Illumination Distribution from Brightness in Shadows:
Adaptive Estimation of Illumination Distribution with
Unknown Reflectance Properties in Shadow Regions
Imari Sato, Yoichi Sato, and Katsushi Ikeuchi
Institute of Industrial Science, University of Tokyo
7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan{imarik, ysato, ki}@iis.u-tokyo.ac.jp
Abstract
This paper describes a new method for estimating theillumination distribution of a real scene from a radiancedistribution inside shadows cast by an object in the scene.
First, the illumination distribution of the scene is approximated by discrete sampling of an extended light source.
Then the illumination distribution of the scene is estimatedfrom a radiance distribution inside shadows cast by an object of known shape onto another object in the scene. Instead of assuming any particular reflectance properties ofthe surface inside the shadows, both the illumination distribution of the scene and the reflectance properties of thesurface are estimated simultaneously, based on iterative optimization framework. In addition, this paper introduces
an adaptive sampling of the illumination distribution of ascene. Rather than using a uniform discretization of theoverall illumination distribution, we adaptively increasesampling directions of the illumination distribution basedon the estimation at the previous iteration. Using the adaptive sampling framework, we are able to estimate overall
illumination more efficiently by using fewer sampling directions. The proposed method is effective for estimating an
illumination distribution even under a complex illumination
environment.

1 Introduction
Image brightness is a function of shape, reflectance, andillumination [4]. The relationship among them has provided three major research areas in physics-based vision:
shape-from-brightness (with a known reflectance and illumination) [6, 7, 8, 16], reflectance-from-brightness (with aknown shape and illumination) [9, 1, 11, 12, 15, 17], andillumination-from-brightness (with a known shape and reflectance).

In the past, shape-from-brightness and reflectance-frombrightness have been extensively explored. In contrast, relatively limited amounts of research have been conducted in
the third area, illumination-from-brightness [3, 14]. Some
researchers attacked this problem as a related analysis ofshape-from-shading. For example, Brooks and Horn determine shape as well as light sources from image brightness [7]. However, their analyses are conducted under very
specific illumination conditions as in, for example, the casewhere there is only one direct light source in the scene; theanalyses cannot be extended for more natural illumination
conditions that include many types of direct and indirect illumination.
Recently, we proposed a method to recover an illumination distribution of a scene from image brightness withknown shape and reflectance of an real object [19]. The
method modeled illumination distribution of the scene withdiscrete sampling of the illumination radiance distribution,then formulated them as a simultaneous linear equation of
unknown point sources. Then their brightness was determined by solving them from observed radiance changes inside shadows cast by an object of known shape onto another object surface of known shape and reflectance.1 Thismethod was effective and could estimate an illumination
distribution even under a complex illumination environment
such as an ordinary office, including reflections from thewall and other objects in the scene.
This method, however, has two limitations. First, it assumes that the reflectance properties of the surface insideshadows are given a priori. Otherwise, the method is applicable only if the surface is a Lambertian surface. Second,since the method uses a uniform discretization of the overall illumination for the estimation, the number of sampling
1 In the past, shadows have been used for determining the 3D shapes andorientations of an object which cast shadows onto the scene [2, 10, 13, 20],
while very few studies have focused on the the illumination information
which shadows could provide.

0-7695-0164-8/99 $10.00 (c) 1999 IEEE

directions of illumination tends to be exceedingly large inorder to accurately approximate the illumination distribution.

2 Formula for Relating Illumination Radiance with Image IrradianceThis paper presents a method to overcome these limitations. The solution consists of two main aspects. First,
we combine the illumination analysis with an estimationof the reflectance properties of a surface inside shadows.
As a consequence, the proposed method becomes applicable to the case where reflectance properties of a surface are
not known. This enlarges the variety of images to which
the method can be applied. Second, we propose an adaptive sampling framework for efficient estimation of illumination distribution. Rather than using a uniform discretization of the overall illumination distribution, we adaptively
increase the sampling directions of the illumination distribution based on the estimation at the previous iteration. Using this adaptive sampling framework, we can avoid unnecessarily dense sampling of the illumination and estimate
the entire illumination distribution more efficiently with asmaller number of sampling directions of the illumination
distribution.

In this section, we obtain a formula which relates an illumination distribution of a real scene with the image irradiance of a shadow image. The formula will later be used asa basis for estimating the illumination distribution of a realscene and reflectance properties of the shadow surface.

Our method estimates the illumination distribution of areal scene by using a single color image of the scene withshadows cast by an object. The rest of the paper refers to
the image with shadows as the shadow image, to the object which casts shadows onto the scene as the occluding
object, and to the surface onto which the occluding object
casts shadows as the shadow surface. In our experiments,
we recovered the camera parameters and the shape of theoccluding object by using a photo-modeling tool interactively.2
The rest of the paper is organized as follows. We firstobtain a formula which relates an illumination distributionof a scene with the image irradiance of the shadow image
in Section 2. In Section 3, we describe the basic steps ofthe proposed method for simultaneously estimating both anillumination distribution of a scene and reflectance properties of the shadow surface. In Section 4, we explain how
to estimate an illumination radiance distribution from given
reflectance parameters of the shadow surface and the observed image irradiance of a shadow image. In Section 5,
we describe how to estimate the reflectance parameters of
the shadow surface for a current estimation of the radiancedistribution of the scene. In Section 6, we introduce anadaptive sampling framework for efficient approximation of
the entire illumination. In Section 7, we show experimental
results of the proposed method applied to real images. In
Section 8, we present concluding remarks.
2 In our examples shown in Section 7, we used a modeling tool called
the 3D Builder from 3D Construction Company [22] for modeling theshape of an occluding object from a shadow image. At the same time,
the plane of z = 0 is defined on the shadow surface.

2.1 From Illumination Radiance to Scene IrradianceFirst, we find a relationship between the illumination distribution of a real scene and the irradiance at a surface pointin the scene. To take illumination from all directions into account, let us consider an infinitesimal patch of the extended
light source, of a size δθi in polar angle and δφi in azimuth
as shown in Figure 1.
Seen from the center point A, this patch subtends asolid angle δω = sinθi δθi δφi . Let L0 (θi , φi ) be theillumination radiance per unit solid angle coming fromthe direction (θi , φi ); then the radiance from the patch is
L0 (θi , φi )sinθi δθi δφi [5], and the total irradiance of thesurface point A is
Z π Z π2L0 (θi , φi )cosθi sinθi dθi dφi
(1)
E=
0

−π

Then occlusion of the incoming light by the occluding object is considered as
Z π Z π2L0 (θi , φi )S(θi , φi )cosθi sinθi dθi dφi (2)
E=
−π

0

where S(θi , φi ) are occlusion coefficients; S(θi , φi ) = 0 if
L0 (θi , φi ) is occluded by the occluding object; Otherwise
S(θi , φi ) = 1.

2.2 From Scene Irradiance to Scene RadianceSome of the incoming light at point A is reflected toward
the image plane. As a result, point A becomes a secondary
light source with scene radiance.
The bidirectional reflectance distribution function(BRDF) f (θi , φi ; θe , φe ) is defined as a ratio of the radiance of a surface as viewed from the direction (θe , φe )to the irradiance resulting from illumination from thedirection (θi , φi ). Thus, by integrating the product of
the BRDF and the illumination radiance over the entire
hemisphere, the scene radiance Rs(θe , φe ) viewed from thedirection (θe , φe ) is computed as
Z π Z π2f (θi , φi ; θe , φe )L0 (θi , φi )Rs(θe , φe ) =−π0-7695-0164-8/99 $10.00 (c) 1999 IEEE

0

S(θi , φi )cosθi sinθi dθi dφi

(3)

n

directional light sources. As a result, the double integral in
Equation 4 is approximated asnθ

P (θe , φe ) =δθiAf (θi , φi ; θe , φe )L(θi , φi )ωi S(θi , φi )cosθi

i=0

A

φ
(a)

n
X

(b)

δφi

Figure 1. (a) the direction of incident and emitted light rays (b) infinitesimal patch of an extended light source

2.3 From Scene Radiance to Image Irradiance
Finally, the illumination radiance of the scene is relatedwith image irradiance on the image plane. Since what we
actually observe is not image irradiance on the image plane,
but rather a recorded pixel value in a shadow image, it isalso necessary to consider the conversion of the image irradiance into a pixel value of a corresponding point in theimage. This conversion includes several factors such as D/A
and A/D conversions in a CCD camera and a frame grabber.
Other studies concluded that image irradiance was proportional to scene radiance [5]. In our work, we calibratea linearity of the CCD camera by using a Macbeth color
chart with known reflectivity so that the recorded pixel values also become proportional to the scene radiance of thesurface. From Equation 3 the pixel value of the shadow image P (θe , φe ) is thus computed as
Z π Z π2f (θi , φi ; θe , φe )L0 (θi , φi )P (θe , φe ) = k(5)
where n is the number of sampling directions, L(θi , φi ) is
the illumination radiance per unit solid angle coming fromthe direction (θi , φi ), which also includes the scaling factor
k between scene radiance and a pixel value, and ωi is a solid
angle for the sampling direction (θi , φi ).
For instance, node directions of a geodesic dome canbe used for uniform sampling of the illumination distribution. By using n nodes of a geodesic dome in a northernhemisphere as a sampling direction, the illumination distribution of the scene is approximated as a collection of directional light sources distributed with an equal solid angle
ω = 2π/n.
In our method, BRDF f (θi , φi ; θe , φe ) in Equation 5
is then parameterized using a simplified Torrance-Sparrowmodel [15, 21]. Using the model, the pixel value of the
shadow image P (θe , φe ), is computed as
P (θe , φe ) =

n
X
i=0

(Kd cosθi + Ks

−γ(θi ,φi )21
e 2σ2 )cosθr

S(θi , φi )L(θi , φi )ωi(6)

where k is a scaling factor between scene radiance anda pixel value. Due to the scaling factor k, we are able
to estimate unknown L0 (θi , φi )(i = 1, 2, .., n) up to scale.
To obtain the scale factor k, we need to perform photometric calibration between pixel intensity and physical unit
(watt/m2 ) for the irradiance.

where θr is the angle between the surface normal and theviewing direction, γ(θi , φi ) is the angle between the surface
normal and the bisector of the light source direction and theviewing direction, Kd and Ks are constants for the diffuse
and specular reflection components, and σ is the standard
deviation of a facet slope of the Torrance-Sparrow reflection
model.
Note that, since each pixel consists of 3 color bands (R,G, and B), each band of radiance L(θi , φi ) is also estimatedfrom the corresponding color band of the image separately.
Also, based on the dichromatic reflection model, five parameters (Kd,R , Kd,G , Kd,B , Ks , and σ) are considered as
the reflectance parameters of the shadow surface. Accordingly, L(θi , φi ) is estimated using Ks , σ, and the corresponding color band of Kd . In this paper, we explain our
method by using L(θi , φi ), Kd , Ks , and σ for the simplicity of our discussion.

2.4 Approximation of Illumination Distribution
with Discrete Sampling

3 Basic Steps of the Proposed Method

In an actual implementation of our method, the illumination distribution is approximated by discrete sampling ofradiance over the entire surface of the extended light source.
This can be considered as representing the illumination distribution of the scene by using a collection of imaginary

Based on the formula in Equation 6 which relates the illumination radiance of the scene with the pixel values of the
shadow image, the illumination radiance distribution of thescene is estimated from image brightness inside shadows as
described in the following steps.

−π0

S(θi , φi )cosθi sinθi dθi dφi(4)0-7695-0164-8/99 $10.00 (c) 1999 IEEE

1. Initialize the reflectance parameters of the shadow surface. Typically, we assume the shadow surface to be
Lambertian, and the diffuse parameter Kd is set to be
the pixel value of the brightest point on the shadow
surface. The specular parameters are set to be zero
(Ks = 0, σ = 0). 3

in real situations, we find through experiments that theseassumptions have little effect on estimated illumination distribution in most cases.
In the following sections, each step of the proposed
method will be explained in more detail.

2. Estimate radiance values L(θi , φi ) of imaginary directional light sources which model the illumination
distribution of a real scene. By using the reflectanceparameters (Kd , Ks , σ) and image brightness insideshadows in the shadow image, the radiance distribution L(θi , φi ) is computed. (Section 4)

4 Estimation of Radiance Distribution basedon Reflectance Parameters of Shadow Surface

3. Estimate the reflectance parameters of the shadow surface (Kd, Ks , σ) from the obtained radiance distribution of the scene L(θi , φi ) by using an optimization
technique. (Section 5)
4. Estimate the radiance distribution of the scene
L(θi , φi ) from the obtained reflectance parameters(Kd , Ks , σ). (Section 4)
5. Proceed to the next step if there is no significant
change in the estimated values L(θi , φi ), Kd , Ks , andσ. Otherwise, go back to Step 3. By estimating
both the radiance distribution of the scene and the reflectance parameters of the shadow surface iteratively,
we can obtain the best estimation of those values fora given set of sampling directions of the illumination
radiance distribution of the scene.
6. Terminate the estimation process if the obtained illumination radiance distribution approximates the realradiance distribution with sufficient accuracy. Otherwise, proceed to the next step.

In this section, we explain how to estimate the radiancedistribution of the scene L(θi , φi ) for a given set of reflectance parameters (Kd , Ks , σ). In the following sections,
we refer L(θi , φi ) as to Li for simplicity.
Using Equation 6 which relates the illumination radianceof the scene with the pixel values of the shadow image, illumination radiance is estimated based on the recorded pixel
values of the shadow image. From Equation 6, a linear
equation is obtained for each image pixel of the shadow image asa1 L1 + a2 L2 + a3 L3 + · · · + a1n Ln = P

where Li (i = 1, 2, .., n) are n unknown illumination radiance specified by n sampling directions of the radiance distribution for the scene. The coefficients ai (i = 1, 2, .., n)−γ(θi ,φi )2

1
represent (Kd cosθi + Ks cosθe 2σ2 )S(θi , φi ) (i =r1, 2, .., n); we compute θi , θr , γ(θi , φi ), and S(θi , φi ) basedon 3D geometry of the surface point corresponding to theimage pixel, the illumination direction, and the shape ofthe occluding object. P is the values of the image pixel
P (θe , φe ).
If we select a number of pixels, say m pixels, a set of
linear equations is obtained as

7. Increase the sampling directions of the illumination
distribution adaptively based on the obtained illumination radiance distribution L(θi , φi ) (Section 6). Thengo back to Step 2.

a11 L1 + a12 L2 + a13 L3 +· · · + a1n Ln= P1

a21 L1 + a22 L2 + a23 L3 +· · · + a2n Ln= P2

a31 L1 + a32 L2 + a33 L3 +· · · + a3n Ln

= P3

···

···

We should clarify the assumptions that we made for the
proposed method. In our method, it is assumed that lightsources in the scene are sufficiently distant from the objects,
and thus all light sources project parallel rays onto the object surface. Also, the method does not take into accountinterreflection between a shadow region and an occluding
object casting the shadow. We also assume that the shadow
surface has uniform reflectance properties over the entire
surface. Although these assumptions are not exactly true

am1 L1 + am2 L2 + am3 L3 +3 Note that the initial value of K is not so important since there is adscaling factor between the reflectance parameters and illumination radiance values in any case. To fix the scaling factor, we need to perform photometric calibration of our imaging system with a calibration target whosereflectance is given a priori.

(7)· · · + amn Ln= Pm (8)Therefore, by selecting a sufficiently large number of image pixels, we are able to solve for a unique solution set of
unknown Li ’s.
In general, the number of image pixels in shadows is farlarger than the number of illumination radiance values tobe estimated. Thus we need to select appropriate image
pixels for better computational efficiency. In our method,
image pixels are selected by considering their coefficients
ai so that the set of linear equations (Equation 8) becomes
sufficiently over determined by a smaller number of image
pixels.

0-7695-0164-8/99 $10.00 (c) 1999 IEEE

5 Estimation of Reflectance Parameters of
Shadow Surface based on Radiance Distribution
In this section, we describe how to estimate the reflectance parameters of the shadow surface (Kd , Ks , σ) byusing the estimated radiance distribution of the scene Li .
Unlike the estimation of the radiance distribution of thescene Li which can be done by solving a set of linear equations (Equation 8), we estimate the reflectance parametersof the shadow surface by minimizing a sum of squared difference between the observed pixel intensities in the shadow
image and pixel values for the corresponding surface points.
Hence the function to be minimized is defined asf=mX(Pj 0 − Pj )2

(9)

j=0

where Pj 0 is the observed pixel intensities in shadows castby the occluding object, Pj is the pixel value of the corresponding surface points computed by using the given radiance distribution of the scene Li in Equation 6, m is thenumber of pixels used for minimization. In our method,the error function in Equation 9 is minimized with respect
to the reflectance parameters Kd , Ks , and σ by the Powell method to obtain the best estimation of those reflectanceparameters.

6 Adaptive Sampling of Radiance Distribution
If the estimated radiance distribution for a set of sampling directions does not approximate the illumination distribution of the scene with sufficient accuracy, we increase
the sampling directions adaptively based on the current estimation of the illumination radiance distribution.
Radiance distribution changes very rapidly around a direct light source such as a fluorescent light. Therefore,
the radiance distribution has to be approximated by usinga large number of samplings so that the rapid change ofradiance distribution around a direct light source is captured. Also, to correctly reproduce soft shadows cast byextended light sources, radiance distribution inside a direct
light source has to be sampled densely.
On the other hand, coarse sampling of radiance distribution is enough for an indirect light source such as a wallwhose radiance remains small. As a result, the number ofsampling directions required for accurately estimating an illumination distribution of a real scene becomes exceedingly
large.
To overcome this problem, we increase sampling directions adaptively based on the estimation at the previous iteration, rather than by using a uniform discretization of theoverall illumination distribution. In particular, we increasesampling directions around and within direct light sources.
Based on the estimated radiance distribution Li for the
sampling directions at the previous step, additional sampling directions are determined as follows.
Suppose three sampling directions with radiance values
L1 , L2 , and L3 are placed to form a triangle M1 as illustrated in Figure 2. To determine whether a new sampling
direction needs to be added between L1 and L2 or not, weconsider the following cost function.
U (L1 , L2 ) = dif f (L1 , L2 ) + αmin(L1 , L2 )angle(L1 , L2 )(10)

where dif f (L1 , L2 ) is the radiance difference between L1and L2 , min(L1 , L2 ) gives the smaller radiance of L1 andL2 , angle(L1, L2 ) is the angle between directions to L1
and L2 , and α is a manually specified parameter which determines the relative weights of those two factors. The firstterm is required to capture the rapid change of radiance distribution around direct light sources, while the second term
leads to fine sampling of the radiance distribution inside direct light sources. The additional term angle(L1, L2 ) isused for avoiding unnecessarily dense sampling inside direct light sources. In our experiments, α is set to 0.5.
If the cost U is large, a new sampling direction is added
between L1 and L2 . In our experiments, we computed thecost function values U for all pairs of neighboring sampling
directions, then added additional sampling directions for the
first 50% of all the pairs in order of the cost function values
U.
L1

L3

M1

L1

Ln+1

L3

L2
L2

Figure 2. Subdivision of sampling directions

7 Experimental Results
We have tested the proposed method by using real images taken in both indoor and outdoor environments.
An image with an occluding object, i.e., shadow image, was taken under usual illumination environment inour office, including direct light sources such as fluorescentlamps, as well as indirect illumination such as reflections
from a ceiling and a wall. The input image is shown in Figure 3 (a).
First, the shape of the occluding object and the camera
parameters of the input image were obtained by using a0-7695-0164-8/99 $10.00 (c) 1999 IEEE

average error
24
22
20
18
16
14

(a)

(b)

12
10

Figure 3. Input image : (a) shadow image taken in an

8indoor scene (b) the region where synthesized images withthe estimated radiance distribution and reflectance parameters are superimposed in Figure 4

6
4
2
0

0

20

40

60

80

100

120

140

the number of samplings

Figure 5. Error Analysis

n = 20n = 40n = 80
(a)

(b)

(c)

n = 140

Figure 4. Adaptive refinement of illumination
distribution estimation: (a) synthesized images withthe estimated radiance distribution and reflectance parameters (b) adaptive refinement of sampling directions witha ground truth of an omni-directional image of the scene(c) the estimated radiance values visualized for comparison
with the ground truth

photo-modeling tool [22]. Then, an illumination distribution of the scene was estimated using the image irradianceinside shadows in the shadow image as explained in Section 3. Starting from a small number of uniform sampling
directions of the illumination distribution, the estimation of
the radiance distribution of the scene was iteratively refinedas described in Section 6. At the same time, the reflectanceparameters (Kd , Ks , and σ) of the shadow surface were estimated as explained in Section 5.
Then an appearance of the shadow surface around theoccluding object was synthesized by using the estimatedradiance distribution of the scene and the estimated reflectance parameters of the shadow surface. To demonstrate
how well the estimated radiance distribution and the reflectance parameters could represent the scene, we replaced
the region inside the red rectangle in Figure 3 (b) with thesynthesized appearances. The left column in Figure 4 shows
the results synthesized by the estimated radiance distribution and the estimated reflectance parameters of the shadow
surface. The number of sampling directions of the radiancedistribution used for the estimation is shown under the resulting images.
We found through our experiments that, the larger number of sampling directions we used, the more the shadows of
the synthetic object resembled those of the occluding object
in the shadow image. Especially in the case of 140 sampling directions, we can see hardly any distinct boundaries
in the shadows, and the synthesized shadow of the occluding object matches the real one in the input image very well:this shows that the estimated illumination distribution gives
a good presentation of that of the real scene.
To see how well the adaptive sampling of radiance distribution works for real images, we took an omni-directional

0-7695-0164-8/99 $10.00 (c) 1999 IEEE

image of the office scene as a ground truth. The middle column of Figure 4 shows the omni-directional image of thescene taken by placing a camera with a fisheye lens looking upward on the shadow surface in Figure 3 (a). The
omni-directional image shows both direct light sources, i.e.,
fluorescent lamps in our office, and indirect light sources
such as a ceiling and walls. The right column of Figure 4
shows the estimated radiance values visualized for comparison with the ground truth. In those images in Figure 4 (b)and (c), we can see that sampling directions of the radiance distribution were nicely added only around the direct
light sources at each step by the proposed adaptive samplingframework, starting from the coarse sampling directions at
the top row.
Figure 5 numerically shows the improvement of the accuracy by adaptive refinement of sampling directions andthe estimation of reflectance properties of the shadow surface. The vertical axis represents average error in pixel values inside the synthesized images in the region shown in
Figure 3 (b) compared with that in the input image Figure 3(a). Here, the initial average pixel values of shadow regionsin the shadow image are set to 100 %. The horizontal axis
represents the number of sampling directions used for theestimation. From the plot in the figure, we can clearly seethat the accuracy improves rapidly as we adaptively increasesampling directions of the radiance distribution. Also thesmall pictures at the bottom show error distributions inside
the region. Darker color represents larger error in a pixel
value in the shadow regions compared with the real shadows of the occluding object in the shadow image.
To confirm the merit of the adaptive sampling framework and the estimation of the reflectance parameters of the
shadow surface, we also estimated the illumination radiancedistribution with uniform sampling and fixed reflectance parameters. In that case, even 300 uniformly sampled directions could not achieve the same level of accuracy as theestimation result obtained by 80 sampling directions withthe method proposed in this work.
Figure 6 (a) shows another example image taken outside
the entrance lobby of our building in the late afternoon. In
this image, we used the rectangular pole with two colors as
an occluding object casting shadows. In the same way as theprevious example, the shape of the occluding object and thecamera parameters of the input image were obtained by using a photo-modeling tool. Then, an illumination distribution of the scene was estimated using the image irradianceinside shadows in the input image as explained in Section 3.
Then an appearance of the shadow surface around theoccluding object, illustrated with a red rectangle in Figure 7(b), was synthesized by using the estimated radiance distribution of the scene and the estimated reflectance parameters of the shadow surface [18]. Figure 7 shows the result-

(a)

(b)

Figure 6. Input image : (a) shadow image taken in
an outdoor scene (b) the region where synthesized images
with the estimated radiance distribution and reflectance parameters are superimposed in Figure 7

n = 20n = 40n = 80n = 140

Figure 7. Adaptive refinement of illumination
distribution estimation: synthesized images with theestimated radiance distribution and reflectance parametersing images by our method. Although the grid pattern on
the shadow surface is missing in those synthesized images
due to the assumption of uniform reflectance on the shadow
image, the appearance of the shadow around the occluding
objects is virtually indistinguishable in the case of 140 sampling directions. This shows that the estimated illumination
distribution gives a good representation of the characteristics of the real scene.

8 Conclusions
In this paper, we have proposed a new method for estimating an illumination distribution of a real scene from aradiance distribution inside shadows cast by a real object

0-7695-0164-8/99 $10.00 (c) 1999 IEEE

of known shape onto other object surfaces of known shapeand known reflectance. By using the occlusion informationof the incoming light, we were able to estimate an illumination distribution of a real scene reliably, even for the images
taken in a complex illumination environment.
In particular, the proposed method has been significantly
extended from our previous approach in two main aspects.
First, we combine the illumination analysis with an estimation of the reflectance properties of a shadow surface. As
a consequence, the proposed method becomes applicable tothe case where reflectance properties of a surface are notknown. Second, we propose an adaptive sampling framework for efficient estimation of illumination distribution.
Rather than using a uniform discretization of the overall
illumination distribution, we adaptively increase the sampling directions of the illumination distribution based on
the estimation at the previous iteration. Using this adaptive sampling framework, we can avoid unnecessarily dense
sampling of the illumination and estimate the entire illumination distribution more efficiently with a smaller numberof sampling directions of the illumination distribution.
To demonstrate the effectiveness of the proposed
method, we have successfully tested our method by using
sets of real images taken in our office with different surface
materials of shadow regions.

Acknowledgments
This research was supported by the Ministry of Education, Science, Sports and Culture grant-in-Aid for Creative
Basis Research 09NP1401.

References[1] R. Baribeau, M. Rioux, and G. Godin, “Color Reflectance
Modeling Using a Polychromatic Laser Range Sensor,”IEEE Trans. PAMI, vol. 14, no. 2, pp. 263-269, 1992.
[2] J. Bouguet and P. Perona, “3D Photography on Your Desk,”
Proc. IEEE Intl. Conference on Computer Vision 98, pp.4350, 1998.
[3] A. Fournier, A. Gunawan and C. Romanzin, “Common Illumination between Real and Computer Generated
Scenes,”Proc. Graphics Interface ’93, pp.254-262, 1993.

[7] B. K. P. Horn and M. J. Brooks, “The Variational Approachto Shape from Shading,” Computer Vision, Graphics, andImage Processing, 33(2), pp.174-208, 1986.
[8] K. Ikeuchi and B. K. P. Horn, “Numerical Shape from Shading and Occluding Boundaries,” Artificial Intelligence 17(13), pp.141-184, 1981.
[9] K. Ikeuchi and K. Sato, “Determining Reflectance using
Range and Brightness Images,” Proc. IEEE Intl. Conference
on Computer Vision 90, pp.12-20, 1990.
[10] J. R. Kender and E. M. Smith, “Shape from Darkness: Deriving Surface Information from Dynamic Shadows,” Proc.
IEEE Intl. Conference on Computer Vision 87, pp.539-546,
1987.
[11] G. Kay and T. Caelli, “Estimating the Parameters of an Illumination Model using Photometric Stereo,”Graphical Models and Image Processing, vol. 57, no. 5, pp. 365-388, 1995.
[12] J. Lu and J. Little, “Reflectance Function Estimation andShape Recovery from Image Sequence of a Rotating Object,”Proc. IEEE Intl. Conference on Computer Vision ’95,
pp. 80-86, 1995.
[13] A. K. Markworth, “On the Interpretation of Drawings as
Three-Dimensional Scenes,” PhD thesis, University of Sussex, 1974.
[14] S. R. Marschner and D. P. Greenberg, “Inverse Lighting for
Photography,” Proc. IS&T/SID Fifth Color Imaging Conference, pp.262-265, 1997.
[15] S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflection:
physical and geometrical perspectives,” IEEE Trans. PAMI,
vol. 13, no. 7, pp. 611-634, 1991.
[16] A. P. Pentland, “linear Shape From Shading,” Intl. J. Computer Vision, 4(2), pp153-162, 1990.
[17] Y. Sato, M. D. Wheeler, and K. Ikeuchi, “Object shape andreflectance modeling from observation,” Proc. SIGGRAPH
97, pp. 379-387, 1997.
[18] I. Sato, Y. Sato, and K. Ikeuchi, “Acquiring a Radiance Distribution to Superimpose Virtual Objects onto a Real Scene”,
IEEE Trans. Visualization and Computer Graphics, vol. 5,
no. 1, pp. 1-12, 1999.
[19] I. Sato, Y. Sato, and K. Ikeuchi, “Illumination from Shadows”, Proc. IEEE Conference on Computer Vision and Pattern Recognition 99, pp.306-312, 1999.

[4] B. K. P. Horn,“Understanding Image Intensities,” Artificial
Intelligence, 8(2), pp.201-231, 1977.

[20] S. A. Shafer and T. Kanade, “Using Shadows in Finding Surface Orientations,” Computer Vision, Graphics, and Image
Processing, 22(1), pp. 145-176, 1983.

[5] B. K. P. Horn, Robot Vision, The MIT Press, Cambridge,
MA., 1986.

[21] K. E. Torrance and E. M. Sparrow, “Theory for off-specularreflection from roughened surface,” J. Optical Society ofAmerica, vol.57, pp.1105-1114, 1967.

[6] B. K. P. Horn, “Obtaining Shape from Shading Information,” The psychology of Computer Vision, McGraw-Hill
Book Co., New York, N.Y., 1975.

[22] 3D
Construction
http://www.3dcomstruction.com

0-7695-0164-8/99 $10.00 (c) 1999 IEEE

Company,