flat sample into a CCD camera with afish-eye lens. By use of a semisilvered mirror, thecamera captures the entire exitant hemisphere atonce for each illumination direction, leaving 2 de-grees of freedom to handle mechanically. Ward’s in-strument is limited by its optics; the hemisphericalmirror only approximates the ideal ellipsoid usedlater by Davis and Rawlings, and vignetting limitsthe quality of measurements near grazing exitance.Ward used the red-green-blue ~RGB! filters of hisCCD camera to yield three bands of spectral infor-mation.

Ikeuchi and Sato11 present a system for estimatingreflectance model parameters using a surface modelfrom a range scanner and a single image from a videocamera. In contrast to Ward’s method, they use acurved sample to capture a set of directions spanninga large range of both incident and exitant directions.Because their goal is to fit a reflectance model, theyuse a single image and make no attempt to samplethe BRDF exhaustively.

More recently, Lu et al.12 use photographs of acylindrical sample to give broad angular coverage inthe incidence plane, using multiple images with dif-ferent source positions to cover all angles. Theirgoals and methods are similar to ours for the specialcase of incidence-plane measurements. However,we present measurements for the full isotropicBRDF, and we verified the accuracy of our results.

Our method improves on this previous research bymeasuring isotropic BRDF’s completely and accu-rately, while retaining simplicity, speed, and sam-pling density. Our results can be used not only torender images, but also to validate reflectance modelsfor particular materials or to investigate BRDF’s thatdo not conform to existing models.

In the following sections we describe the specifics ofour system, give the results of measuring severalmaterials, and demonstrate the accuracy of these re-sults by comparing them with measurements from agonioreflectometer.

3. Method

A. Measurement Setup and Technique

Our system, pictured in Fig. 1, uses digital photo-graphs to record light reflected from the surface of atest sample of known shape and unknown but uni-form BRDF. It measures the three dimensions of anisotropic BRDF by using the curvature of the surfaceto vary two of the three angles and a sequence of

1 June 2000 y Vol. 39, No. 16 y APPLIED OPTICS 2593

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photographs to vary the third. To do this, we illu-minate the sample from a sequence of known posi-tions, using a fixed primary camera to take aphotograph for each position ~Fig. 2!. The pixels ineach of the resulting images give measurements oflight reflected from various points on the surface; theknown geometry of the surface, light source, and cam-era allows the incident and exitant directions to becomputed for each pixel. Each pixel in each imagethus provides a measurement of the BRDF for a par-ticular configuration of incident and exitant direc-tions. Depending on the sample geometry, we mayobtain several independent measurements for eachconfiguration, which can be compared to verify themeasurement or averaged to reduce random errors.

We can completely measure the BRDF in the planeof incidence by using a cylindrical sample. Becausethe sample’s curvature lies along a single direction,we can arrange for the light source, camera, and sur-face normal always to lie in a plane. Each imagewill give measurements along a range of ~ui, ue! pairs,

ith Df 5 0 ~Fig. 3!. A set of these images, eachcquired with the light source in a different position,roduces a family of such curves, which together fillhe entire 2-D parameter space of the incidence-planeRDF. We move the light source along a path fromear the camera ~where we measure near retroreflec-ion! to opposite the camera ~where we measurerazing-angle reflection!.

Fig. 1. Measurement setup.

Fig. 2. Schematic of the measurement setup.

594 APPLIED OPTICS y Vol. 39, No. 16 y 1 June 2000

To measure the BRDF over the complete hemi-phere for an isotropic surface, we use a sphericalample, which has curvature in both directions. Inhis case, the same set of light source positions leadso measurements on a family of 2-D surfaces of ~ui, ue,f! triples, which together fill the three-dimensional

3-D! parameter space of the isotropic BRDF.

B. Apparatus

Our photographic BRDF measurement technique re-quires a well-characterized camera, a stable and uni-form light source, and a means for measuring theirpositions. Also required are curved samples of ac-curately known shape.

Our system comprises the following parts:

• the primary camera: a cooled 12-bit CCD stillcamera ~Photometrics PXL 1300L!;

• the light source: a consumer electronic flashpowered by a regulated dc power supply ~Nikon

B-16 and HP 6030A!;• a secondary CCD camera for position measure-

ment ~Kodak DCS 420!; and• the samples: metal spheres painted with var-

ious sprayed coatings and metal cylinders paintedsimilarly or wrapped with sheets of flexible material.

The primary camera, which remains fixed, makesthe actual measurements of radiance reflected fromthe test sample. We adjust its overall sensitivityusing neutral-density filters as appropriate to allowmeasurement of bright reflections without clipping.If a wavelength-dependent measurement is required,

Fig. 3. Mapping from the surface to the BRDF parameter space inthe incidence plane. If both camera and source were at an infinitedistance from the sample, ue 2 ui would be constant and the diag-onal lines would be straight as shown; in our measurements, theyare slightly curved.

we make sequential exposures using color separationfilters.

We attach the secondary camera to the light sourceto measure the position of the source using automaticphotogrammetry. Each measurement exposure ismade by our opening the shutter of the primary cam-era, then triggering the secondary camera during theexposure. The secondary camera triggers the flash,so we obtain a calibration image directly correlatedwith the source position, acquired at exactly the sametime as the measurement image. Each calibrationimage includes a field of machine-readable targetswith known 3-D positions relative to the test sampleand the primary camera. These targets are visiblein Fig. 1, below the test sample, and actual-size ex-amples are shown in Fig. 4. By analyzing these im-ages, we can automatically determine the poses of thesecondary camera. Both an a priori error estimateand residuals from the fitting processes involved ~seeSubsection 3.D! confirm that these poses are accurateto within a few millimeters. With the light sourcerigidly attached to the camera, its position is easilyfound for each exposure.

Because we measure the light source position inthis way, the light source can be placed freely; thelight source and secondary camera are placed on atripod and moved manually from one position to thenext over the course of the measurement. We typi-cally use 32 light source positions ranging from 1.3 to2.5 m from the sample.

C. Calibration

To interpret a pixel value as a measurement ofBRDF, the following must be known:

• the responsivity of the pixel sensor to scene ra-diance;

• the irradiance due to the light source at therelevant surface point; and

• the geometric arrangement of the surface nor-mal, the viewing direction, and the illumination di-rection.

We undertook several calibration steps to ensure thateach of these items was well controlled.

Because our primary camera uses a CCD array~Kodak KAF-1300i, serial no. MA-3254, chilled to225 °C!, we expect that the response of each CCDelement is directly proportional to scene radiance.13,14

This was confirmed experimentally for our camera.15

Physical variation between sensors and limitations ofthe lens optics cause a variation in the constant ofproportionality across the image. We measured this

Fig. 4. Examples of photogrammetric targets.

nonuniformity by imaging the exit port of an inte-grating sphere ~Labsphere CSTM-USS-1200!. Thevariation over the entire image plane was of the orderof 10%, but we used only the central portion wherevariation was limited to within 2% of uniform, asshown in Fig. 5.

We modeled our source as a point with uniformangular distribution. To confirm this, we measuredthe angular variation of the source by photographinga white surface illuminated by the flash; this showedthe irradiance to be uniform to within 63% over the65° range of angles we use, as shown by the contourplot in Fig. 6. We reduced the variation from flash toflash, shown in Fig. 7, to less than 1% from the meanby replacing the flash’s battery pack with a regulatedvoltage. We also verified that the flash’s output wasessentially unpolarized.

These steps allow radiance and irradiance to bedetermined in relative units, but we still need to es-tablish a global scale factor to compute the absoluteBRDF. We measured this factor by illuminating a

Fig. 5. Field flatness of camera: normalized pixel response ver-sus radius for image area used.

Fig. 6. Contour plot of relative flash irradiance: contour lines at62.5% mean irradiance of center region.

1 June 2000 y Vol. 39, No. 16 y APPLIED OPTICS 2595

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calibrated diffuse reference sample ~Spectralon SRS-99-010, calibrated by Labsphere in Report 14424-A!in a known geometry and measuring the camera sig-nal through each of the color filters. All BRDF mea-surements were then relative to the known BRDF ofthe calibration sample.

The final prerequisite to BRDF measurement is toknow the incident and exitant directions. To calcu-late these, we must know the positions of the lightsource, test sample, and camera. Any errors in thedirection to the camera or light source will causeerrors in the calculated angles corresponding to eachpixel; also, every 1% error in light source distanceleads to a 2% error in the estimated irradiance. Toestablish the positions of the targets used to measurethe location of the light source ~see Subsection 3.B!,

e used the secondary camera and the photogram-etric technique of self-calibrating bundle adjust-ent.16,17 This determines the targets’ positions to

submillimeter precision, as estimated from residualerrors in the least-squares fit.

We estimate the solid angle of our detector from thef-number of the lens, ranging from f:11 to f:22 inthese measurements, and the distance from detectorto sample, which was 1.3 m. From the nominal28-mm focal length of the lens, we can calculate

Vmin 5 pS0.028

22 D2

1.32

5 3.0 3 1026 sr, (1)

Vmax 5 pS0.028

11 D2

1.32

5 1.2 3 1025 sr. (2)

The effective solid angle of the source is somewhatharder to estimate, both because of the varying dis-tance from the sample and because its output is not

Fig. 7. Repeatability of flash with 30-s cycle time.

596 APPLIED OPTICS y Vol. 39, No. 16 y 1 June 2000

evenly distributed across its face. Measurementsbased on an image of the front of the flash ~Fig. 8!uggest that it has an effective radiating surface of 50m 3 13 mm. From the maximum ~2.6-m! and min-

mum ~1.3-m! distances used in the measurements,e can calculate

Vmin 5 p0.050 3 0.013

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5 3.0 3 1024 sr, (3)

Vmax 5 p0.050 3 0.013

1.32

5 1.2 3 1023 sr. (4)

Our cylindrical samples were aluminum tubing ofnominally 152 mm outside diameter; the sphereswere spun copper, with a diameter of nominally 203mm. The size of each sample was measured in theimage plane, and camera parameters were adjustedfrom the size and position of the image in the primarycamera.

D. Data Processing

The data that result from the measurement of a sin-gle BRDF are

• 32 measurement images from the primary cam-era ~or 96 when three filters are used for RGB!, witha record of the lens aperture and neutral-density fil-ter used for each; and

• 32 light source calibration images from the sec-ondary camera.

The major steps involved in processing these data are

1. Use the targets visible in the calibration im-ages to establish the poses of the secondary camera,and from them compute the light source positions.

2. Find the image of the test sample in one of thephotographs from the primary camera, and use itssize and position to determine the sample’s position.

3. Sample the images to obtain measurementscovering part or all of the surface’s BRDF.

Fig. 8. Radiance across face of flash ~nonlinear mapping!.

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The first step is performed by fully automatic soft-ware, which locates targets in each secondary cameraimage and calculates camera poses. The targets ineach calibration image are used as input to a nonlin-ear fitting procedure that solves for the camera poseby minimizing the image-space discrepancy betweenthe projections of the targets’ known 3-D positionsand their measured locations in the image.

The only human intervention required is in thesecond step, where the user clicks on a number ofpoints along the boundary of the sample in one mea-surement image; these points are used to allow sub-pixel precision in the determination of the positionand size of the sample’s image.

The final step works by ray tracing: For eachpixel in the primary camera image, the correspondingsurface point and normal are determined, then thedirection of illumination is computed. The relativeirradiance is computed from the known source geom-etry; then the relative value of the BRDF is computedby division of the pixel value, which is proportional toradiance, by the irradiance. All that remains is tonormalize this relative value to the measured andknown BRDF value of our reference sample. Thiscomputation can be carried out once per pixel to ob-tain a scattered set of raw samples, which will fall ona set of 2-D surfaces, or sheets, in the 3-D domain ofthe BRDF.

The generation of BRDF values at arbitrary pointsrequires the reconstruction of a full 3-D function.Where such arbitrary evaluation was necessary forthe figures in this paper, we employed a local qua-dratic regression procedure,18 using an elliptical ker-nel to span the distances between the sheets definedby individual images without unnecessarily blurringthe data along the sheets.

4. Verification

To verify the technique, we began with a cylindricalsample, which allowed measurement of BRDF in theincidence plane. This type of measurement pro-vided simpler data for verification and analysis be-fore we moved on to measuring the full BRDF. Italso allowed us to average several scan lines to reducenoise. We also measured flat samples of each mate-rial independently, using a gonioreflectometer thatwas designed and verified for accuracy within 5%.19

We validated the image-based measurements both byverifying reciprocity and by comparing the data fromthe two independent measurement systems. Thenew method gives results comparable in accuracy tothe gonioreflectometer: Consistency is excellent outto 75° incidence ~or exitance! and reasonable out topproximately 85°.We measured a piece of ordinary photocopy paper

Xerox 4200DP, 20 lb.! by wrapping it around a cyl-nder. The resulting measurements fall on a planarlice of the BRDF, yielding a function of two angles:bd~ui, ue!. In Fig. 9, we plot the data as a height field

over the ~ui, ue! plane; each curve contains the datafrom a single image. The dense sampling of ourmethod yields over 4000 points even for this small

subset of the total BRDF. Even for such a diffusesurface, we see noticeable directional variation; thegraph of an ideal Lambertian surface would be a flatplane. Reciprocity demands that the plot be sym-metric left to right, providing an initial check on thedata.

We further check our measurements quantita-tively, both for reciprocity and by comparing againstan instrument of known accuracy. Reciprocity canbe evaluated from Fig. 10, in which the dashed curvesshow the data for three fixed values of ui and the solidcurves show the data for fixed ue. Each pair ofurves represents two independent measurements:he data are measured from different parts of theurface, except in the specular direction. Note thelose correlation for all angles up to 85°. The rmseviation over all data out to 75° is 1.5%, and data outo 85° still satisfy reciprocity to within 6%. The er-or figures reported in this paper are the rms averagef the relative error between the two sets of data,fter linear interpolation to match the sample pat-erns. Figure 11 compares the data from the image-ased measurements with independently measuredata from the gonioreflectometer. The discrepan-

Fig. 9. Incidence-plane BRDF measurements plotted against in-cident and exitant angles.

Fig. 10. Reciprocity comparison for white paper. BRDF mea-surements plotted for three fixed incident and exitant angles.Dashed curves are the fixed incident angles; solid curves are fixedexitant angles.

1 June 2000 y Vol. 39, No. 16 y APPLIED OPTICS 2597

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cies between the two systems are 2.8% ~to 75°! and.7% ~to 85°!.We also measured a flat gray primer; this surface

hows greater deviation from a Lambertian BRDF,enerating a much greater dynamic range. A reci-rocity comparison is shown in Fig. 12; the data arelotted at two scales to show the entire range of mag-itudes. Reciprocity held within 2.5% to 75° andithin 7.8% to 85°.

5. Results

We used the system described above to measure thefull isotropic BRDF of three paints, shown photo-graphed in Fig. 13. These are a gray primer, a blueenamel, and a red metallic automotive lacquer. The

Fig. 11. Gonioreflectometer comparison for white paper. Image-based BRDF measurements ~solid curves! and gonioreflectometermeasurements of the same material ~dashed curves!.

Fig. 12. Reciprocity comparison for gray primer. BRDF mea-surements are plotted for three fixed incident and exitant angles.Dashed curves are fixed incident angles; solid curves are fixedexitant angles.

598 APPLIED OPTICS y Vol. 39, No. 16 y 1 June 2000

red and blue paints were coated with a gloss-reducingfinish. For the two colored paints we used RGB colorseparation filters, and for the primer we made a sin-gle broadband measurement. The data for eachcolor channel of each BRDF comprise some 1.5 mil-lion samples; approximately 6000 of these, corre-

Fig. 14. BRDF sampling pattern for a single incident direction.Each ring is derived from a single digital image.

Fig. 15. Scattering diagram for the gray primer at u 5 45°. Thescale is double that used for the red and blue paints.

Fig. 13. Photographs of actual test samples used.

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sponding to a single exitant angle, are plotted in Fig.14. Each ring of points is extracted from a singlemeasurement image.

Figure 15 shows a 3-D scattering diagram of theprimer for an incident angle of 45°. The surface isclearly non-Lambertian, showing a broad forward-scattering peak. Figure 16 shows similar plots forthe RGB wavelength bands of the two colored paints.

We measured the red paint with the gonioreflecto-meter to validate our results over the entire hemi-sphere. Figure 17 shows the gonioreflectometermeasurements alongside the image-based measure-ments from Fig. 16. These plots indicate that ourtechnique has successfully captured the BRDF. Thedifferences in red and blue channels are accountedfor, we believe, by the different wavelength ranges ofthe two instruments; the CCD camera’s sensitivityextends beyond the gonioreflectometer’s limit of'710 nm, and our system’s signal-to-noise ratio is farsuperior below approximately 450 nm.

6. Conclusions and Future Work

We have described a simple technique that can ex-haustively measure the BRDF of many materials

Fig. 16. Resampled scattering diagrams of the BRDF measure-ments of two paints: a blue enamel ~top row! and a red automo-tive lacquer ~bottom row!. The RGB color measurements arehown from left to right.

Fig. 17. Image-based measurements of the red paint ~top row;dentical to bottom row of Fig. 16! with the corresponding mea-urements from the gonioreflectometer ~bottom row!. The go-

nioreflectometer data were triangulated directly from the samplepoints, whereas the image-based data, which do not come in sets offixed u, were resampled.

with general-purpose equipment. We achieve accu-racy rivaling that of a specialized gonioreflectometerbut with much greater speed and angular resolution.The technique is rapid because the two dimensions ofa camera image sample two angular degrees of free-dom instantaneously, leaving only one to be handledby sequential measurement. Our system can ac-quire 1.5 million monochrome samples covering anentire isotropic BRDF in less time than it takes toprepare a test sample. The resulting data are inter-nally consistent and agree closely with independentmeasurements.

Our technique is limited to measurement of curvedsurfaces with uniform BRDF’s. To measure the fullhemispherical BRDF, we must apply the finish to acompound-curved surface by spraying, dipping,grinding, etc., but we can also measure the incidence-plane reflectance of any material that can be wrappedaround a cylinder.

We have demonstrated measurements of isotropicBRDF’s, but the technique can also be extended tomeasure the BRDF of an anisotropic surface. To dothis, we must rotate the sample to provide a fourthdegree of freedom. Either a spherical sample withuniform anisotropic BRDF and known orientationcan be used or anisotropic samples of flat, flexiblematerials can be measured in the plane of incidencewhen the sample is rotated on the cylinder to achievedifferent values of f.

We also plan to extend our technique to glossiersurfaces. Our detector handles a dynamic range ofthe order of 3.5 orders of magnitude, so we applied alow-gloss finish to the colored paints to simplify thisinitial demonstration of the technique. We can ex-tend our dynamic range by making multiple expo-sures through different neutral-density filters andcombining them as did Debevec and Malik.20 As wemeasure glossier surfaces, we will also have to ac-count for the finite solid angles of source and detector.

This method already uses equipment much lessexpensive than a traditional gonioreflectometer ~theonioreflectometer used for validation cost more thanour times as much as the equipment used for ourmage-based measurements!, but the cost of ouretup could be reduced even further.

• A simpler secondary camera could be used;color is unneeded, and lower resolution would stilllocate the light source with sufficient accuracy. Sev-eral consumer CCD camera models should be adapt-able for this purpose.

• A less expensive primary camera could be used,but the higher noise of such a camera would reducedynamic range. Multiple-exposure techniques couldrecover some dynamic range, but would ultimately belimited by blooming in the CCD and optical flare.

The authors were supported by the National Sci-ence Foundation ~NSF! Science and Technology Cen-ter for Computer Graphics and ScientificVisualization ~ASC-8920219! and by NSF grant ASC-523483. S. R. Marschner was also partly sup-

1 June 2000 y Vol. 39, No. 16 y APPLIED OPTICS 2599

terometer apparatus and process,” U.S. patent 5,241,369 ~31

2

ported by the Hewlett-Packard Corporation, who alsodonated several of the workstations used in this re-search. Measurement equipment was provided byNSF grant CTS-9213183 and by a donation from theImaging Science Division of the Eastman KodakCompany.

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