Surface Reflectance Modeling of Real Objects with Interreflections
Takashi MachidaÝ, Naokazu YokoyaÞ, and Haruo TakemuraÝ
ÝCybermedia Center, Osaka UniversityÞGraduate School of Information Science, Nara Institute of Science and Technology
E-mail: machida@ime.cmc.osaka-u.ac.jp, yokoya@is.aist-nara.ac.jp, takemura@ime.cmc.osaka-u.ac.jp

Abstract
In mixed reality, especially in augmented virtuality
which virtualizes real objects, it is important to estimate
object surface reflectance properties to render the objects
under arbitrary illumination conditions. Though several
methods have been explored to estimate the surface reflectance properties, it is still difficult to estimate surface
reflectance parameters faithfully for complex objects whichhave non-uniform surface reflectance properties and exhibit
interreflections. This paper describes a new method for
densely estimating non-uniform surface reflectance properties of real objects constructed of convex and concave surfaces with interreflections. We use registered range and surface color texture images obtained by a laser rangefinder.
Experiments show the usefulness of the proposed method.

1

Introduction

In mixed reality (MR), it is needed that a virtualized object is seamlessly merged into the real world [1]. In order torepresent a virtualized object photo-realistically, there are
two approaches to the problem of virtualizing real objects.
One is called an image based rendering (IBR) that has often been used to reproduce real objects in computer graphics (CG). Generally, IBR methods require a large numberof real images to represent the virtualized object under arbitrary illumination conditions and arbitrary viewing directions. Mukaigawa et al. [15] have proposed a photometric IBR in which a virtualized object is represented with a
few real images. However, in the case of using a limited
number of images, a problem occurs; i.e., the appearanceof object is not faithfully reproduced since some part of theobject is interpolated linearly. The other method is calleda polygon based rendering (PBR). This method reproduces
the object shape and surface reflectance properties. If theobject surface reflectance properties are estimated at once,the virtualized object can be rendered appropriately undervirtualized illumination conditions estimated from real en-

vironments [5, 16]. A number of methods for estimatingreflectance properties of an object surface have been developed [2, 8, 9, 10, 11, 13, 17]. In these methods, surface
reflectance models with several parameters are employed,
and shape and color information of the object are used toestimate the reflectance parameters.
Object surface reflection consists of diffuse and specularcomponents. The diffuse reflection component is easily observed due to its nature of reflection in omni-direction. On
the other hand, the specular reflection component is limitedly observed within a fixed range of angles with respect
to a viewing position, light source and object surface normal vector. In some works [2, 8, 13], it is assumed thatan object has a uniform reflectance property over the entire
surface. Reflectance parameters are estimated by using thestandard least-squares method to fit a reflectance model toa given color image. Due to the assumption, such methods
cannot be applied to objects which consist of several different materials and have non-uniform reflectance properties.
On the other hand, to treat non-uniform surface objects,
some works have used multiple images of an object under
different lighting conditions and have estimated reflectanceparameters by solving simultaneous equations [9, 10, 11].
However, such methods still have a problem such that results are not stable especially when the specular reflection
component is very small.
Sato et al. [17] have developed a methodology to estimate non-uniform reflectance properties. They set up an
object on a robot arm and measure the object with a CCD
camera and a rangefinder from a large number of viewpoints
by rotating the robot arm. In the method, reflectance parameters are stably acquired by decomposing the surface reflection into two components based on the singular value decomposition (SVD) technique. Although the method can beapplied to objects with non-uniform reflectance properties,
the shape of object should be limited. This is because it isdifficult to observe the specular reflection component overthe entire surface, since the lighting condition for a poseof the object against the camera cannot be changed in themethod.

Moreover, if the object has a complicated shape, interreflections may occur. Here, we take notice of the radiosity.
The radiosity models interreflections in the real world. Thismethod can represent interreflections based on the transmission of heat energy of light. Fournier et al. [7] have originally developed a method for estimating surface reflectanceproperties using the radiosity method in an indoor scene.
This method assumes uniform reflectance on an object surface and determines only the diffuse reflectance parameter.
There are some other attempts to estimate both diffuse andspecular reflectance properties of a room [3, 12, 20]. They,
however, also assume that all objects have the uniform reflectance properties in the region, therefore, their algorithm
also cannot be applied to an object which has non-uniform
surface reflectance properties.
In this paper, we propose a new method for densely estimating non-uniform reflectance properties of objects withinterreflections. First, we select optimum light positions
in order to decompose diffuse and specular components ateach surface point. Then, we densely estimate the object
surface reflectance parameters considering interreflections
on the surface. The proposed reflectance modeling method
is based on the radiosity and Torrance-Sparrow model. In
experiments, the proposed method is qualitatively and quantitatively evaluated with reflectance parameter estimationand virtual relighting. The radiosity method can usually beapplied to a closed environment. However, we experimentally verify that the radiosity can also be applied to an open
environment in which the influence of the environment lightis negligible.

2

Surface reflectance modeling from range
and color images

Figure 1 illustrates a flow diagram of surface reflectancemodeling. Our process consists of three parts: measurementof an object (A, C), selection of light source positions (B),and estimation of reflectance parameters (D, E).
1. Measurement of 3-D geometry and surface texture
An object shape is acquired with a laser rangefinder ina dark room. Multiple surface texture images are also
obtained under different light sources whose positions
are selected in the process (B).
2. Selection of light source
According to the object shape and the position of thecamera, multiple light positions are automatically selected among a number of possible positions of thelight source to measure both diffuse and specular reflection components densely on the surface.
3. Estimation of reflectance parameters
Reflectance parameters are estimated by substituting

A. Measurement
Range data
B. Selection of optimum positions of light source
Selected light position 1. . . .

Selected light position m

C. Measurement
Surface texture image 1. . . .

Surface texture image m

D. Estimation of diffuse reflectance parameter based on radiosity
Diffuse reflectance parameter
E. Estimation of specular and surface roughness parameters
based on Torrance-Sparrow model

Figure 1. Flow diagram of surface reflectancemodeling.
the object shape and textures under selected illumination conditions into the surface color reflection model.
Surface interreflections are considered in this process.

2.1

3D Measurement of object

We use a laser rangefinder (Cyberware 3030RGB) withknown positions of point light sources and a camera for acquiring range and surface color images, which is located ina dark room as shown in Figure 2(a). This system can simultaneously obtain registered range and surface color texture
images rotating the rangefinder and the camera around an
object. Figure 2(b) shows the illustration viewed from the
top of the device. A camera is located at  and a texture
image is acquired through mirrors which are located at and . We thus assume that the camera is virtually locatedat  and the camera looks toward the center of rotation.
Here, because a range image has some noises including quantization errors, we locally fit the range image toquadratic surfaces to acquire the normal vector correctly byusing the Yokoya-Levine operator [19].






2.2



Selection of positions of light sources

Here we address the problem of determining light source
positions for effectively observing diffuse and specular reflections on an object surface. In the present experimental
setup, multiple positions of a light are determined among 60
possible positions prepared around the laser rangefinder andthese are two-dimensionally arranged at the interval of 5 cm
as shown in Figure 3. The positions of a camera and a lightsource are calibrated in advance. When optimum light positions are selected, a single light is attached at the selected
positions in turn. Therefore, the calibration of brightness
among multiple lights is not needed.
In this study, we employ the Torrance-Sparrow model[18] to represent surface reflections physically.
The

Center of rotation be the number of pixels which include only the diffuse
reflection component in  , and  be the number of pixels
which include the strong specular reflection in  .
First, the following conditions are examined for eachpixel in the object surface texture under each light position,:

Laser rangefinder
X1
X2
CameraX3 Virtual camera
X4

Measurability of light reflection,
Measurability of only diffuse reflection,
 Measurability of strong specular reflection.
(a) Appearanceof 3D-Digitizer(b) Direction of camera

Figure 2. 3D-Digitizer.

 Torrance-Sparrow model is given as:








     

  

 

(1)





where represents an observed intensity,
is an attenuation coefficient concerning the distance between a point
light source and an object surface point,
represents thestrength of a light source.  ,  and are the diffuse
reflectance, the specular reflectance and the surface roughness parameters, respectively.  is an angle between a lightsource vector and a surface normal vector,  is an angle between a viewing vector and a surface normal vector, and 
is an angle between a viewing vector and a reflection vector. Note that the reflection vector is a vector to which alight vector is mirrored against a normal vector.  is used
for judging whether the specular reflection occurs or not.
To densely estimate non-uniform reflectance parameters,
it is required to observe each surface point under at least
three different lighting conditions: One for determining one
unknown parameter  and others for acquiring two unknown parameters  and . Therefore, the selection oflight source position is repeated until almost all pixels in
the range image satisfies three different lighting conditions.
As a result of this process, a certain number of light positions, say , are selected to densely observe both diffuse
and specular reflection components.
Let  be a color image which is to be obtained with apossible light position        and consists ofpixels       , where  means a color intensity,

 





















Laser rangefinder

Possible light position

Figure 3. Multiple possible light source positions.






Second, the light positions and which satisfy        and        are selected. In the next light source position selection, the position which satisfies the same condition is selected among
the rest except for light source positions decided so far.
Then, light positions are selected to densely estimate reflectance parameters. The selection of light positions is repeated until almost all pixels are observed once for only the
diffuse reflection component and twice for the strong specular reflection component.
We introduce a threshold , i.e., the ratio of the measurability of both reflection components to stop the processof selecting light positions. With respect to determining thethreshold , we judge the ratio of the measurability of the
specular reflection with all possible positions. This ratio
is a limit of measuring the specular reflection component.
Using the threshold, we can terminate the light selection
process in the case that the ratio of measurability of specular reflection component cannot increase more, even if thenumber of positions of light source is increased. In sucha way, reflectance parameters can be efficiently estimatedalmost the whole object surface using a limited number of
texture images. In the following, the three measurability
conditions above are described in detail.









2.2.1 Measurability of light reflection
In order to measure the light reflection at a specific pointof the object surface, the surface point must be observablefrom the camera position and the light must illuminate thesurface point. Thus the positional relationship among thecamera, the surface point and the light source must satisfy
the following conditions.

Î  Æ  ¼ Ä  Æ  ¼

Î Ä

Æ

(2)

where  ,  , and  are the viewing direction, the lightsource direction, and the surface normal at the -th pixel,
respectively. Note that the viewing direction  and thesurface normal  are independent of the light source position . Even when the above equations are both satisfied,there is a possibility that a shadow is casted on the pixel.
In other words, a point on the object may be covered by ashadow casted by the light source . Such a case can be
judged by an existing technique[6].

Æ



Î

L

2.2.2 Measurability of diffuse reflection only



Ä











Î  Ä¼ 

 

V

Ä

where   is a threshold angle between  and ¼ . Eq.
(3) implies that only the diffuse reflection component is observed if  is greater than   as illustrated in Figure 4.
When this condition stands and the pixel is not in a shadow,
the pixel is judged to have diffuse reflection only and iscounted in  .



θr

θ th1

Range of observing
both reflection
components(3)ÎObject surface

V



L
N
L’

θth2

2.2.3 Measurability of strong specular reflection











Î  Ä¼    



2.3

Î

Ä
















2.3.1 Estimation of diffuse reflectance parameterbased on radiosity
In the following, we describe a new method for densely estimating diffuse reflectance parameter of objects with interreflections. We assume that interreflections do not have an
influence from the specular reflection component but only
from the diffuse reflection component. Therefore, pixels
categorized in 
are used in the estimation of diffuse
reflectance parameter. In this paper, in order to consider
interreflections, we employ the radiosity equation given as:   




 

  where  and   represent the radiosity of-th and -th patches, respectively. Note that is the number of object patches.  is a form factor between the patch
and the patch .  represents an emission term which
has an influence on the patch and actually  means thelight patch in the environment. Since the object is measured
in a dark room in the present study, we can assume thatthe influence of environment light can be ignored. In otherwords, the form factor between each patch of the object andthe wall of the dark room is not calculated.  represents
the diffuse reflectance parameter on the patch .
In the proposed method, the hemi cube method [4] can beused for calculating the form factor  because the object
shape has already been measured by the laser rangefinder.
Since the range and texture images are registered at eachpixel, the radiosity  of the patch is calculated basedon the sum of the values of the pixels which correspond to
the patch . Then, the diffuse reflectance parameter  isdetermined as follows:







 









Estimation of reflectance parameters

This section is concentrated on the determination of reflectance parameters from registrated range and color texture images. A texture image is obtained with a selected
light position as described in the previous section. Eachpixel is classified into three types  ,  and   .
means a pixel containing only the diffuse reflection
component and  means a pixel containing strong specular reflection component.   means a pixel which isclassified neither  nor  and is not used to estimate
reflectance parameters.



Figure 5. Observation of the specular reflection.

(4)

where   is a threshold angle between  and ¼ . Eq.
(4) means that both the diffuse and specular reflection components are observed if  is smaller than   as illustrated
in Figure 5. The above condition is based on the fact that the
specular reflection is observed strongly in a limited range ofviewing angle. When this condition stands and the pixel is
not in a shadow, the pixel is judged to have strong specularreflection and is counted in  .

Range of observing
the specular reflection
component strongly

θr

Object surface

When the -th pixel exhibits the strong specular reflection,
the reflection vector ¼ satisfies the following equation.

Ä

Range of observing
only the diffuse
reflection component

Figure 4. Observation of only the diffuse reflection.





N

L’

When the -th pixel exhibits only the diffuse reflection, thereflection vector ¼  satisfies the following equation.

(5)





















  

(6)   where  is 0 since there is no emission at the patch on
the object. Finally, the diffuse reflectance parameter at eachsurface point is estimated by calculating the average amongneighbouring patches which share the point.
Here, we describe the calculation of the radiosity  ofthe patch in more detail. Each patch consists of four
points and  is represented as the sum of the color values of the pixels which correspond to these points. Let us
suppose that the patch contains pixels and as shownin Figure 6. It should be noted that pixel values  and of and in 
are obtained with different light positions  and  , respectively, because the light source
attached with the rangefinder moves during measurement.
In calculating the  , it is required to use the color value 












 
















Laser rangefinder

3.1

p(t)

Objects u tp(s)Figure 6. Calculation of radiosity.







of the pixel with the light position  . From the Lambert’s law, the color value  can be obtained by:  ÆÆ ÄÄ      



(7)

where Æ and Æ are normal vectors at pixels  and .
Ä and Ä are light vectors with the light position at pixels  and . Note that in the case of Æ Ä , should be 0 to consider the measurability of light reflection.

2.3.2 Estimation of specular reflectance and surface roughness parameters based on TorranceSparrow modelThe specular reflectance parameter  and the surface
roughness parameter  at the -th pixel which is categorized in  are estimated by solving the simultaneous
equation of Eq. (1) with the values of the specular reflection component extracted from two images taken under two
different illumination conditions and  estimated above.
Note that  estimated above should be scaled to Eq. (1)before computing the specular and surface roughness parameters.
When strong specular reflection is observed less than
twice, the specular reflectance and surface roughness parameters cannot be uniquely determined and thus are obtained by linear interpolation within a    window. If thewindow is small compared with the area, values of the reflectance parameters are interpolated linearly by scanning
the texture image horizontally.











3

Experiments

In experiments, we first demonstrate results of estimating non-uniform surface reflectance properties as well as
the effectiveness of the light position selection mechanism.
We then examine the effect of considering interreflections insurface reflectance parameter estimation using objects withuniform and non-uniform surface properties. We fix someparameters as    ,    ,   in all theexperiments.







Dense estimation of surface reflectance parameters

Figure 7(a) shows an object with non-uniform diffuse
and specular reflections which is used in the first experiment. The proposed light selection method has determined
12 light source positions for the Object A. Estimated parameters for the Object A are given in Figure 8(a)(d), whereparameter values are coded in color or intensity in the cylindrical coordinates. Figure 8(a) illustrates the diffuse reflectance parameter estimated over the object surface. Figure 8(b) does the specular reflectance parameter. This image clearly shows that the specular reflectance parametersof the doll’s beak and leg are different from the rest. Actually, the beak and legs are highly reflective as can be seenin Figure 7(a). Figure 8(c) shows the surface roughness parameter with gray-scale where the largest value is coded as
white. This image means that the smaller the value is, thesmoother the object surface is. Figure 8(d) shows the ratioof pixels where specular reflectance and surface roughness
parameters are computed. The black part means that bothparameters are not directly estimated.
Figure 8(e) and (f) illustrate the measurability of bothreflection components with respect to the number of lightsources. Note that the horizontal axis is represented until 20, since these graphs does not change even if all 60
possible positions are used. In Figure 8(e), with respect
to the diffuse reflectance parameter, when the number of
selected light source positions is 5, the ratio of the measurability of the diffuse reflection component is  . In Figure8(f), as for the specular reflectance and the surface roughness parameters, even when the object is measured with all
the possible positions, the ratio of the measurability of the
specular reflection component is   . In our method,
the ratio of measurability of the specular reflection component is   with automatically selected 12 light source
positions. Since this figure is comparable to that with all
the possible light source positions, the experiment showsthat the proposed method is effective. The measurability ofboth reflection components and the number of selected lightsources for estimating reflectance parameters of Objects A
and C are shown in Figure 7(d). The number in the bracket
means the number of selected positions of light source required to estimate the diffuse reflectance parameter. Notethat it takes about 4 hours to calculate the form factor andestimate reflectance parameters of each object with a PC
(CPU: Pentium4 3.06GHz, Memory: 1GB).





3.2

Effect of considering interreflections

We show that the proposed method can remove the influence of interreflections in a preliminary experiment. We
separate the Object B into two regions I and II as shownObject
Number of selected
light positions
Ratio of the measurability ofdiffuse reflection component
Ratio of the measurability of
specular reflection component

Region I

Region II(a) Object A(b) Object B(c) Object C

A

C

12(5)

10(3)

100.00%100.00%83.46%

89.17%(d) Measurability of both reflection components

Ratio of measurability ofdiffuse reflectance parameter

Figure 7. Three objects used in experiments and the measurability of both reflection components.












%















        

Number of selected light source positions(a) Diffuse reflectance parameter (b) Specular reflectance parameter
 
 



%

Ratio of measurabilityof specular reflectance andsurface roughness
parameters

(e) Possibility of estimating the diffuse
reflectance parameter


























        

Number of selected light source positions(c) Surface roughness parameter(d) Area of observing specularreflection(f) Possibility of estimating the specularreflectance and the surface roughness
parameter

Figure 8. Estimated reflectance parameters and measurability of both reflection components for
Object A.
in Figure 7(b). We have conducted two setups. One is thatthe same white paper with a uniform diffuse reflectance surface is pasted up on both regions (setup1). The other is thatthe same glossy paper with a uniform reflectance surface ispasted up on both regions (setup2). In both setups, the Object B is put on the table obliquely, so that the influence ofinterreflections can be observed. The proposed method iscompared with our previous research [14] which does notconsider interreflections in estimating reflectance parameters. It is expected that, if interreflections occur, the estimated value in the conventional method must be incorrect inthat part. Results for diffuse (setup1) and specular (setup2)
surfaces are shown in Figures 9 and 10, respectively. Eachgraph represents RGB channels of the diffuse reflectanceparameter estimated by both methods. The horizontal axis
means the position of the surface point in the vertical direction of the Object B and the vertical axis means the averageof diffuse reflectance parameters in the horizontal directionof the object. In Figure 9, it is observed that the diffuse reflectance parameters estimated by the conventional method
are large around the boundary between the regions I and
II. On the other hand, such an effect is eliminated in the
proposed method. This clearly shows the effectiveness ofthe proposed method. However, the influence of interreflections still remains in the glossy surface as slightly observedin Figure 10, because interreflections due to the specular reflection also ocurr at the boundary between the regions I and
II in the second setup.
The next experiment is conducted for showing the effect of considering interreflections in reflectance parameter
estimation of non-uniform objects A and C shown in Figure 7. Figures 11(a) and (b) illustrate the sum of differences in RGB channels of the diffuse reflectance parameters between the conventional and proposed methods. These
images are represented in the cylindrical coordinates withgray-scale where the maximum value is 255. The difference





Proposed method

Region A

Region B










       Conventional method






Proposed method

Region A

Region B










       

The average of the diffuse
reflectance parameter

Conventional methodThe average of the diffuse
reflectance parameter

The average of the diffuse
reflectance parameter




Conventional method






Proposed method







T he position of pixel in virtical direct ion

T he posit ion of pixel in virtical direct ion

Region A

Region B       

T he posit ion of pixel in virt ical direction(b) G channel

Conventional method

140
130
120
110

Proposed method

Region A

Region B

100
1

21

41

61

81 101 121 141 161 181 201 221

T he posit ion of pixel in vert ical direction

150

Conventional method

140
130
120
110

Proposed method

Region A

Region B

100
1

21

41

61

81 101 121 141 161 181 201 221

The average of the diffuse
reflectance parameter

150

The average of the diffuse
reflectance parameter

The average of the diffuse
reflectance parameter(a) R channel(c) B channel
Figure 9. A comparison with previous work for a uniform diffuse reflection surface in a preliminary
experiment.
150

Conventional method

140
130
120
110

Proposed method

Region A

Region B

100
1

21

T he posit ion of pixel in vertical direct ion

4161

81 101 121 141 161 181 201 221

T he position of pixel in vert ical direction(b) G channel(a) R channel(c) B channel
Figure 10. A comparison with previous work for a uniform diffuse and specular reflection surface ina preliminary experiment.

(b) Object C(a) Object A

Figure 11. Difference in estimated diffuse reflectance parameters between the proposed and conventional methods for Objects A and C.
is large in the parts where interreflections occur. These results show that the proposed method is effective for objects
which have non-uniform surface reflectance properties andexhibit interreflections. There are some parts whose differences are larger than other parts. This is because the difference includes the influence of specular interreflections.
In the proposed method, the diffuse reflectance parameteris calculated as the average of four patches as explained in
Section 2.3.1. Therefore, the diffuse reflectance parameter which includes the influence of specular interreflections
is also smoothed and that process causes a large differencecompared with the conventional method.

3.3

Rendering results with Torrance-Sparrowmodel under a virtual light source

Finally, we demonstrate the virtual relighting of virtualized objects. Figure 12(a) and (b) show the rendering ofvirtualized objects A and C under a virtual lighting condition. A virtual light source is fixed at (0.0, 0.0, 200.0) as theorigin of the coordinate is at the center of the object. Eachobject rotates around the vertical axis of the object. Figures 12(a) and (b) contain three views such as right, front
and left views, respectively. Each object is fairly renderedeven at the part which contains interreflections. These results qualitatively show the effectiveness of the proposed
surface reflectance modeling method.

4

Conclusions

In this paper, we have proposed a new surface reflectancemodeling method which is based on densely estimating
non-uniform reflectance properties for almost the whole object surface using the laser rangefinder for virtualizing real
objects. In our approach, multiple light source positions
around the laser rangefinder are automatically selected, sothat diffuse and specular reflection components are observed densely. We have considered diffuse interreflections
in estimating surface reflectance properties based on the radiosity. The experiments have proven that the proposed
method is useful for estimating the reflectance parametersright viewleft view
front view(a) Rendering results of Object A

left view

right view
front view(b) Rendering results of Object C

Figure 12. Rendering results of virtualized objects with Torrance-Sparrow model.
of objects with diffuse interreflections which exhibit nonuniform surface reflectance.
In the future, we will extend the method for considering
specular interreflections, which is suggested in experiments
in Section 3.2. We will also investigate a method for automatically estimating illumination conditions in real environment which is required for merging virtualized objects
into real images for mixed reality applications.

Acknowledgments
This work was supported in past by Grant-in-Aid for Scientific Research and also by NAIST-IS 21st Century COE
Program from the Ministry of Education, Culture, Sports,
Science and Technology.

References[1] R. T. Azuma. A survey of augmented reality. Presence,
6(4):355–385, 1997.
[2] R. Baribeau, M. Rioux, and G. Godin. Color reflectancemodeling using a polychromatic laser sensor. IEEE Trans.
on Pattern Anal. Mach. Intell., 14(2):263–269, 1992.
[3] S. Boivin and A. Gagalowicz. Image-based rendering of diffuse, specular and glossy surfaces from a single image. Proc.
SIGGRAPH 2001, pages 107–116, August 2001.
[4] M. F. Cohen and D. P. Greenberg. A radiosity solution forcomplex environments. Proc. SIGGRAPH 1985, pages 31–
40, 1985.
[5] P. Debevec. Rendering synthetic objects into real scenes:
Bridging traditional and image-based graphics with global
illumination and high dynamic range photography. Proc.
SIGGRAPH ’98, pages 189–198, 1998.
[6] J. Foley, A. van Dam, S. Feiner, and J. Hughes. Computer
Graphics Principles and Practice. Addison-Wesley Publishing Company, 2nd edition, 1993.
[7] A. Fournier, A. S. Gunawan, and C. Romanzin. Interactive
common illumination for computer augmented reality. Proc.
Graphics Interface 1993, pages 254–262, May 1993.
[8] K. Ikeuchi and K. Sato. Determining reflectance propertiesof an object using range and brightness images. IEEE Trans.
on Pattern Anal. Mach. Intell., 13(11):1139–1153, 1991.

[9] G. Kay and T. Caelli. Inverting an illumination model fromrange and intensity maps. CVGIP: Image Understanding,
59:183–201, 1994.
[10] S. Lin and S. W. Lee. Estimation of diffuse and specularappearance. Proc. 7th Int. Conf. on Computer Vision, 2:855–
860, 1999.
[11] S. Lin and S. W. Lee. A representation of specular appearance. Proc. 7th Int. Conf. on Computer Vision, 2:849–854,
1999.
[12] C. Loscos, G. Drettakis, and L. Robert. Interactive virtual relighting of real scenes. IEEE Trans. Visualization and Computer Graphics, 6(4):289–305, December 2000.
[13] J. Lu and J. Little. Reflectance function estimation and shaperecovery from image sequence of a rotating object. Proc. 5thInt. Conf. on Computer Vision, pages 80–86, June 1995.
[14] T. Machida, H. Takemura, and N. Yokoya. Dense estimationof surface reflectance properties for merging virtualized objects into real images. Proc. 5th Asian Conf. on Computer
Vision, pages 688–693, January 2002.
[15] Y. Mukaigawa, H. Miyaki, S. Mihashi, and T. Shakunaga.
Photometric image-based rendering for image generation inarbitrary illumination. Proc. 8th Int. Conf. on Computer Vision, pages 643–649, July 2001.
[16] I. Sato, Y. Sato, and K. Ikeuchi. Acquiring a radiance distribution to superimpose virtual objects onto a real scene. IEEE
Trans. on Visualization and Computer Graphics, 5(1):1–12,
January 1999.
[17] Y. Sato, M. D. Wheeler, and K. Ikeuchi. Object shape andreflectance modeling from observation. Proc. SIGGRAPH’97, pages 379–387, 1997.
[18] K. E. Torrance and E. M. Sparrow. Theory for off-specularreflection from roughened surfaces. Journal of Optical Society of America, 57(9):1105–1114, 1967.
[19] N. Yokoya and M. D. Levine. Range image segmentation based on differential geometry: A hybrid approach.
IEEE Trans. Pattern Anal. Mach. Intell., 11(6):643–649,
June 1989.
[20] Y. Yu, P. E. Debevec, J. Malik, and T. Hawkins. Inverse
global illumination: Recovering reflectance models of realscenes from photographs. Proc. SIGGRAPH ’99, pages
215–227, August 1999.