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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
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Journal of the Applied Mathematics, Statistics and Informatics (JAMSI), 9(2013), No. 2
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
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.
©University of SS. Cyril and Methodius in Trnava
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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
c 2002], [ ˇ
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
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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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
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.,
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. xΘisays
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
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,xΘ)= dΦr(λ,xΘr)
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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,
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:
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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:
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,ΘiΘr)= 1
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/120LAMBERTIAN with power input 2.5W, luminous flux
100-120 lm, radiation angle 120and 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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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 20and 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
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,ΘiΘr)= dddΦr
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.
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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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:
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:
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:
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+(1F0)(1cos θ)5,(12)
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,
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:
(yjf(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
c 2011]. Compared measurements were taken
under the angles θi=θr=60and θi=θr=20in 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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car paint Neysha. Results are in Table I evaluated in the form of the relative root mean
square defined by:
relative RMSE =n
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
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
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:
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 (%)
diffuse surface 2.826 1.427
copper 14.687 0.192
Neysha 4.350 5.132
e 5.695 0.335
Table I. Relative root mean square error of the reflectance along the wavelength.
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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 kth bitmap where xand yare image coordinates and k[0..6],
then for the texture t(x,y)we have
Example of 8-bit texture is depicted in Figure 5. Hence, kth bit determines if there
is a visible sparkle in the kth digital image where the angle of incidence was θi=
=70k10 . Slope from the facet normal to the average surface normal Nis approxi-
mated as θh=35k5, 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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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
where Csis the color of sparkles estimated from the digital images. We set e=24 that de-
termine the shininess of sparkle. Difference αθhis 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.
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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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:
780 380 ,R)= ¯x(λ),t(λ380
780 380 ,G)= ¯y(λ),t(λ380
780 380 ,B)=¯z(λ).
To compute X, Y and Z values of CIE XYZ color model we performed following summa-
tion using GPU:
780 380 ,R)Lr(λ,xΘr),
780 380 ,G)Lr(λ,xΘr),
780 380 ,B)Lr(λ,xΘr),
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:
2.3706 0.9000 0.4706
0.5138 1.4253 0.0885
0.0052 0.0146 1.009
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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Fig. 7. Left column: Neysha. Right column: Cendr´
e. First row: sample photograph. Middle row: rendered planar
sample. Bottom row: renderd car model.
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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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.
We would like to thank to Duˇ
san Chorv´
at from ILC for his help with laboratory measure-
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Authors’ addresses:
Andrej Mih´
Mathematics, Physics and Informatics,
Comenius University,
842 48 Bratislava, Slovak Republic
Roman ˇ
Faculty of Mathematics, Physics and Informatics,
Comenius University,
842 48 Bratislava, Slovak Republic
Received October 2013
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... Method of BRDF measurement and modelling of effect coatings was introduced in (Mihálik andˇDurikovič andˇ andˇDurikovič, 2013). Kim et al. (Kim et al., 2010) proposed a novel image-based method of pearlescent paints spectral BRDF measurement using a dedicated goniometric setup relying on a spherical sample and derived a non-parametric bivariate reflectance model. ...
... The AxF format builds on this compressed representation. Later,Ďurikovič and Mihálik described a similar approach [9]. They used an 8 Bit texture to generate the sparkle effect. ...
Realistic virtual reality applications require highly-detailed geometry as well es convincing surface representations. In many applications, especially in the automotive industry, the realistic rendering of metallic effect paints is necessary. Due to their complex appearance, this is a demanding problem. Previous methods either use a computationally heavy-weight and often hand-tuned simulation approach or a data-driven approach. The former are thus not well-suited for real-time applications. The latter have the advantage of lower computational complexity and virtually no manual hand-tuning, but the disadvantage of requiring large amounts of the graphics card’s memory, making them problematic for larger scenes with numerous materials as required in VR applications. In this paper, we describe an efficient representation for metallic car paints, based on computing the statistical properties of measured real-world samples. Our approach is suited for real-time rendering, poses only moderate requirements on the computing power, uses a low amount of memory and displays high-quality results, as shown in our evaluation section. As an additional advantage, our representation allows the generation of BTFs of arbitrary resolution.
The aim of this article is to propose a model to automatically predict visual judgement of sparkle and graininess of special effect pigments used in industrial coatings. Many applications in the paint and coatings, printing and plastics industry rely on multi-angle color measurements with the aim of properly characterizing the appearance, i.e., the color and texture of the manufactured surfaces. However, when it comes to surfaces containing effect pigments, these methods are in many cases insufficient and it is particularly texture characterization methods that are needed. There are two attributes related to texture that are commonly used: (1) diffuse coarseness or graininess and (2) sparkle or glint impression. In this paper, we analyzed visual perception of both texture attributes using two different psychophysical studies of 38 samples painted with effect coatings including different effect pigments and 31 test persons. Our previous work has shown a good agreement between a study using physical samples with one that uses high-resolution photographs of these sample surfaces. We have also compared the perceived (1) graininess and (2) sparkle with the performance of two commercial instruments that are capable of capturing both attributes. Results have shown a good correlation between the instruments’ readings and the psychophysical studies. Finally, we implemented computational models predicting these texture attributes that have a high correlation with the instrument readings as well as the psychophysical data. By linear scaling of the predicted data using instruments readings, one can use the proposed model for the prediction of graininess and both static and dynamic sparkle values.
Conference Paper
Metallic car paints are visually complex materials that, among others effects, exhibit a view-dependent metallic sparkling, which is particularly difficult to recreate in computer graphics. While capturing real-world metallic paints is possible with specialized devices, creating these materials computationally poses a difficult problem. We present a method that allows for interactive interpolation between measured metallic automotive paints, which can be used to generate new realistic-looking metallic paint materials. By clustering the color information present in the measured bidirectional texture function (BTF) responsible for the metallic sparkling effect, we set up an optimal transport problem between metallic paints' appearances. The design of the problem facilitates efficiently finding a solution, based on which we generate a representation that allows for real-time generation of interpolated realistic materials. Interpolation happens smoothly, no flickering or other visual artifacts can be observed. The developed approach also enables to separately interpolate the larger-scale reflective properties, including the basic color hue, the local color hue, and the sparkling intensity of the metallic paint. Our method can be used intuitively in order to generate automotive paints with a novel appearance and explore the space of possible metallic paints spanned by given real-world measurements. The resulting materials are also well suited for real-time rendering in standard engines.
Full-text available
Paint manufacturers strive to introduce unique visual effects to coatings in order to visually communicate functional properties of products using value-added, customized design. However, these effects often feature complex, angularly dependent, spatially-varying behavior, thus representing a challenge in digital reproduction. In this paper we analyze several approaches to capturing spatially-varying appearances of effect coatings. We compare a baseline approach based on a bidirectional texture function (BTF) with four variants of half-difference parameterization. Through a psychophysical study, we determine minimal sampling along individual dimensions of this parameterization. We conclude that, compared to BTF, bivariate representations better preserve visual fidelity of effect coatings, better characterizing near-specular behavior and significantly the restricting number of images which must be captured.
This paper discusses the method to display the surfaces that exhibit sparkling and depth effects. Sparkling effects are usually caused by the metallic flakes diffused in the paint or coating. The novelty of the approach is to explicitly model the sparkle normal vectors for rendering using an embedded device that allows us perceive depth effects in virtual reality like application. Light redirected by flakes to miscellaneous directions causes random twinkling particle effect. Since, each eye perceives light from different direction, there are two distinct perceived images with random particles for each eye. This effect causes the particles to be perceived within certain depth. We have created an application which allows us to render sparkling effect with arbitrary distributions of sparkles.
In this article, we propose a methodology to measure the light reflectance of the material surface using a simple hardware set-up consisting of generally available mobile phones. The designed method incorporates two mobile phones to facilitate a time-consuming procedure. One device serves us as the light source and second one as the detector aperture. The user will move two phones with two hands above a measured sample, and the method will take into account only the correctly captured images. In this work, we propose a method to estimate the view direction of a phone camera and light source. A subsequent problem we solve is the fast Wi-Fi Direct device communication. We outline the enumeration of the bidirectional reflectance distribution function (BRDF) from the light intensities reflected off the planar samples. We present the satisfactory results measured with mobile phone cameras in a casual environment.
Conference Paper
We present an approximate model for predicting the appearance of car paint from its paint composition. Representing the appearance of car paint is not trivial because of its layered structure which is composed of anisotropic scattering media. The Radiative Transfer Equation (RTE) is commonly used to represent the multiple scattering for the underlying structures. A number of techniques including the Monte Carlo approach, the discrete ordinates, the adding-doubling method, the Eddington approximation, as well as the 2-stream and diffusion approximations have been proposed so far to improve visualization accuracy. Each of these techniques hold advantages over the others when their appropriate conditions are met. The adding-doubling method, in particular, is recognized to be computationally simple and accurate. Jakob et al. [JAM 10] has generalized the RTE for anisotropic scattering structures and proposed to use a micro-flake model based on double-sided specularly reflecting flakes. They also developed an anisotropic diffusion approximation to solve the corresponding RTE. In this paper, considering the translucent micro-flakes we proposed to use a modified version of the model which was developed by Jakob et al. We utilized the adding-doubling method instead of the diffusion-approximation for the new micro-flake model. The proposed approach also provided a good ground for data compression used in the evaluation of RTE. Empirical comparisons have been made to assess the accuracy and computational efficiency of the proposed model. Based on the sample data, we showed that our model provides visually satisfactory results for the appearance of multi-layered car paint.
Full-text available
This paper reports on our attempts to simulate light reflection from surfaces that exhibit sparkling and depth effects that are associated with paint coatings containing metallic flakes. The novelty of the approach is to explicitly model the sparkle geometry for rendering the surface of a graphic object. The light scattering within the system of metal flakes or particles creates the sparkling and glare effects with radial streaks of light around high intensity particles. The 3D geometry of the simulated flakes creates a view-dependent reflectance pattern that makes the surface appear differently in the two images rendered for each eye's view in a stereoscopic display. The results of 3D geometry-based rendering are then compared to the surfaces rendered using 2D random dot patterns that provide no cues to depth variation at the surface. Stereoscopic display of 3D objects with and without the 3D geometry-based surface rendering was used to validate the difference in perceived depth effects associated with the two cases. To confirm the applicability of the technique, we adopted a standard test in common use by paint designers in which the appearance of paints with different sparkle density is observed on silver plates. Our results showed typical variation in sparkling on plates with different statistical distributions of sparkles, which confirmed the robustness of the 3D sparkle modeling system. In a final application test, the technique was used to simulate the appearance of an expensive variety of Japanese lacquerware made using the nashiji technique.
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Abstract Metallic and pearlescent paints contain flakes and exhibit strong texture (spatial fluctuations of luminance) and spar- kles (rare, extremely bright tiny points). We present an al- gorithm for calculating these texture and sparkles during image rendering. Keywords: BRDF, paint texture.
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The directional distribution of radiant flux reflected from roughened surfaces is analyzed on the basis of geometrical optics. The analytical model assumes that the surface consists of small, randomly disposed, mirror-like facets. Specular reflection from these facets plus a diffuse component due to multiple reflections and/or internal scattering are postulated as the basic mechanisms of the reflection process. The effects of shadowing and masking of facets by adjacent facets are included in the analysis. The angular distributions of reflected flux predicted by the analysis are in very good agreement with experiment for both metallic and nonmetallic surfaces. Moreover, the analysis successfully predicts the off-specular maxima in the reflection distribution which are observed experimentally and which emerge as the incidence angle increases. The model thus affords a rational explanation for the off-specular peak phenomenon in terms of mutual masking and shadowing of mirror-like, specularly reflecting surface facets.
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In recent years, it is required to develop a system for 3D capture of archives in museums and galleries. In visualizing of 3D object, it is important to reproduce both color and glossiness accurately. Our final goal is to construct digital archival systems in museum and internet or virtual museum via World Wide Web. To achieve our goal, we have developed gonio-photometric imaging system by using high accurate multi-spectral camera and 3D digitizer. In this paper, gonio-photometric imaging method is introduced for recording 3D object. 5-bands images of the object are taken under 7 different illuminants angles. The 5-band image sequences are then analyzed on the basis of both dichromatic reflection model and Phong model to extract gonio-photometric property of the object. The images of the 3D object under illuminants with arbitrary spectral radiant distribution, illuminating angles, and visual points are rendered by using OpenGL with the 3D shape and gonio-photometric property.
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We present a novel image-based BRDF (Bidirectional Reflectance Distribution Function) measurement system for materials that have isotropic reflectance properties. Our proposed system is fast due to simple set up and automated operations. It also provides a wide angular coverage and noise reduction capability so that it achieves accuracy that is needed for computer graphics applications. We test the uniformity and constancy of the light source and the reciprocity of the measurement system. We perform a photometric calibration of HDR (High Dynamic Range) camera to recover an accurate radiance map from each HDR image. We verify our proposed system by comparing it with a previous image-based BRDF measurement system. We demonstrate the efficiency and accuracy of our proposed system by generating photorealistic images of the measured BRDF data that include glossy blue, green plastics, gold coated metal and gold metallic paints.
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Measurement of the appearance of an object consists of a group of measurements to characterize the color and surface finish of the object. This group of measurements involves the spectral energy distribution of propagated light measured in terms of reflectance and transmittance, and the spatial energy distribution of that light measured in terms of the bidirectional reflectance distribution function (BRDF). In this article we present the virtual gonio-spectrophotometer, a device that measures flux (power) as a function of illumination and observation. Virtual gonio-spectrophotometer measurements allow the determination of the scattering profile of specimens that can be used to verify the physical characteristics of the computer model used to simulate the scattering profile. Among the characteristics that we verify is the energy conservation of the computer model. A virtual gonio-spectrophotometer is utilized to find the correspondence between industrial measurements obtained from gloss meters and the parameters of a computer reflectance model. Keywordsappearance measurements–gloss–BRDF
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This paper presents a new reflectance model for rendering computer synthesized images. The model accounts for the relative brightness of different materials and light sources in the same scene. It describes the directional distribution of the reflected light and a color shift that occurs as the reflectance changes with incidence angle. The paper presents a method for obtaining the spectral energy distribution of the light reflected from an object made of a specific real material and discusses a procedure for accurately reproducing the color associated with the spectral energy distribution. The model is applied to the simulation of a metal and a plastic.
Material models are essential to the production of photo‐realistic images. Measured BRDFs provide accurate representation with complex visual appearance, but have larger storage cost. Analytical BRDFs such as Cook‐Torrance provide a compact representation but fail to represent the effects we observe with measured appearance. Accurately fitting an analytical BRDF to measured data remains a challenging problem. In this paper we introduce the SGD micro‐facet distribution for Cook‐Torrance BRDF. This distribution accurately models the behavior of most materials. As a consequence, we accurately represent all measured BRDFs using a single lobe. Our fitting procedure is stable and robust, and does not require manual tweaking of the parameters.
Conference Paper
The Bidirectional Reflectance Distribution Function (BRDF) describes the appearance of a material by its interaction with light at a surface point. A variety of analytical models have been proposed to represent BRDFs. However, analysis of these models has been scarce due to the lack of high-resolution measured data. In this work we evaluate several well-known analytical models in terms of their ability to fit measured BRDFs. We use an existing high-resolution data set of a hundred isotropic materials and compute the best approximation for each analytical model. Furthermore, we have built a new setup for efficient acquisition of anisotropic BRDFs, which allows us to acquire anisotropic materials at high resolution. We have measured four samples of anisotropic materials (brushed aluminum, velvet, and two satins). Based on the numerical errors, function plots, and rendered images we provide insights into the performance of the various models. We conclude that for most isotropic materials physically-based analytic reflectance models can represent their appearance quite well. We illustrate the important difference between the two common ways of defining the specular lobe: around the mirror direction and with respect to the half-vector. Our evaluation shows that the latter gives a more accurate shape for the reflection lobe. Our analysis of anisotropic materials indicates current parametric reflectance models cannot represent their appearances faithfully in many cases. We show that using a sampled microfacet distribution computed from measurements improves the fit and qualitatively reproduces the measurements. 1.
State-of-the-art car paint shows not only interesting and subtle angular dependency but also significant spatial variation. Especially in sunlight these variations remain visible even for distances up to a few meters and give the coating a strong impression of depth which cannot be reproduced by a single BRDF model and the kind of procedural noise textures typically used. Instead of explicitly modeling the responsible effect particles we propose to use image-based reflectance measurements of real paint samples and represent their spatial varying part by Bidirectional Texture Functions (BTF). We use classical BRDF models like Cook-Torrance to represent the reflec-tion behavior of the base paint and the highly specular finish and demonstrate how the parameters of these models can be derived from the BTF measurements. For rendering, the image-based spatially varying part is compressed and efficiently synthesized. This paper introduces the first hybrid analytical and image-based representation for car paint and enables the photo-realistic rendering of all significant effects of highly complex coatings.