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Journal of the Applied Mathematics, Statistics and Informatics (JAMSI), 9(2013), No. 2

METALLIC PAINT APPEARANCE

MEASUREMENT AND RENDERING

ROMAN ˇ

DURIKOVIˇ

C AND ANDREJ MIH´

ALIK

Abstract

Humans recognize objects visually on the basis of material composition as well as shape. To acquire a certain

level of photorealism, it is necessary to analyze, how the materials scatter the incident light. The key quantity

for expressing the directional optical effect of materials on the incident radiance is the bidirectional reﬂectance

distribution function (BRDF). Our work is devoted to the BRDF measurements, in order to render the synthetic

images, mostly of the metallic paints. We measured the spectral reﬂectance off multiple paint samples then used

the measured data to ﬁt the analytical BRDF model, in order to acquire its parameters. In this paper we describe

the methodology of the image synthesis from measured data. Materials such as the metallic paints exhibit a

sparkling effect caused by the metallic particles scattered within the paint volume. Our analysis of sparkling

effect is based on the processing of the multiple photographs. Results of analysis and the measurements were

incorporated into the rendering process of car paint.

Mathematics Subject Classiﬁcation 2000: 65C20, 78M22, 93A30

Additional Key Words and Phrases: BRDF, texture, rendering, metallic paint, measurements

1. INTRODUCTION

The appearance of all objects is determined by the how object surface scatters incident

light [Tonsho et al. 2001]. To measure the surface properties, a gonio-spectrophotometer

device [Achutha 2006] that measures the spectral distribution of reﬂected radiant power

as a function of the illumination and observation angles, is used. The device consists of a

light source aperture and a receptor aperture. Mechanical elements have four degrees of

freedom to measure the complete reﬂectance function by moving the receptor aperture and

the light source. The disadvantages of the device are their time inefﬁciency and inaccuracy

related to their mechanism.

To decrease the degrees of freedom, the spherical sample rather then a planar one can be

used [Kim et al. 2008]. This allows to keep the camera (receptor aperture) in ﬁxed position.

Furthermore, the system without any mechanical element was constructed [Rump et al.

2008]. This system consists of multiple cameras mounted on a hemispherical gantry and

each camera is equipped with a ﬂash unit.

10.2478/jamsi-2013-0010

©University of SS. Cyril and Methodius in Trnava

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ALIK

A large database of tabular BRDF of spherical samples is available online [Matusik et al.

2003]. Unfortunately, it is hard to ﬁt the data in to the rendering pipeline and it is difﬁcult

to use it with importance sampling methods [Bagher et al. 2012]. Hence, the analytical

representation of BRDF is more common then tabular representation.

There are variety of analytical models, that describe the light reﬂection off the surface

[Ashikhmin and Shirley 2000]. An example is the empirical Wards’s model [Ward 1992],

that uses the combination of functions capturing the reﬂection attributes such as the diffuse

reﬂectance in all directions or the concentration of light scattering in a direction near the

specular direction for glossy materials. Besides empirical models there are the models,

that apply the basic principles of physics to the surface microscopic structure, such as the

Cook-Torrance’s model [Cook and Torrance 1982].

To make the products visually more appealing, producers, especially in the automotive in-

dustry, tend to utilize the glittering effects of metallic paints. Metallic paint coatings, that

exhibit sparkling and depth effects, contain metallic ﬂakes [ ˇ

Durikoviˇ

c 2002], [ ˇ

Durikoviˇ

c

and Martens 2003]. The ﬂake faces act as tiny mirrors. The ray reﬂected by a ﬂake can

reach observer either directly, or after scattering. Each reﬂection then substantially atten-

uates the light energy. Flakes seen directly are the brightest spots, that look like sparkles

[Sergey Ershov 1999].

Metallic paints have different micro and macro appearance. Macro appearance, when the

paint is being observed from far distance, can be described by the BRDF, on the other hand

the micro appearance can be represented by the irregular random texture that looks like

bright sparkles dusted on the paint. Commonly, the statistical characteristics such as ﬂuc-

tuations due to scattering by ﬂakes are estimated and then the paint texture is reproduced

by superimposing random ﬂuctuations on the image [Sergey Ershov 1999]. That method,

however, does not focus on rendering of sparkles itself and the approach is limited to static

scenes with pre-computed procedural texture.

Another approach [ ˇ

Durikoviˇ

c and Martens 2003] uses the explicit modeling of sparkles by

the given geometrical shape and distribution along the model surface. This will allow to

render the dynamic scenes with camera zoom in, zoom out, and stereo observation of the

scene with sparkling effect. The draw back is that the proposed method is not a real time

rendering approach but it can be implemented easily.

We propose the design and methodology devoted to the measurement of spectral reﬂectance

from material samples in order to render photo-realistic images. We propose a simple de-

vice, that allows us to measure spectral reﬂectance under arbitrary angle in the plane of

incidence. We ﬁt the unknown parameters of the analytical BRDF model to the measured

spectral data. We performed ﬁtting by the nonlinear least square optimization [Bjorck

1996]. To validate the ﬁtting results we utilized our virtual gonio-spectrophotometer. In

order to render sparkles, we captured the texture of a car paint sample.

The remaining of this paper is organized as follows. First we deﬁne the basic terminol-

ogy of reﬂectance function, Section 1.1. Following Section 2 describes how to convert the

measured reﬂectance into a BRDF. In Section 3 we introduce the set up of our measure-

ment device. In the Section 4 we introduce the process of BRDF measurement. Section 5

describes an acquisition of analytical BRDF model from the measured data. In the Section

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METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

Fig. 1. Bidirectional reﬂectance function. Flux of the light entered unit sphere through dωiand reﬂected from the

area dA through solid angle dωr.

6 we describe modeling of sparkling and glittering effects. Section 7 introduces the ren-

dering process utilizing graphics processing unit (GPU) and in Section 8 we conclude our

work.

1.1 Reﬂectance Function

A mathematical representation of surface reﬂection behavior can be achieved by consid-

ering a number of variables such as wavelength, angle of incidence, observation position

etc. A common approach is to use a simpliﬁed model by considering the directional and

spectral properties of reﬂection. Bidirectional reﬂectance distribution function (BRDF) is

deﬁned by the ratio of outgoing radiance and incident irradiance [Rushmeier 2001], i.e.,

fr(λ,x,Θi→Θr)=Lr

Ei

=Lr(λ,x→Θr)

Li(λ,x←Θi)cosθidωi

,(1)

where λis wavelength of the light. Index iindicates incident light, whereas the index r

indicates reﬂected light (see Figure 1). Θ=(θ,ϕ)denotes the light direction, whereas θ

and ϕare spherical coordinates and θis angle between the surface normal and particular

light direction. Arrow notation indicates the direction of light transport i.e. x←Θisays

the light traveling from the incident direction Θihits the surface point x.

Solid angle is deﬁned by the projected area of a surface patch onto a unit sphere of a point,

meaning that a solid angle is subtended by a point, S0, and a surface patch, dA:

dω=dAcos θ

r2,(2)

where dAcos θis the foreshortened area of dA on the direction of S0. The distance between

S0and dA is r, and the angle between surface normal nand the point direction is θ.

Radiance. Frequently, we use outgoing radiance to measure the lighting sources, but use

irradiance to measure the lighting intensity received by a patch. By deﬁnition, the radiance

of an area lighting source is

Lr(λ,x→Θ)= dΦr(λ,x→Θr)

cosθrdArdωrdλ,(3)

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R. ˇ

DURIKOVIˇ

C, A. MIH´

ALIK

Fig. 2. Reﬂected parallel light from the surface to the receptor aperture through the solid angle. Θ0is the direction

of surface normal, whereas Θris arbitrary direction.

where Φris the radiant power (ﬂux), dAr=dA is the fragment of lighting surface area

around the location point x,Θr=(θr,ϕr)is used to represent the lighting direction, and

dωris solid angle fragment.

Irradiance. On the other hand, we use irradiance to represent the lighting received by a

surface patch dAi. By deﬁnition,

Ei=dΦi(λ,x←Θi)

dAi

.(4)

2. CONVERSION OF REFLECTANCE TO BRDF

Reﬂectance is basically the ratio of energy reﬂected off the surface to the incident energy.

We are able to measure the reﬂectance using measuring devices. However, a BRDF differs

from the reﬂectance because; the BRDF is not really a function itself, but a distribution

or generalized function. Like a probability density, a BRDF can contain distributions that

make sense only inside integrals, but correspond to straightforward computational opera-

tions. In this section we propose a methodology to covert the reﬂectance measurements

from a device to a values of BRDF.

PROPOSITION 1. To acquire the BRDF of diffuse surface we can measure reﬂectance

using directional light source, see Figure 2. Then the estimation of BRDF could be done

by the following formula:

fr(x,Θi→Θr)≈1

cosθrΔωr

ΔΦr

ΔΦi

,(5)

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METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

Fig. 3. Device setup for the reﬂectance measurements of material samples.

where Δωris the projected area of receptor aperture to the unit sphere. Angle between

surface normal and direction to the receptor is θr. Total ﬂux reﬂected from the spot at the

surface of area ΔAis denoted as ΔΦr, whereas total ﬂux of incident light at that spot is

denoted as ΔΦi.

PROOF. We can prove above statement for the diffuse surfaces by the following consid-

eration. Substitute the deﬁnitions from Eqn. 3, 4 into a BRDF deﬁnition Eqn. 1:

fr(x,Θi→Θr)=Lr

Ei

=

dΦr(x→Θr)

cosθrdArdωr

dΦi(x←Θi)

dAi

=dΦr

dΦi

dAi

cosθrdωrdAr

.

Lighting is received by a surface patch dAi=ΔAon the other hand the surface patch dAr=

ΔAis illuminating the receptor in solid angle dωr. Assume that solid angle subtended by

the receptor is dωr=Δωrthe last term simpliﬁes to

fr(x,Θi→Θr)= 1

cosθrΔωr

ΔΦr

ΔΦi

.(6)

3. DEVICE SETUP

Spectral reﬂectance measurement device with two degrees of freedom, Fig. 3, consists of

the ﬁxed light source and receptor moving around the sample. Light source is the LED

STAR 2,5 WHITE 120LM/120◦LAMBERTIAN with power input 2.5W, luminous ﬂux

100-120 lm, radiation angle 120◦and color temperature 6500-8000K. The receptor is con-

nected by the optical cable to the spectrometer Solar S100 (grating 300l/mm, TCD linear

image sensor, spectral range 190-1100nm, spectral resolution 1nm, dynamic range 900:1).

The distance between the source and the sample is 90cm. The sample itself can be rotated

in arbitrary angles. Receptor with mounted lens is located on the arm within the 40cm

distance from the sample.

The device calibration is done before the actual BRDF measurements. First, we capture

the background noise with spectrometer. Second, we subtract the background noise from

all measurements. Similarly since, the exposure curve of spectrometer is linear, we also

divide the resulting current value by the exposure time. The light source spectral power

density, ΔΦiin Eqn. 5, is captured by the spectrometer using a perfect mirror.

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4. BRDF MEASUREMENTS

In this section we describe how to measure the BRDF of diffuse and specular surfaces. The

diffuse BRDF is estimated from the ratio of reﬂected ﬂux ΔΦrand the light source spectral

power density ΔΦi. The BRDF of specular surface is estimated from the ratio of reﬂected

ﬂux from sample, dΦr, and the ﬂux reﬂected from the white diffuse standart, ΔΦrs.

4.1 Diﬀuse surfaces

In order to measure the diffuse surface we set the exposure time to 2999ms. Diffuse sample

surface is illuminated under the angle of incidence 20◦and the receptor aperture measures

the reﬂected ﬂux, ΔΦr, in normal direction, i.e. 0◦. Finally, the BRDF is evaluated for

every given wavelength by substituting light source spectral power density, ΔΦi, to Eqn. 5.

The solid angle from Eqn. 5 can be approximated as

Δωr≈πw2

4d2,(7)

where d=40cm is distance from the sample to the receptor aperture and w=0.4cm is the

diameter of aperture. We measured the spectral distribution from the diffuse surface in the

band from 380nm to 780nm with the interval step 5nm.

4.2 Metallic surfaces

The BRDF measurement of metallic surface is more complicated. However, if we know

the BRDF values of a sample surface, we can derive the BRDF values of metallic sample

using the measured reﬂectance of both samples. We choose the reference sample a white

diffuse surface standard and measure the sample BRDF, frs. Finally, we derive the BRDF,

fr, of the metallic sample using the following ratio [Ward 1992]:

fr(x,Θi→Θr)= dddΦr

dAcosθrdωr

dEi(x←Θi)=dΦr

dΦrs

dddΦrs

dAcosθrdωr

dEi(x←Θi)=dΦr

dΦrs

frs(x,Θi→Θr),(8)

where the BRDF of the standard is frs,Φrsis reﬂected ﬂux off the standard and Φris ﬂux

reﬂected of measured metallic sample under the same directions.

We have measured two car paint samples, copper surface and the white diffuse stan-

dard. The reﬂectance was measured under the angles of incidence θi∈{20◦,60◦}. The

receptor was positioned to obtain reﬂected ﬂux off the surface under the angles θr∈

{10◦,20◦,30◦,40◦,50◦,60◦,70◦}to the surface normal in the plane of incidence. The

exposure time for the mirror reﬂection is set to 102ms to decrees the highlight and for

off-specular reﬂection to 2999ms. Total reﬂected ﬂux is calculated for all wavelengths in

the visible band 380nm to 780nm sampled by 5nm using Eqn. 8.

5. FITTING MODEL PARAMETERS

To achieve realistic appearance of material surfaces in real-time rendering the analytical

models are commonly used. In particular the Cook-Torrance model is a physically-based

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METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

microfacet model that is focused on (glossy) specular reﬂection. It uses the surface rough-

ness model developed by Torrance & Sparrow in [Torrance and Sparrow 1967]. This model

treats surface as a collection of microscopic facets. The macroscopic optical properties of

a surface are then analytically derived from properties of individual facets and statistical

distributions of such properties.

5.1 Analytical BRDF Model

Although, the surface has a normal N, at a microscopic level the surface has height varia-

tions that result in many different surface orientations at a detailed level. At the perfectly

ﬂat surface a viewer is able to see light source reﬂection, if angular bisector Hof light and

viewing direction is in the direction of surface normal N. However, due to different surface

orientations at a detailed level, light source may be partially seen at surface positions where

His not at direction of the surface normal. At this particular positions, however, Hhas the

same direction as a microfacet normal.

A statistical model of the variation in surface height generally takes the form of giving the

distribution of facets that have a particular slope. Most commonly used is the Beckmann

distribution function based on physical theory on scattering of electromagnetic waves:

D=e−tan2α

m2

m2cos4α,(9)

where αis the angle between surface and facet normal and mis the root mean square slope

of microfacets parameterizing the surface’s roughness.

If we assume V-grooved surface, then we need to take into account with self shadowing

and masking. The geometric attenuation factor Gmodels the geometric effects shadowing

and masking between microfacets that occur at larger angles of incidence or reﬂection. It

is deﬁned by the formula:

G=min(1,2(H·N)(V·N)

H·V,2(H·N)(L·N)

H·V),(10)

where Land Vare the unit vectors in the direction to the light source Θiand in the direction

of observation Θr, respectively.

The Cook-Torrance model provides a good reproduction of the appearance of many real

materials. Especially metallic surfaces proﬁt from the increased realism of the specular

factor. Effects like the characteristic color shift towards the color of the incident light

near grazing angles and the off-specular peak for very rough surfaces greatly improve the

perceived realism of renderings. The off-specular peaks are the consequence of shadowing

and masking causing asymmetries.

BRDF of the Cook-Torrance can be compactly written as:

fr(x,Θi→Θr)=kd

π+ks

Fr(θh)DG

π(cosθi)(cosθr),(11)

where θhis angle between Land H,θiis angle between Land Nand θris angle between

Vand N.Fris the reﬂection coefﬁcient which gives the fraction of incident light that

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is reﬂected from the surface and stems from the Fresnel equations. To model Fresnel

reﬂectance we use Schlick approximation:

Fr(θ)=F0+(1−F0)(1−cos θ)5,(12)

where

F0=1−n1

n2

1+n1

n22

is reﬂectance of incident light from the direction parallel to the surface normal. n1nad

n2are indices of refraction of the volume above the surface and the material beneath,

respectively.

5.2 Analytical BRDF Model

To obtain analytical model based on measured data we have to perform ﬁtting algorithm.

Fitting analytical reﬂectance models is usually done in two steps [Ngan et al. 2005]. First

compute diffuse and specular RGB coefﬁcients using a linear least square optimization,

then compute the model parameters through second optimization.

In our approach we computed the reﬂectance model parameters separately for each wave-

length. This allows us to incorporate wavelength effects. As the ﬁtting algorithm we used

Levenberg-Marquardt optimization algorithm implemented in the open source numerical

analysis and data processing library ALGLIB [Bochkanov and Bystritsky 2013].

The least squares curve ﬁtting problem is to ﬁnd the parameters pminimizing the sum of

squares errors:

min

p

n

∑

j=1

(yj−f(xj,p))2,. (13)

where yjare the estimated BRDF values. We approximate the measured BRDF by the

Cook-Torrance’s analytical model (see Equation 11). In order to acquire its parameters

p=(kd,ks,m,F0)for the particular wavelength we utilized Cook-Torrance’s function fras

the function representing analytical model with unknown parameters. After total number

of measurements n(2 ×7, we have 2 angles of incidence and 7 receptor positions), we

assigned resulting measured BRDF to the dependent variable yj. Independent variables

represent angles of measurements xj=(θij,θrj). We performed the ﬁtting for each wave-

length in the band from 380nm to 750nm with interval step 5nm separately. Hence, as a

result of optimization, we got wavelength dependent parameters kd(λ),ks(λ),m(λ)and

F0(λ)of Cook-Torrance BRDF for particular wavelength.

5.3 Validation

We compared the measured reﬂectance with the reﬂectance computed by the virtual gonio-

spectrophotometer [Mih´

alik and ˇ

Durikoviˇ

c 2011]. Compared measurements were taken

under the angles θi=θr=60◦and θi=θr=20◦in the plane of incidence. These angles are

prescribed in standardized gloss measurements [ISO2813 1994]. We have measured white

diffuse surface sample, copper surface, gray metallic car paint Cendr´

e and blue metallic

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METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

car paint Neysha. Results are in Table I evaluated in the form of the relative root mean

square deﬁned by:

relative RMSE =n

∑

λ

1002

ˆ

Φ(λ)2(ˆ

Φ(λ)−Φ(λ))2%,(14)

where ˆ

Φ(λ)is the reﬂected ﬂux measured on real sample and Φ(λ)is the ﬂux computed

by the virtual gonio-spectrophotometer using acquired reﬂectance model at the particular

wavelength. The sum is computed over the band from 380nm to 750nm with interval step

5nm.

6. SPARKLE MEASUREMENTS

As mentioned earlier there are basically two approaches to simulate ﬂakes in the paint:

procedural texture based on the ﬂakes distribution and explicitly modeled geometry of the

ﬂakes. Second approach is more strait forward, but ineffective if we consider real-time

animation. Approaches more suitable for real-time rendering involve the sparkle textures

created using the distribution of ﬂakes within the paint.

To capture the sparkling effect we take multiple photographs of reﬂected light from metal-

lic samples. Since, the reﬂectance of metallic ﬂakes is specular, sparkling effect is highly

dependent on the angle of observation and the direction of incident light. Our measure-

ment takes into account the light source position changed in the plane perpendicular to the

sample surface and camera positioned in the same plane. Camera view direction is in the

direction of surface normal (see Figure 4). Angles of incidence were θi∈{10◦,20

◦,30

◦,

40◦,50

◦,60

◦,70

◦}.

Specular surface reﬂects most intensity when the surface normal is in the same direction

as vector H. Vector His the halfway vector between the vectors Land V. All vectors are

in the same plane and the angle between Land His same as the angle between Vand H.

This motivated us to deﬁne the angle:

θh=θi

2.(15)

Consider facet that reﬂects the light under the angle of incidence θispecularly in the di-

rection of N. Hence the angle between surface normal of this facet and average normal of

sample surface Nis θh.

Every sample image illuminated under the angles of incidence θi, was cropped to the rect-

angular area 233 ×233. We have applied segmentation techniques to ﬁnd the pixels with

surface sample relative RMSE (%)

20◦→20◦60◦→60◦

diffuse surface 2.826 1.427

copper 14.687 0.192

Neysha 4.350 5.132

Cendr´

e 5.695 0.335

Table I. Relative root mean square error of the reﬂectance along the wavelength.

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DURIKOVIˇ

C, A. MIH´

ALIK

Fig. 4. Photographing of metallic car paint under the multiple angles of incidence.

highest intensities and store them in a bit map, the most intense pixels have assigned value

1. Next we pack all bitmats into a single image texture with 8 bits per pixel.

If we denote bk(x,y)as k−th bitmap where xand yare image coordinates and k∈[0..6],

then for the texture t(x,y)we have

t(x,y)=

6

∑

k=0

bk(x,y)2k.(16)

Example of 8-bit texture is depicted in Figure 5. Hence, k−th bit determines if there

is a visible sparkle in the k−th digital image where the angle of incidence was θi=

=70◦−k10 ◦. Slope from the facet normal to the average surface normal Nis approxi-

mated as θh=35◦−k5◦, according to Eqn. 15. If the facet surface acts as a mirror, the

sparkle will be visible when cos θh=N·H.

6.1 Sparkle Rendering

How do we use the above sparkle texture to check if the sparkle is shinning? First, we

calculate angle between Nand Hby α=arccos(N·H). Knowing the angle α, we can ﬁnd

out if there is a visible sparkle at the particular position. We check the texture for particular

bit of 8-bit pixel corresponding to angle θh=αif it is set to 1 at given coordinates (x,y).

The problem is, that during the rendering process, αdoes not have to reach same value as

θh. We have to include also angles of incidence in between measured ones and attenuate

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METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

Fig. 5. 8-bit sparkle texture. The level of gray determines θhof the sparkle. Smaller values of angle θh, the image

pixel is darker. White color means that there is no sparkle.

the sparkle according the slight change in angles. This idea leads to the following equation

Ir=Cs(cos(α−θh))e,(17)

where Csis the color of sparkles estimated from the digital images. We set e=24 that de-

termine the shininess of sparkle. Difference α−θhis the approximation of angle between

the facet normal and H.

The problem with this method is that the small sparkle texture is repeatedly used to over

the object surface and a repeated sparkle pattern can we visible on the surface.

7. IMPLEMENTATION AND RESULTS

We measured the spectral reﬂectance of samples, however common displays support RGB

color format. Therefore, it is required to convert spectral reﬂectance to RGB color space.

Our rendering process consisted of three parts. First, the intensity for each wavelength was

computed. Since we found the parameters of Cook-Torrance’s model, we could compute

intensities for each wavelength using this model. Second, we transformed the spectral

distribution to CIE XYZ color space and then to RGB color space. Finally, we added the

sparkle intensity Irto the resulting color according to the sparkle texture.

7.1 Implementation of GPU

Since we are dealt with GPU, we used the 1D ﬂoating point texture as a storage of spectral

distributions. For each wavelength we stored the particular parameters to the texture as an

array. Particularly parameters kd(λ),ks(λ),m(λ)and F0(λ)of Cook-Torrance’s model that

were acquired by the ﬁtting process. For the purpose of the conversion to XYZ color space

we had to store also CIE color-matching functions ¯x(λ),¯y(λ)and ¯z(λ)(see Figure 6). If

we denote the texture as t(s,c), where s∈[0,1]and c∈{R,G,B}is the channel, then we

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R. ˇ

DURIKOVIˇ

C, A. MIH´

ALIK

Fig. 6. Mapping the spectral power distribution to the texture as an array.

can map the CIE color-matching functions to the 1D texture as follows:

t(λ−380

780 −380 ,R)= ¯x(λ),t(λ−380

780 −380 ,G)= ¯y(λ),t(λ−380

780 −380 ,B)=¯z(λ).

To compute X, Y and Z values of CIE XYZ color model we performed following summa-

tion using GPU:

X=

780

∑

λ=380

t(λ−380

780 −380 ,R)Lr(λ,x→Θr),

Y=

780

∑

λ=380

t(λ−380

780 −380 ,G)Lr(λ,x→Θr),

Z=

780

∑

λ=380

t(λ−380

780 −380 ,B)Lr(λ,x→Θr),

where Lris computed radiance given by standart rendering equation using the BRDF, fr

from Eqn. 11 with the estimated and stored parameters of Cook-Torrance model for partic-

ular wavelength. To obtain RGB values, vector (X, Y, Z) is needed to multiply by the XYZ

to RGB transformation matrix:

⎡

⎣

R

G

B⎤

⎦=⎡

⎣

2.3706 −0.9000 −0.4706

−0.5138 1.4253 0.0885

0.0052 −0.0146 1.009 ⎤

⎦⎡

⎣

X

Y

Z⎤

⎦.(18)

We measured and then rendered two metallic car paints sample. The sample called Neysha

had blue basecoat with small metallic grains. The sample called Cendr´

e contained gray

pigments. The rendered results of these metallic pains are shown in Figure 7.

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37

METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

Fig. 7. Left column: Neysha. Right column: Cendr´

e. First row: sample photograph. Middle row: rendered planar

sample. Bottom row: renderd car model.

8. CONCLUSION

We set up measuring device to BRDF acquisition of real materials. The device consists

of common laboratory equipments. We have experimentally studied simple materials and

compared the obtained results to simulations based on the analytical BRDF. We simulated

the rendering results to validate acquired reﬂectance model obtained by ﬁtting process from

measurements of real samples. The sample surface is represneted by Cook-Torrance model

for particular wavelength with estimated parameters. We found out that it is possible to get

plausible results despite the sparse angular resolution of measurement using suitable model

and ﬁtting method.

To achieve effects such as sparkling of metallic paints we made multiple photographs of

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R. ˇ

DURIKOVIˇ

C, A. MIH´

ALIK

the surface under the variety of light incidence. We created the sparkle texture where direc-

tional light effects were incorporated. Finally, we rendered surface color using GPU. This

process consisted of spectrum transformation to RGB color and adding sparkle intensity

according to the sparkle texture.

9. ACKNOWLEDGMENT

We would like to thank to Duˇ

san Chorv´

at from ILC for his help with laboratory measure-

ments.

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METALLIC PAINT APPEARANCE MEASUREMENT AND RENDERING

Authors’ addresses:

Andrej Mih´

alik

Mathematics, Physics and Informatics,

Comenius University,

842 48 Bratislava, Slovak Republic

http://www.fmph.uniba.sk

email: mihalik@sccg.sk

Roman ˇ

Durikoviˇ

c

Faculty of Mathematics, Physics and Informatics,

Comenius University,

842 48 Bratislava, Slovak Republic

http://www.fmph.uniba.sk

email: roman.durikovic@fmph.uniba.sk

Received October 2013

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