Acquiring Multispectral Light Transport
Using Multi-Primary DLP Projector
Kayano Maeda1 and Takahiro Okabe1
1 Department of Artificial Intelligence

Kyushu Institute of Technology
e-mail: okabe@ai.kyutech.ac.jp

Abstract— Acquiring the light transport (LT) of a scene isimportant for various applications such as radiometric analysis,
image-based relighting, and controlling appearance of the scene.
The multispectral LT, i.e. the LT in multiple primary colors
enables us not only to enhance the color gamut but also toinvestigate wavelength-dependent interactions between light anda scene. In this paper, we propose a method for acquiring themultispectral LT by using a single off-the-shelf multi-primary
DLP (Digital Light Processing) projector; it does not require
any self-built equipment, geometric registration, and temporalsynchronization. Specifically, based on the rapid color switch
due to a rotating color wheel in the projector, we present a
method for estimating the spectral properties of the projector
in a non-destructive manner, and a method for acquiring theimages of a scene illuminated only by one of the primary colors.
We conducted a number of experiments by using real images,
and confirmed that our method works well and the acquired
multispectral LT is effective for radiometric analysis and imagebased relighting.
Keywords— Light Transport, Multispectral Imaging, DLP Projector, Color Switch, Reverse Engineering

I. I NTRODUCTION
The relationship between the lighting conditions illuminating a scene and its images taken under those lighting
conditions is called light transport (LT). The LT describes
how the light radiated from a light source interacts with ascene before arriving at a camera. Acquiring the LT of ascene is important for various applications such as radiometricanalysis [10], [8], [4], image-based relighting [13], [16], [17],and controlling appearance [14], [3], [1] of the scene.
Conventionally, the LT of a scene is acquired by using
projectors or displays with three primary colors, i.e. RGB.
Unfortunately, however, such sampling in the spectral domain
is sparse because the interactions between light and a scene
often depend on the wavelength of light. If we can acquire
the multispectral LT, i.e. the LT in 𝑁 (> 3) primary colors,
it enables us to investigate the interactions highly dependent
on the wavelength such as refraction, diffraction, interference,scattering, and fluorescence. In addition, multi-primary lightsources enhance the color gamut, and therefore make imagebased relighting and controlling appearance more accurate.
Accordingly, we propose a method for acquiring the multispectral LT of a scene by using a single off-the-shelf projector.
Specifically, we use a single-chip multi-primary DLP (Digital
Light Processing) projector in which a color wheel consistingof multiple color filters with different spectral transmittances

978-1-4673-8910-5/16/$31.00 ©2016 IEEE

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Fig. 1. (a) A color wheel consisting of multiple color filters with different
spectral transmittances. (b) A scene where wavelength-dependent interactionsof light are observed. See Fig. 7 for the results of direct-global separation.

as shown in Fig. 1 (a) is placed between a white light source
and a DMD (Digital Micromirror Device). The color wheel
rotates at high speed in front of the light source, and generates
various colors by mixing the transmitted lights with different
SPDs (Spectral Power Distributions) via time-division multiplexing.
Compared with the existing technique [18] using multiple
projectors with different three primary colors, the advantage ofour proposed method using a single projector is that ours does
not require geometric registration and temporal synchronization. In addition, compared with the existing techniques [18],[11], [7], [6] using self-built equipments, our method using a
consumer projector does not require such an equipment andis easy to implement. On the other hand, the use of an offthe-shelf multi-primary DLP projector has some issues to beaddressed. In order to acquire the multispectral light transport
by using the projector, its spectral properties such as the SPDsof the 𝑁 primary colors are necessary. Unfortunately, however,those properties of consumer DLP projectors are not publicly
available.
To cope with this problem, our proposed method exploits
the rapid color switch due to the rotating color wheel of asingle-chip DLP projector that is observed when the output
light is captured by a sensor with a short integration time.
Specifically, we estimate the SPDs of the 𝑁 primary colors in a
non-destructive manner by using a spectral sensor with a short
exposure time, and acquire the images of a scene illuminatedonly by one of the primary colors by using a color camera witha short exposure time. We conducted a number of experiments
using real images, and confirmed that our method works well.
In addition, we showed that the acquired multispectral LT
is effective for multispectral separation of direct and global

components and image-based spectral relighting.
The main contribution of this study is threefold. First, we
propose an easy-to-implement method based on a single consumer multi-primary DLP projector for acquiring multispectral
LT; it does not require any self-built equipment, geometricregistration, and temporal synchronization. Second, based on
the rapid color switch due to the rotating color wheel, we
propose a method for estimating the spectral properties of the
projector in a non-destructive manner. Third, we propose a
simple method for acquiring the images of a scene illuminatedonly by one of the primary colors on the basis of the color
switch, and show that the acquired multispectral LT is effective
for radiometric analysis and image-based relighting.
II. R ELATED W ORK
In this section, we briefly describe the relationship between
our proposed method and related work, in particular, researchusing multi-primary light sources and research on reverse
engineering of DLP projectors.
A. Multi-Primary Light Sources
Yamaguchi et al. [18] propose a 6-primary projection
display by using two 3-primary projectors in which color
filters are inserted so that the three primary colors of one
projector are different from those of the other projector. Theyshow that the proposed display has wider color gamut thanconventional three-primary projectors. Unfortunately, however,their method using multiple projectors requires cumbersome
geometric registration and temporal synchronization.
Kauvar et al. [7] propose an adaptive color display by usinga three-primary projector. The proposed display dynamicallychoose the three primary colors by combining 6 LEDs withdifferent SPDs in a context-adaptive and user-centric manner.
Hirai et al. [6] also propose a 6-primary projector by combining a programmable light source in the spectral domain and a
DMD for modulating light intensity in the spatial domain.
Park et al. [11] propose a method for recovering the spectralreflectance of an object of interest by using multi-primary
LED clusters. In order to reduce the number of images
required for the spectral reflectance recovery, they make useof the multiplexed illumination in the spectral domain andthe low-dimensional linear model for spectral reflectance [12].
They show that the proposed method achieves the spectralreflectance recovery of a moving object at 30 fps.
Compared with the above techniques, our proposed method
does not require any self-build equipment. Therefore, our setup
using only an off-the-shelf DLP projector is easy to implement.
B. Reverse Engineering of DLP Projectors
Narasimhan et al. [9] propose an approach to fast active
vision by using a DLP projector. The DMD in a DLP projector
controls the intensity of emitted light from the projector byswitching mirrors “on” and “off” at high speed. They exploit
such temporal dithering of illumination captured by using ahigh-speed camera. They show that the temporal dithering isuseful for various applications such as structured light-based
range finding, photometric stereo, separating direct and global
components and so on. In our study, we focus more attention
on the color switch and does not explicitly take the temporaldithering into consideration.
Han et al. [5] propose a method for recovering the spectralreflectance of a moving object by using a three-primary DLP
projector. Specifically, they rapidly change the lighting colors
illuminating the object on the basis of the color switch, andcapture its images by using a high-speed camera. They also
make use of the low-dimensional model for spectral reflectanceand show that the proposed method achieves the spectralreflectance recovery of a moving object at 100 fps.
Our proposed method is similar to Han et al. [5] in thesense that we also make use of the color switch. However,
the reverse engineering of the multi-primary DLP projector is
far more difficult than that of a three-primary DLP projector;
we can directly measure the SPDs of the latter three primarycolors by setting the projector input to (𝑅, 𝐺, 𝐵) = (255, 0, 0),(0, 255, 0), and (0, 0, 255), but cannot measure the SPDs of
the former multi-primary colors. This is because the mappingfrom the projector input (3-D) to the projector output (𝑁 D) is non-trivial when 𝑁 > 3 as described in Section III.A.
Therefore, the reverse engineering proposed in the next section
is necessary. In addition, our method uses a regular-frameratecamera with a short exposure time instead of an expensive
high-speed camera.
III. P ROPOSED M ETHOD
In this section, we propose a method for acquiring themultispectral LT by using a multi-primary DLP projector. First,
we describe the color generation model of single-chip multiprimary DLP projectors. Second, we present a method for
estimating the spectral properties of the multi-primary DLP
projectors in a non-destructive manner. Third, we present a
method for acquiring the multispectral LT, i.e. the LT per
primary color.
A. Color Generation Model
As described in Introduction, in a single-chip multi-primary
DLP projector, a color wheel consisting of multiple color
filters with different spectral transmittances rotates at highspeed, and generates various colors by mixing the transmitted
lights with different SPDs via time-division multiplexing.
Let us denote the number of color filters, i.e. the number ofthe primary colors by 𝑁 (> 3) and the SPDs of those primarycolors by 𝑝𝑛 (𝜆) (𝑛 = 1, 2, 3, ..., 𝑁 ). Here, 𝜆 is the wavelengthof light. When we observe the emitted light from the projector
with a certain exposure time, its SPD 𝑙(𝜆) integrated over thetime is represented by a convex combination of those of the
primary colors as𝑙(𝜆) =

𝑁∑𝑛=1

𝑐𝑛 𝑝𝑛 (𝜆).

(1)Here, 𝑐𝑛 (≥ 0) are the mixing coefficients of the primarycolors. If the exposure time is long enough so that no color
switch is observed, the mixing coefficients are determined by
the RGB value input to the projector. Note that the mappingfrom the RGB value (3-D) to the mixing coefficients (𝑁 -D)
is non-trivial and difficult to estimate when 𝑁 > 3.
The acquisition of the multispectral LT is easy if the spectral
properties of a multi-primary DLP projector such as the SPDs𝑝𝑛 (𝜆), the mixing coefficients 𝑐𝑛 , and the mapping function
are known. Unfortunately, however, those properties of consumer DLP projectors are not publicly available. Accordingly,
in the next two subsections, we present a method for estimating
the SPDs of the primary colors and a method for acquiring themultispectral LT on the basis of the rapid color switch due toa rotating color wheel.
B. Estimating SPDs of Primary Colors
We use a white image as the input to a multi-primary
DLP projector1 , and illuminate a white target object such as awhite balance reflectance target. Then, we observe the reflected
light on the target object by using spectral sensors such as aspectrometer and a hyperspectral camera. The key idea of our
proposed method is that, when the integration time of sucha sensor is short enough, e.g. 0.1 ms, we should observe thelight transmitting only one of the color filters of a color wheel.
Therefore, when we plot a number of SPDs, each of which
is observed with a short exposure time, in a certain space,
we should see some clusters; the number of clusters is equal
to the number of the primary colors and the center of eachcluster corresponds to the SPD of each primary color. Hence,
we can estimate the SPDs of the primary colors 𝑝𝑛 (𝜆) (andthe number of primary colors 𝑁 if necessary) by clustering
the observed SPDs.
In our experiments, we map the observed SPDs to the CIE
xy chromaticity space. We use the mean shift clustering [2]for estimating the cluster centers in that space.
C. Acquiring Multispectral Light Transport
In a similar manner to the above, we use a white image as
the input to a multi-primary DLP projector, and illuminate ascene and a white target object at the same time. Then, we
capture their images by using a color camera with a short
exposure time.
For the same reason as described above, when we plot a
number of RGB values, each of which is observed on thewhite target object, in a certain space, we should see someclusters; the number of clusters is equal to the number of the
primary colors and the center of each cluster corresponds tothe observed RGB value of each primary color. Therefore,
we can see that the image of the scene corresponding to
the cluster center is captured when it is illuminated only by
the corresponding primary color. Thus, we can acquire the
1 We assume that all of the primary colors are used when we set the projector
input to (255,255,255).

Fig. 2. The closeups of the captured hyperspectral image of a white balance
reflectance target at various wavelengths; 450, 500, 550, 600, and 650 nm
from left to right.

multispectral LT by using a consumer multi-primary DLP
projector.
In our experiments, we map the observed RGB values tothe rg chromaticity space, where 𝑟 = 𝑅/(𝑅 + 𝐺 + 𝐵) and
𝑔 = 𝐺/(𝑅 + 𝐺 + 𝐵). We use the mean shift clustering [2] for
estimating the cluster centers in that space.
Note that we need to capture 𝑀 (≫ 𝑁 ) images so that allof the 𝑁 primary colors are observed. Taking the samplingin the spatial domain into consideration, we denote the spatial
resolution of the LT, i.e. the number of the projector pixels(or patches) in our case, by 𝑆. We need to capture 𝑆 × 𝑀
images in total although the exposure time per image is shortenough. We can use the multiplexed illumination [15] in thespatial domain if necessary.
IV. E XPERIMENTS
In this section, we show the SPDs of the primary colors andthe images of a scene illuminated by those primary colors2
estimated on the basis of the rapid color switch. In our
experiments, we tested two off-the-shelf projectors; an NPVE282 from NEC and an MS524 from BenQ.
A. SPDs of Primary Colors
We used a white image as the input to the projector from
NEC, and illuminated a white balance reflectance target. Then,
we captured an image of the target by using a hyperspectral
camera from EBA Japan3 with an exposure time of 0.1 ms.
Fig. 2 shows the captured hyperspectral image of the target
at various wavelengths. Because this camera is based on aline scanner, different rows of the image have different timestamps. Therefore, a number of SPDs of the emitted lightfrom the projector at different time are included in the single
hyperspectral image.
We converted those SPDs into the CIE XYZ values, andplotted them as shown in Fig. 3 (a). We can see that there
are 6 linear clusters, i.e. the projector has 6 primary colors; it
is consistent with the specification document of the projector.
The reason why the clusters’ shapes are not spherical but linear
is that the intensity of the emitted light from the projector ismodulated by temporal dithering. In addition, we can see some
2 Due to limited space, we focus on the LT in the spectral domain anddo not consider the LT in the spatial domain, i.e. we illuminate a scene byspatially uniform lighting. See Section V.A for spatially nonuniform lighting.
3 As described in the previous section, we can use other spectral sensors
such as a spectrometer.

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filters next to each other within the exposure time.
Then, we converted the above SPDs into the CIE xy values,
and plotted them as shown in Fig. 3 (b). Similar to Fig. 3(a), it is clear that there are 6 clusters, in other words, theprojector has 6 primary colors. Here, ∘ stands for the centerof the cluster computed by using the mean-shift clustering
under the assumption of 𝑁 = 6. Fig. 3 (c) shows the SPDscorresponding to the cluster centers. We can see that thoseSPDs corresponds to 6 primary colors; Red, Green, Blue,
Cyan, Yellow, and White from upper left to lower right.
The experimental results on the projector from BenQ are
shown in Fig. 4. Fig. 4 (a) and (b) show that the projector has
6 primary colors and Fig. 4 (c) shows that the primary colors
are R, G, B, C, Y, and W. Those results are consistent withthe color wheel shown in Fig. 1 (a), that was taken from the
projector in a destructive manner.
B. Multispectral Light Transport
In a similar manner to the above, we used a white image as
the input to the projector from NEC, and illuminated a scene
and a white target object at the same time. Then, we captured
their images by using a color camera FL3-U3-13E4C-C from
Point Grey with an exposure time of 0.1 ms. Because thiscamera has a global shutter, all pixels in a single image has
the same time stamp.
We captured 1000 images and plotted the RGB and rg values
observed on the white target in Fig. 5 (a) and (b) respectively.

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Fig. 3. Reverse engineering of a projector NP-VE282 from NEC; (a) the
CIE XYZ and (b) xy values converted from the observed SPDs. A whitebalance reflectance target illuminated by the projector was captured by usinga hyperspectral camera. (c) The estimated SPDs of the 6 primary colors; R,
G, B, C, Y, and W from upper left to lower right.

(b)Fig. 4.

Reverse engineering of a projector MS524 from BenQ.

Those results are consistent with those using a hyperspectral
camera; the projector has 6 primary colors. Here, ∘ stands forthe center of the cluster computed by using the mean-shift
clustering under the assumption of 𝑁 = 6.
Fig. 5 (c) shows the images of a scene illuminated by the 6
primary colors; R, G, B, C, Y, and W from upper left to lower
right. Here, the white target (left) and an X-Rite ColorChecker
Passport (right) were captured at the same time. This result
qualitatively shows that the proposed method works well. Notethat the scales between the estimated SPDs shown in Fig. 3 (c)and the acquired images shown in Fig. 5 (c) are adjusted byusing the spectral sensitivity of the color camera calibrated inadvance.
The experimental results on the projector from BenQ are
shown in Fig. 6. Fig. 6 (a) and (b) show that the projector has 6
primary colors and Fig. 6 (c) shows that the proposed method
works well for capturing the images of a scene illuminatedby the 6 primary colors. Interestingly, in Fig. 6 (a), we canclearly observe some paths between two clusters caused bylight passing through two color filters next to each other within
the exposure time. We can see that the order of the color filtersin the color wheel is R, G, B, C, W, and Y; it is also consistent
with the color wheel shown in Fig. 1 (a).
V. A PPLICATIONSIn this section, we show two applications of our proposed
method; one is multispectral separation of direct and global
components and the other is image-based spectral relighting.
A. Multispectral Separation of Direct and Global Components
We can combine our proposed method with the separationof direct and global components of a scene by using high-

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Fig. 5. Multispectral LT using a projector NP-VE282 from NEC; (a) the
RGB and (b) rg values of a white balance reflectance target illuminated by
the projector and captured by using a color camera. (c) The images of a scene
illuminated by the 6 primary colors; R, G, B, C, Y, and W from upper left tolower right.

frequency illumination in the spatial domain [10], and achieve
the direct-global separation in multi-primary colors. Specifically, we used a set of shifted checkerboard illumination
patterns in black and white for the input to a projector,
and acquired the images of a scene illuminated by thecheckerboard patterns in multi-primary colors as shown in
Fig. 7 (a). Here, we used 4 checkerboard patterns and theircomplementary ones for stably separating direct and global
components although some artifacts are still visible.
Fig. 7 (b) and (c) show the direct and global components ofthe scene respectively. Interestingly, the direct components ofa toy gun and a tennis ball, in particular those under blue
light (upper right) show that they are made of fluorescentmaterials; they absorb the light with certain wavelengths andemit the light with different (longer) wavelengths [19]. The
global components include subsurface scattering of the toygun, interreflections between the tennis ball and a floor, and soon. More importantly, we can observe that the light refracted
by a prism appears at different positions according to thewavelength of light since the refraction coefficient depends
on the wavelength.
B. Image-Based Spectral Relighting
We can use the SPDs of the primary colors and the imagesof a scene under the primary colors acquired by using our
proposed method for image-based spectral relighting. Specifically, we synthesized the image of the scene under a novel
illuminant SPD by linearly combining those images under the

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Fig. 6.

Multispectral LT using a projector MS524 from BenQ.

primary colors. Here, the coefficients of the linear combinationis computed from the SPDs of the primary colors and the novel
illumination.
Fig. 8 shows (a) the images of pastels under the primarycolors, (b) the images under a fluorescent lamp, and (c) thoseunder an incandescent lamp respectively. The RMS errors of
the synthesized images in the rgb chromaticity space are shownin Table 1. Those results show that the spectral relighting
using multi-primary colors (𝑁 = 6) works better than theconventional one using three primary colors (𝑁 = 3), but thedifference between them is not so large. This is because theSPD of C (Y) is similar to those of B+G (G+R) in the low-end
consumer projectors used in our experiments. Emphasizing thedifference between the SPDs of the primary colors by using
bandpass filters in front of the projector for example is one of
the future directions of our study.
VI. C ONCLUSION AND F UTURE W ORK
In this paper, we proposed a method for acquiring themultispectral LT by using a single off-the-shelf multi-primary
DLP projector on the basis of the rapid color switch due
to a rotating color wheel in the projector. We conducted
a number of experiments and confirmed that our proposed
method works well and the acquired multispectral LT iseffective for radiometric analysis and image-based relighting.
Our future study includes the enhancement of the SPDs of the
primary colors.
ACKNOWLEDGMENTS
This work was supported by Support Center for Advanced
Telecommunications Technology Research (SCAT) and JSPS

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Fig. 8. Image-based spectral relighting; (a) the images of pastels under the
primary colors, i.e. R, G, B, C, Y, and W from upper left to lower right,(b) the images under a fluorescent lamp, and (c) those under an incandescentlamp. In (b) and (c), the ground truth, the synthesized images when 𝑁 = 6
and 𝑁 = 3 are shown from left to right.
Table 1. The RMS errors of the synthesized images using 𝑁 primary colors.

(b)

(c)
Fig. 7. Multispectral direct-global separation; (a) the acquired images ofa scene illuminated by high-frequency illumination patterns in multi-primarycolors, (b) the direct and (c) the global components of the scene in multiprimary colors. R, G, B, C, Y, and W from upper left to lower right.

KAKENHI Grant Number JP16H01676.
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