9Bull. Soc. Photogr. Imag. Japan. (2018) Vol. 28 No. 2: 9–17

Original Papers

Ease-to-use approach of BRDF recovery from 360°Light Probe
Ryota Domon(1), Shoji Yamamoto(2), Hiroshi Kintou(3), Norimichi Tsumura(1)Abstract:

 e present an easy-to-use measurement of BRDF for material appearance of three-dimensional object based on the estimation of surface
Wreflectance properties with 360-degree light probe. Conventional methods of BRDF measurement such as gonio-reflectometry have someproblems relating to the size, cost, and difficulty of operation. Appearance from Motion Method proposed by Dong et al. is appropriate toconquer above problems. Their method attempted to estimate the surface reflectance under unknown incident light component. However, ause of multiple unknown parameters causes the loss of convergence, and sometimes sacrifices the accuracy and computational cost. Therefore,
we improved their algorithm of Appearance from Motion method by using an omni-directional camera as a light probe. We demonstratevaluable results: Higher reproducibility and lower cost of computation than those of the conventional method.

Key words:

BRDF, Measurement, 360-degree light probe, Reproduction

1. Introduction
The important information of surface reflectance is useful for thefield of computer graphics. This information is defined as bi-directional reflectance distribution function (BRDF) to calculate an appearance of object. Especially, since Spatially-Varying BRDF(SVBRDF) has information of spatially variation of the objects,
therefore, SVBRDF is used for the rendering of virtual object withmultiple textures. Various profile of this BRDF changes the material appearance based on dichromatic reflection model. Specular reflection represents the surface smoothness by its degree of reflection.
Conventionally, the use of BRDF information was limited in thefield of computer science. Recent revolution of three-dimensional(3D) reproduction gives us the useful chance of BRDF informationin commercial production. Actually, there are many applications ofinternet shopping, reproducing in digital mock-up, arts, and regenerative medicine. The most expected contribution of BRDF information is application for rapid proto-typing that is compatible to
final product with same property of surface roughness. Therefore, themethod of BRDF measurement attracts attention as the essential
tool for advancement of 3D reproduction.
Various measurement methods have been proposed for the accurate BRDF of real object. However, the currently used method or
instruments such as gonio-reflectometer has large scale, needs highcalculation cost and difficult to acquire BRDF information. Moreover, it is difficult for non-expert user to measure the appearance ofthe object. For this reasons, the measurement system, which is commercially available, rapid and compact, is required for handling theappearance.
In this paper, therefore, we propose a rapid and compact measureReceived 25th April, 2018; Accepted 6th October, 2018(1)

ment system that is expected to be equipped with 3D reproduction
system. Our method refers to Appearance from Motion method
proposed by Dong et al.1), whereas we make a goal to ascend theindustrial value by adding an extra procedure which is the use ofenvironment map captured by omni-directional camera instead ofthe estimation of an incident lighting component. This improvement provides the accuracy and simplification compared with theconventional method.

2. Related Work
Appearance reproduction is well-studied with BRDF, which is
physical model for representing photon propagation. There are manykinds of appearance measurement method or instruments as previous works 2)-5). In general, the recovery of object appearance needs
three information, such as geometry (normal vector), surface reflectance (BRDF), and incident lighting component 6). When the shapeof object is assumed as a flat plate to fix the geometrical parameter,
the gonio-reflectometer can be useful to acquiring the BRDF parameters for reproduction of various appearances. Unfortunately,
accurate BRDF measurement needs 6 DOF movement and precious position arrangement. Therefore, a tangled repeat setting andlong measurement time are required. In order to decrease the timeand effort, multiple lighting or wide view camera system was proposed to detect much reflectance information at one shot 7)-14). Although these ideas can reduce the measurement cost dramatically,
the flexibility of the BRDF measurement was lost by reason of fixedand limited measurement equipment.
A breakthrough idea for this complicated BRDF measurement
was proposed by Dong et al. in ACM SIGGRAPH Asia 2014 1).

Graduate School of Advanced Integration Science, Chiba University, CHIBA, JAPANTokyo Metropolitan College of Industrial Technology, TOKYO, JAPAN(3)Nikon Corporation, TOKYO, JAPAN
(2)

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Bull. Soc. Photogr. Imag. Japan. Vol. 28 No. 2 (2018)

Their method can reconstruct the BRDF information at spatiallyvarying isotropic surface (SVBRDF) by solving ill-posed problem
between the reflectance and illumination without the knowledge ofincident light. Only capturing the video while rotating the objects,
non-expert users are also accessible and easy to control, because acquisition scheme of this method is greatly simplified. In this method, they estimated three unknown variables; distribution of specular
highlights, diffuse albedo, and lighting component, under the condition that the shape of object is known. Moreover, their group expanded their method to estimate the shape information with theestimation of reflectance and illumination by using the temporal
trace processing from the measured data 15).
Although it is arguable for the estimation of all information since
the measurement technology for 3D shape is remarkably developed 16),
their state-of-the-art method is undeniably useful for the reconstruction of object appearance. This method proposed by Dong et al.
was based on the attempt to set various restrictions to solve thiscomplex problem and demonstrated feasible result of acquiring thesurface reflectance. However, the estimation of several variables suchas albedo, specular, and illumination in their method causes less convergence and more computational cost. Moreover, lighting component calculated by their method indicated uncertain artifacts in the
result of their estimation. For example, the edge of estimated lighting components are affected by target object or immoderately saturated in Fig. 17 of SIGGRAPH paper, since their method converges
their calculation when the edge of illumination was sharpened.
Here, it is noticed that the estimation of lighting component will
have an insignificant importance because incident lighting is easy tomeasure by using omni-directional cameras that become compact
and low price. Therefore, we improve and simplify the Dong's method for the guarantee of convergence and rapid estimation underknown lighting condition, which is derived environmental image
captured by omni-directional cameras.

3. Method
3.1 Acquisition and Calibration
Our proposed method requires the measured images of object
that is rotating on the table, environmental image to provide an incident lights on the target object, and geometry data of target object.

TargetWe captured images of object on the rotating table by digital camera(D5100, Nikon) equipped with varifocal lens (AF-S NIKKOR 24120mm, Nikon) as shown in Fig.1. Intrinsic camera parameters wereprecomputed by using the method of Zhang et al. 17) and the captured image was saved every one degree of rotating angle as a radiometrically linear RAW image with single exposure. Environmental
image as the 360-degree light probe was also captured by omni-directional camera (Theta, Ricoh). In order to use this image captured
with omni-directional camera as the incident light component, it isnecessary to consider the radiometrically linearity and color matching with digital camera. To solve this problem, we reproduced highdynamic range (HDR) image by capturing 11 images with different
exposure time. HDR composition was carried out with the method
proposed by Debevec et al. 18). After that, we used Munsell color
chart for linear correction and performed the color matching between digital camera and omni-directional camera. Through theseprocessing, we derived incident light component from omni-directional camera as shown in Fig.2. The feature of object was measured
in sequence by using a rotational stage (SGSP-60YAW, Sigma-Koki). In this experiment, we prepared real object which was simple
plate or cylinder as the measurement target. Since the shape of theseobjects is fully axisymmentrical, we also prepared the polygon model based on the measured data with real size of each object. The
polygon model was registered to the first frame of image sequencesby hand with GUI application. Here, it is noted that the subsequent
frames are automatically registered between real object and its polygon data, because the rotational position of each frames are known
and the center of rotation is consistent.
3.2 Assumption and input data
Our proposed method refers to the pioneering idea proposed by
Dong et al.1) We assume that surface reflectance is isotropic and it isexpressed by microfacet reflectance model. As the dichromatic
BRDF model is used in our system, the surface reflectance at a point
x is defined by Eq.1.
f (ω i , ω o ; x) =ρ d ( x)+ ρ s ( x) f s (ω i , ω o ; x)π(1),where ωi and ωo are the incident and reflected directions, ρdand ρs are the diffuse and specular reflectance, and fs(ωi, ωo ; x) is
the specular reflectance function, which is proposed by Asikhmin etOmnidirectional
cameraRotational
Table
CameraFigure 1 Illustration of our experimental setup for BRDF measurement and incident light capturing by 360-degree omni-directional camera.

Ryota Domon, Shoji Yamamoto, Hiroshi Kintou, Norimichi Tsumura

11

Ease-to-use approach of BRDF recovery from 360°Light Probe

Figure 2 Example of light probe which is HDR image captured by 360-degree omni-directional camera.

al. as follows 19) .

appropriate value (surface reflectance properties) with residual simultaneously. It can be regarded as the smaller residual is suitable forrepresenting the surface reflectance properties. For the reduction ofcomputational cost, we employed Smith's shadowing and masking
term, which has relatively less computation cost. In our method,
three variables for each surface point are determined separately. To
derive these parameters, we solve minimization problem denoted by
Eq.3,

D(ω h )G (ω i , ω o ) F (ω i , ω o )
f s (ω i , ω o ) =4(i ⋅ n)(o ⋅ n)(2),where D(ωh) indicates the normal distribution function (NDF)
of the halfway direction ωh with microfacet, F(ωi, ωo) indicates
Fresnel reflectance function (we assumed a fixed index of refractionof 1.3 for all materials as same as Dong et al.) , and G(ωi, ωo) indicates the shadowing and masking function. Because specular highlights are quite effective factor for appearance reproduction, it is very
important to select the spatial distribution of specular highlights,
namely NDF. We observed two major trends of spatial distributionof highlights in real world. Ceramic plates have weak tail in highlights as shown in Fig.3 (a). On the other hands, wooden flooring
plate has relatively strong tail in highlights as shown in Fig.3 (b).
Therefore, we employed two NDFs owing to represent these characteristics. First, we adopt Beckmann distribution model to express the
weak tail in highlight as shown in Fig.3 (a). In other case, GGX
model is adopted to express the strong tail in highlight as shown in
Fig.3 (b) 20). These models determine the spatial distribution by theangles between halfway direction ωh and surface normal. For thesimplification of acquiring the surface reflectance properties, we seek
the roughness parameters of each model as the objective function
instead of the 1-dimensional tabulated function that monotonicallydecreased used in previous study.
By solving the minimization problem, it is possible to obtain an(a)arg min ∑∑ || I (ω ′o , x, t ) − L(ω ′o , x, t ) || 2

t
x
(3),
where I(ω'o, x, t) is the observation value of rotating target object,
L(ω'o, x, t) is the outgoing radiance at a surface point x at time t. ω'oindicates the outgoing (viewpoint) vector, and prime symbol is the
direction in global coordinate. L(ω'o, x, t) is determined by registered object geometry n(x,t) and incident light component E(ω'i)
captured with omni-directional camera as denoted in Eq.4.
( ρd ,ρs ,D)x

L(ω′o , x, t ) = ∫ f r (ω i ( x, t ), ω o ( x, t ); x) E (ω′i )(n( x, t ) ⋅ ω′i )dω′i(4),where ωi and n indicates the lighting vector and surface normal
at the surface point x. ωi is the sampling area from environmental
map captured by omni-directional camera. Based on the prior work,
we set the range of sampling area less than 0.5π from the mirror
reflection with respect to the viewpoint vector. This idea is very simple but it is effective to reduce the computational cost. Figure 4
shows the illustration of acquiring incident light component from
Ω

(b)

(c)

Figure 3 Various spatial distribution of highlights in real world material, (a) Ceramic plate, (b) Wooden flooring plate, (c) Red gum plate.

12Bull. Soc. Photogr. Imag. Japan. Vol. 28 No. 2 (2018)

the environmental map which is captured with omni-directional
camera.
3.3 NDF Recovery
Our proposed method solves Eq.3 with each surface point separately. Thus, we rewrite Eq.3 to denote the equation of a single surface point x,
arg min( ρd ,ρs ,D)x

∑ || T (ω′ , t ) − L(ω′ , t ) || (5),
2

o

t

o

where T(ω'o, t) is equal to I(ω'o, x, t), which represents the temporal variation at the surface point x as shown in Fig.5. It is difficult
to solve Eq.5 because there are still three variables. Therefore, wetake temporal gradient of observation and outgoing radiance on thesurface point x. Temporal gradient of the outgoing radiance can be
expressed as Eq.6.
∇ t L (ω o , t ) = ∇∫ f (ω (t ), ω (t )) E (ω′ )(n (t ) ⋅ ω′ )dω′
r

Ω

ix

ox

i

x

i

i

ρ dx
∫Ω π E (ω′i )(n x (t ) ⋅ ω′i )dω′i+ ∇ t ∫ ρ sx f sx (ω ix (t ), ω ox (t )) E (ω ′i )(n x (t ) ⋅ ω ′i )dω ′i

= ∇t

Ω

ρ
= dx ∇ t ∫ E (ω ′i )(n x (t ) ⋅ ω ′i )dω ′iΩπ+ ρ sx ∇ t ∫ f sx (ω ix (t ), ω ox (t )) E ( R nx ( t ) (ω i ))ω iz dω ′i(6).
There are two terms in Eq.6, diffuse reflection component andspecular reflection component. Because temporal variation of diffuse
component is comparatively small, temporal gradient of the diffuseΩ

component can be assumed approximately zero. Hence, specularcomponent, which is principally effected by lighting, is the dominant factor of outgoing radiance denoted as Eq.7.
L(ω′o , x, t ) ≈ ρ s ( x)∫ f (ω , ω (t ))ω E ( R(ω i ))dω′i(7).
Taking that approximation, we can simply solve the minimization
problem denoted in Eq.8 with temporal gradient of the observationand outgoing radiance denoted in Eq.7.
arg min

Ω

sx

i

o

iz

nx ( t )∑ || ∇ T (ω′ , t ) − ∫ f (ω , ω (t ))ω E ( R
t

o

sx

i

o

iz

nx ( t )(ω i ))dω ′ || 2

(8),where D'x is the unnormalized NDF biased by specular albedo
ρsx. Finally, the NDF Dx is recovered from D'x via unit integration.
In our implementation, we employ two NDFs, Beckmann distribution and GGX distribution. It is expected that residual of minimization problem may be reduced if the characteristics of NDF is suitable for representing the surface reflectance of target object. We
adopt the result which has smaller residual value for verifying theaccuracy of our proposed method.
Dx

′

t

Ω

3.4 Albedo Recovery
Given the recovered NDF Dx from previous formulation, we can
now determine the diffuse component and specular component ofoutgoing radiance denoted as Eq.9.

Figure 4 Illustration of acquiring incident light component from the HDR image captured with omni-directional camera.

Figure 5 Temporal variation of pixel value during the measurement with a rotational table.

Ryota Domon, Shoji Yamamoto, Hiroshi Kintou, Norimichi Tsumura

Tdx (ω o , t ) = ∫ f r (ω ix (t ), ω ox (t )) E (ω ′i )(n x (t ) ⋅ ω ′i )dω ′iΩρ= dx ∫ E (ω ′i )(n x (t ) ⋅ω ′i )dω ′iπ Ω+ ρ sx ∫ f sx (ω ix , ω ox ) E (ω ′i )(n x (t ) ⋅ ω ′i )dω ′iΩ= ρ dx Tdx (ω ′o , t ) + ρ sx Tsx (ω ′o , t )(9).
Tdx(ωo, t) and Tsx(ωo, t) are diffuse trace and specular trace of theoutgoing radiance. It can be regarded that the observation trace
T(ω'o, t) is the weighed sum of normalized diffuse trace and specular trace. As a result, recovery of the albedo components are formulated as non-negative least squares minimization problem as shownin Eq.10.
arg min( ρd ,ρs ) x∑|| T (ω′ , t ) − ( ρ T (ω′ , t ) + ρ T (ω′ , t )) ||
t

x

o

dx

dx

o

sx

sx

o

2

(10).

4. Verification
4.1 Evaluation for estimated BRDF
In order to validate our proposed method, we prepare synthetic
image generated by Mitsuba renderer 21). We rendered three kinds ofobjects by changing surface reflectance as shown in upper row of
Fig.6. These images rendered with the office window environmentmap (Fig.2) and used Beckmann distribution, and lower row images
were rendered by using the acquired surface reflectance from our
proposed method. Comparing upper to lower images, it can be confirmed that the calculated surface reflectance properties can make areasonable image with our proposed method. Though the calculatedparameters of the most right one in upper and lower row are different, visual difference is slightly small.
We also evaluated the validity of our proposed method by comparing with the NDF acquired by gonio-reflectometer (GCMS-4,
Murakami Color Research Laboratory). To measure the surface reflectance of the objects, we take three type of flat board objects, blue

Ease-to-use approach of BRDF recovery from 360°Light Probe13

ceramic, wooden flooring plate and red gum (Also shown in Fig.3) .
Figure 7 shows the results of measurement by using gonio-reflectometer and our proposed method, where blue line in the Fig.6 ismeasured by gonio-reflectometer, and red line and green line in
Fig.7 are Beckmann distribution model and GGX distribution
model, respectively. As we expected, surface reflectance of each target object is recovered by appropriate NDF to represent each material. Figure 8 shows the reproduced image by using acquired NDF
value. It is apparent that NDFs of each of the subjects are estimatedaccurately as same as the gonio-reflectometer and rendered imagesof appearance is observed as a quite similar to original board objects.
4.2 Evaluation for SVBRDF measurement
Next, we challenged to reproduce the SVBRDF profile which is
set up in the surface of aluminum can with multiple texture. Figure
9 shows the picture of real object (left) and measured result of diffuse albedo map (right) by using our system. From the result, oursystem can obtain the meaningful albedo map which can recognize
as a combination of different textures. It can distinguish each texture
and positional relationship, unfortunately, it is hard to make reasonable result for measurement of SVBRDF. This result indicates that
our measurement system has some incompleteness and improvement for SVBRDF measurement. For its causes and solutions, wewill describe in the latter discussion part in this paper.
4.3 Subjective appearance evaluation
In this section, we verified the BRDF recovery by using real 3D
objects, which has distinctive surface appearance. Four types of 3D
object with different surface profile were selected, such as green gum
ball, urethane coated bowl, white ceramic vase and blue plastic cone.
Figure 10 shows the results of this verification under the same condition and measurement instrument as Fig.7. The left side image in
Fig.8 shows real objects, and right side image shows rendered ob-

Figure 6 R
 esults of synthetic image generated by Mitsuba renderer based on the calculated three variables, which are roughness, diffuse albedo, and specularalbedo. Each numerical value indicates the comparison between measured ground truth and calculated result by using our method.

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Bull. Soc. Photogr. Imag. Japan. Vol. 28 No. 2 (2018)

Figure 7 Comparison results of reflectance distribution between our proposed method and gonio-reflectometer.

(a)

(b)

(c)

Figure 8 Reproduced images by using acquired NDF value. (a) Blue ceramic plate, (b) Wooden flooring plate, (c) Red gum plate.

(a)

(b)

Figure 9 Result of SVBRDF measurement by using aluminum can with multiple texture, (a) Real object, (b) diffuse albedo map.

jects by using Mitsuba renderer with Reinhard's tone mapping operator 22). The calculation for matching the distribution model was
performed by using the Beckman and GGX models, and we selected
the best matching model between estimated and modeled reflectance.
Here, it is noted that we have no choice but to evaluate the appearance by appreciation since it is difficult to acquire the ground truth ofthese 3D object. Therefore, we applied subjective evaluation to verify
each rendering result. The color corrected display (CX241-CNX,
EIZO) was used, and fifteen participants with normal color visionassessed by using five grade evaluation, (5:quite similar, 4:rather similar, 3:similar, 2:rather not similar, 1: not similar). Figure 11 shows theresult of histogram for five grade in this subjective evaluation.

As a comprehensive evaluation, our proposed method is possible
to measure and reproduce the surface appearance of material even if
the target is 3D object. The highest score was granted for the resultof white ceramic vase. From the participant's comment, a clear surface reflectance of specular represents the appearance of ceramicmaterial gradely. On the other hand, the reproduction of blue plastic
cone had the lowest score, since the contrast between specular anddiffuse color was ill-balanced in comparison to real 3D object. Commonly, it is difficult to use the best tone mapping in changing from
32bit to 8bit signals because the measured BRDF is expressed byhigh dynamic range data. In this experiment, we made the visualappearance close to real object by controlling the exposure of omni-directional images. However, a slight difference of tone balanceRyota Domon, Shoji Yamamoto, Hiroshi Kintou, Norimichi Tsumura

provides an unpleasant impression in rendering reproduction such as
the case of blue plastic cone and green gum ball. The other results ofurethane coated bowl was satisfied by almost participants. They appreciated the matching of specular distribution on the surface of 3D
object, although ill-balanced contrast between specular and diffuse
color is slightly concerned. Therefore, for visual verification, the consideration for model matching is necessary to attach importance as
either specular or diffuse reflectance. In our case, the colored object
should be attached importance to the diffuse reflection and monotone object should be attached importance to the specular reflection.

15

Ease-to-use approach of BRDF recovery from 360°Light Probeis estimated by using the different normal vector. In order to decrease the mixture of diffuse and specular reflection, the use of polarizer may be appropriate 4). Unfortunately, this workaround idea invites an additional measurement in order to change the direction of
Real

5. Discussion

Rendered(a) Urethane coated bowl

5.1 Measurement setting and SVBRDF recovery
In this paper, it is blindingly clear that our proposed system canmeasure accurate BRDF when the target object consists of uniquematerial. For this result, we infer that position-independent and integrated best solution is obtained by the calculation in an optimized
process. On the other hand, more rigid measurement about position
matching is required for the SVBRDF measurement, since the
BRDF profiles are changed according to the measurement position.
Therefore, all of the geometries in our work are formulated by combination of simple geometries, such as a sphere, cuboid, cylinder andso on. Moreover, many number of trial for position alignment were
executed for the SVBRDF measurement, although this alignment
was performed manually. However, this result indicates that ourmeasurement system has some incompleteness.
From the result as shown in Fig.9, we can observe several unnatural features which are related to the position misalignment. At first,
we notice a blurred edge at the part of trade name into the rotateddirection. Moreover, we found that the detail part of "d" or "u" character have a serious blur compared with the first character "R". This
unnatural result of blur leads us to some assumptions that the rotated table is hard to keep accurate one degree of angle, the center ofobject is out of alignment from the rotated center, and the shape ofreal object is partly distorted compared with polygon geometry. It is
obvious that the blur image is generated as the mixture of diffuse
albedo and specular reflection since the BRDF at misaligned point

RenderedReal(b) Blue plastic cone
RenderedReal(c) Green gum ballRenderedReal(d) White ceramic vase
Figure 10 I mages for subjective evaluation. The Left images show the captured image of 3D real objects, and the right images show therendered results by our proposed method.

Number of participants (N=15)
Quite similar

0 2 4 6 8

0 2 4 6 8

0 2 4 6 8

0 2 4 6 8

(a)

(b)

(c)

(d)

Rather similar
SimilarRather not similar
Not similar
Ave = 3.80
Std = 0.65

Ave = 2.93
Std = 0.57

Ave = 3.13
Std = 0.72

Figure 11 Result of subjective evaluation for our rendered images.

Ave = 4.27
Std = 0.57

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Bull. Soc. Photogr. Imag. Japan. Vol. 28 No. 2 (2018)

polarization, and more than all, the user always should prepare thepolarizer every time.
Other unnatural feature in Fig.9 is found that the irregularity ofup and down is existed in the horizontal linear edge. This misalignment infers that the slight movement of up and down side may begenerated every movement by the rotating table. As just described, it
is necessary to improve the precision of position alignment and stability of movement with careful consideration of requisite resolutionin SVBRDF measurement. As an essential solution for this problem,
it may be useful to measure the shape of object together by using
digital camera. However, it might bring the trade-off between an
accuracy of SVBRDF and computational cost, since a complicate
and corrective calculation is necessary to measure the shape of object
which has specular reflection on its surface. Recent novel instrumentof 3D measurement may be possible to obtain the accurate shapeeven if target has the specular reflection 16). Unfortunately, it is necessary to match the position and shape between measured shape andmeasurement point of BRDF finally.
5.2 Calculation cost reduction
Another priority of our proposed method is reduction of computational cost. Since our proposed method uses environmental map as
the incident light component, the computational cost is simply reduced. Not to require the estimation of incident light component,
we can estimate each surface reflectance independently. This independence of calculation will provide several merits that the parallel
computing technique is easy to apply for our proposed method, andit can accelerate estimation process dramatically. In order to confirm
our superiority, we tried to compare the performance of calculation
between conventional and our method. Unfortunately, it is only provided the fragmentary specification of computation and the conceptof algorithm in Dong's paper. Therefore, we make two kinds of hypothetical comparison; one is clock speed competition and the otheris simulation for each algorithm. Table 1 shows that the comparisonof clock speed of ours and conventional methods. Clock speed ofconventional method is calculated by their paper. Our implementation environment uses Intel Corei7 processor with 16 GB memory.
On the other hand, conventional method uses dual Intel Xeon E52690 processor with 64GB memory. Our computational specification is obviously less powerful than their condition, however we canachieve faster calculation for BRDF recovery.
For the simulation of each algorithm, we estimate the computational cost of both methods with the object as shown in Fig.7(a).
With same polygon size of object, same measured pixel, and same
optimization algorithm, both BRDF and environmental illumination map was estimated as the conventional method. On the other
hand, only the BRDF was estimated by using our proposed method
under the condition that the incident lighting component was
known. As the result of simulation, our method achieves this process

about 10 seconds, and conventional Dong's method is necessary to
calculate about 101 seconds. As a conclusion, we can acquire precious BRDF value about ten times faster than conventional method.

6. Conclusion and future work
In this paper, we present a simple BRDF measurement methodwith well-convergence and rapid estimation by adding the lighting
component derived from omni-directional camera. Our proposed
method accomplished compatibility between accuracy and speed-up
of calculation by using environmental image as light probe. The accuracy of our measurement was verified by comparing the surface
reflectance between our system and gonio-reflectometer, and it isconfirmed that the surface reflectance of flat board objects is almost
completely reproduced by appropriate NDF with fitting to the
Beckmann and GGX distribution model. The accuracy of visual reproduction is verified by comparing the appearance between real andreproduced 3D object, and it is confirmed that most of the participants selected their answers as "rather similar", or "similar" in thesubjective evaluation. Moreover, our proposed method achieves the
speed ten times faster than that of conventional method owing to
the simplification of incident light components.
Geometric data selection can also affect the result of both NDF
and albedo recovery of SVBRDF. If the misalignment and variation
between measuring point and shape position are existed, the imageof reproduced surface texture becomes blurred. Therefore, it is necessary to take careful position alignment and stability of rotational
movement for the acquisition of shape and reflection data. The misalignment and variation between measuring point and shape position make the image of reproduced surface texture blurred. Here, it
is noted that they have a trade-off relationship both accuracy andcalculation cost.
Comments by participants in the evaluation of our proposed
method prompted us to evaluate the target object with more complex shape. Therefore, high density measurement of geometry dataand precise position matching between 3D model and environmental image are necessary as a future work. Moreover, an appropriate
control of HDR measured data should be developed for practicaluse of our method. The HDR measurement for light probe and object feature was embedded in proposed method. Therefore, a precise
tone mapping for the visual reproduction of material appearance isalso necessary as a future work.

Acknowledgments
This research was partially supported by the Ministry of Education, Science, Sports, and Culture, Japan Grant-in-Aid for Scientific Research of 24500267 and 15K00415, and Brain and Information
Science on SHITSUKAN of 25135707.

Table 1 Result of comparison for computational speed between conventional and proposed method
MethodMaximum clock speed

Minimum clock speed

Intel Core i7 (Ours)

53.28GFlops

13.2GFlops

Dual Intel Xeon (Conventional)

396.8GFlops

6.2GFlops

Ryota Domon, Shoji Yamamoto, Hiroshi Kintou, Norimichi Tsumura

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