Image-Based Relighting with 5-D Incident Light Fields
Shinnosuke Oya
Takahiro Okabe
Kyushu Institute of Technology
680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japanokabe@ai.kyutech.ac.jp

Abstract
In this paper, we propose a method for image-based relighting with 5-D incident light fields: 4 DoF of the positionand direction and 1 DoF of the color of an incident ray.
Specifically, we illuminate a scene with various rays by using a two-layer 5 DoF lighting system consisting of a rearprojection display and a transmissive LC panel, and synthesize images under desired 5-D incident light fields by combining the images captured under those rays. Our proposed
method efficiently acquires the required images by using
coded illumination; it reduces the number of captured images and the measurement time, and enhances their SNRs.
In addition, we propose a method for removing the effectsof the black offsets due to the projector and the LC panelin the two-layer setup. The experimental results using theprototype system show that our method enables us to synthesize photo-realistic images of scenes where wavelengthdependent phenomena such as fluorescence are observed.

1. Introduction
Image-based relighting (IBRL) [3] is a technique forsynthesizing images of a scene under novel lighting environments by linearly combining the images of the scene
captured under various illumination conditions on the basis of the superposition principle of illumination. Although
IBRL requires a large number of captured images in general, it enables us to synthesize photo-realistic images since
it directly synthesizes novel images from real images without intervening the geometric and photometric modeling of
the scene.
In the real world, rays with various wavelengths (colors) propagate from various positions to various directions.
Such a lighting environment is called a light field [1], andthe amount of ray is described by a 6-D plenoptic function
with respect to the position (x, y, z), direction (θ, φ), andwavelength λ under the assumption of static scenes and unpolarized rays. The light field in clear media is described

Figure 1. The synthesized images of the first scene by using our
proposed method with various 5-D incident light fields.

by a 5-D plenoptic function. This is because the radiancealong a ray remains constant due to negligible absorption
and scattering, and then one degree of freedom (DoF) in theposition and direction of a ray is redundant.
Unfortunately, however, the conventional methods for
IBRL illuminate a scene with low-dimensional slices of 5-D
incident light fields. A light stage-based approach [3, 4], adisplay-based approach [19, 18], and a projector-based approach [20, 24] control the 2-D positions or the 2-D directions (and the 1-D colors) of incident rays. Therefore, they

Figure 2. A sketch (top) and a prototype (bottom) of a two-layer 5
DoF lighting system consisting of a rear-projection display and atransmissive LC panel.

cannot synthesize images under 5-D incident light fields,
which include point light sources at varying positions andwith varying angular profiles and their combinations for example. The existing method for IBRL with 4-D incident
light fields [15] controls both the 2-D positions and 2-D directions of incident rays by using a moving projector, butdoes not take their colors into consideration. Therefore,
it cannot synthesize images of scenes where wavelengthdependent phenomena such as fluorescence are observed asshown in Figure 10 (e) and Figure 11 (e). Note that fluorescent materials emit light with longer wavelengths than thoseof absorbed light [8, 22, 26]. It is reported that fluorescentmaterials are common and present in 20% of randomly constructed scenes [2].
Accordingly, we propose a method for IBRL with 5-D
incident light fields: 4 DoF of the position and direction and
1 DoF of the color of an incident ray (see the synthesizedimages in Figure 1 and Figure 12 and the supplementary
video1 ). Specifically, we use a two-layer 5 DoF lighting system consisting of a rear-projection display and a transmissive liquid crystal (LC) panel as shown in Figure 2, and illuminate a scene by rays propagating from various positions
to various directions with various colors. Then, novel images of the scene under desired 5-D incident light fields aresynthesized by combining the images of the scene captured
under those rays. Our proposed method enables us to synthesize images under rays not only from various positions
to various directions but also with various colors. The DoFof the color is important for synthesizing images of scenes
where wavelength-dependent phenomena such as fluorescence are observed as shown in Figure 10 (f) and Figure 11(f).
IBRL using the 5 DoF lighting system has two diffi1 https://www.dropbox.com/s/0gkwykv1jx9ws10/supplementary video.
mp4?dl=0

culties; one is that a large number of captured images are
required due to high DoF of the lighting system, and theother is that the signal-to-noise ratios (SNRs) of the captured images are small because the radiance of each ray issmall. To cope with those difficulties, our proposed method
efficiently acquires the required images by using coded illumination, which is used also for image acquisition [19],separating direct and global components [16], shape recovery [13], reflectance recovery [5, 17, 10], and material classification [12, 23]. Specifically, our method reduces thenumber of captured images by generating multiple rays that
do not interfere each other at the same time, and enhances
the SNRs on the basis of multiplexed illumination [19].
In addition, the lighting system using a projector and an
LC panel has the problem of black offset; they are not able
to generate perfect black, even though we set the input tothe projector and/or the transmittance of the LC panel to
0. The problem is serious because the offset due to each“black” ray is small but the number of the rays is large.
Accordingly, we reveal how the offsets of the projector andthe LC panel propagate to the images captured by using thetwo-layer setup, and then propose a method for removing
the effects of those offsets from them.
The main contribution of this study is threefold. First,
we achieve IBRL that can synthesize images under desired
5-D incident light fields, i.e. rays propagating from various positions to various directions with various colors. We
show that our proposed method enables us to synthesize
photo-realistic images of scenes which contain fluorescentmaterials. Second, we propose an efficient method for acquiring the required images by using coded illumination.
Our method reduces the number of captured images andthe required time for measurement, and enhances the SNRs.
Third, we reveal the relationship between the black offsetsof the projector and the LC panel and the images captured
by using the two-layer setup, and then remove the effects of
the offsets from them.
The rest of this paper is organized as follows. We briefly
summarize related work in Section 2. A method for IBRL
with 5-D incident light fields by using a two-layer 5 DoF
lighting system is proposed in Section 3. We report the experimental results in Section 4 and present concluding remarks in Section 5.

2. Related work
3D display:
A number of methods for generating desired light fields
have already been proposed in the context of 3D display.
For example, Lanman et al. [11] propose a 3D display basedon the parallax barriers using a two-layer LC panel, andWetzstein et al. [25] extend it by using a multi-layer LC
panel and uniform or directional backlighting. Hirsch etal. [7] propose a large-scale 3D display by combining a lightfield projector and an angle-expanding screen.
Whereas the objective of the above methods is glassesfree 3D display, i.e. generating light fields so that users viewthe displayed content stereoscopically in real time, our objective is IBRL, i.e. illuminating a scene by various rays andcombining the images under those rays afterward. Therefore, the methods for glasses-free 3D display are not suitedfor IBRL. Specifically, the dynamic range of the light fields
generated by those methods is limited because the numberof images used for temporal multiplexing in real time is limited. In addition, they do not take the black offset due to a
projector and an LC panel into consideration because image
subtraction is impossible in real-time display.
Lighting simulation with light fields:
As the most closely related work to ours, Masselus etal. [15] achieve IBRL with 4-D incident light fields; they
control both the 2-D positions and 2-D directions of incident rays by moving a single projector around a scene of interest. Unfortunately, however, their method does not takeaccount of the colors of those rays, and therefore it cannot
synthesize images of scenes which contain fluorescent materials. Although they propose a method for efficient image
acquisition under the assumption that each ray has local influence, it is not applicable to transparent and translucent
materials with non-local influence.
Zhou et al. [27] propose a light field projection system
for lighting reproduction by using rear-projection projectors and a lens array. Their method controls not only the2-D positions and 2-D directions but also the 1-D colors ofincident rays, and therefore is applicable to scenes with fluorescent materials. Unfortunately, however, their proposed
method for real-time lighting reproduction shares the limitations with the methods for glasses-free 3D display: limited dynamic range and black offset.

3. Proposed method
3.1. Two-layer 5 DoF lighting system
As shown in Figure 2, we use a two-layer 5 DoF lighting system; a transmissive LC panel is placed in front of arear-projection display consisting of a projector and a rearprojection screen. When a ray with an arbitrary color is
projected from the projector to an arbitrary point (x, y) on
the screen, it is scattered to various directions. Then, we
set the transmittance at an arbitrary point (u, v) on the LC
panel to 1 and set those at the other points to 0. Thus, thelighting system generates a ray with an arbitrary color andpassing through arbitrary points (x, y) and (u, v), i.e. a 5
DoF incident ray.
In this study, we divide the rear-projection display andthe LC panel into N blocks (e.g. N = 128) respectively,
and control the pixel values of the display and the transmit-

Figure 3. The naive method generates a single ray in turn and captures an image when a scene is illuminated by a single ray. The
number of captured images is N × N .

Figure 4. The parallel method generates multiple rays that do notinterfere each other at the same time. The number of captured
images is N × M , where M = N/4 in this example.

tances of the LC panel in a block-wise manner2 . Supposethat the projector has L color channels (L = 3 in general),the number of rays generated by the 5 DoF lighting system
is L × N × N (e.g. 3 × 128 × 128 = 49152) in total.

3.2. Efficient image acquisition
IBRL requires a large number of images of a scene, eachof which is captured when the scene is illuminated by each
ray. Accordingly, we propose a method for efficiently acquiring those required images on the basis of coded illumination. Here, we address the 4 DoF of the positions (x, y)and (u, v) followed by the 1 DoF of the color.
Naive method:
Let us denote the intensities of the N blocks of the rearprojection display and the transmittances of N blocks of
the LC panel by N -D vectors s and t respectively. Then,the intensities of N × N rays generated by the two-layer
lighting system are represented as
s⊗t

(1)

by using a direct product ⊗ [11]. As shown in Figure 3, thenaive method, which generates a single ray in turn, sets oneof the elements in s and one of the elements in t to 1 andsets the other elements to 0.
Unfortunately, however, the naive method has two limitations as the resolution of the positions (x, y) and (u, v) of
2 In this paper, we call the bundle of rays passing through a block on therear-projection screen and a block on the LC panel “a ray” for the sake ofsimplicity.

Figure 5. The multiplexed naive method is obtained by multiplexing the naive method. The number of captured images is N × N .

Figure 6. The multiplexed parallel method is obtained by multiplexing the parallel method. The number of captured images is
N × M , where M = N/4 in this example.

der the coded illumination and then decode them.
Specifically, the N -D vector s, which represents the intensities of the N blocks of the rear-projection display, isgiven by the N × N S-matrix [21] that is constructed fromthe Hadamard matrix of order (N + 1). For the example
in Figure 6, we concatenate the M -D vector (M = N/4)
given by the M × M S-matrix N/M (= 4) times, and obtain the N -D vector t, which represents the transmittancesof the N blocks of the LC panel. The images taken under
the coded illumination are sequentially decoded by using
the inverses of the S-matrices in two steps.
5 DoF coded illumination:
Let us denote the intensities of L color channels of aray projected from the projector by an L-D vector c. In
a similar manner to the above, we capture images under themultiplexed color and then decode those images. For usual
projectors with L = 3, we project CMY instead of RGB.
Our proposed method combines the multiplexed parallel method and the multiplexed color, and captures images
under the 5 DoF coded illumination represented asc ⊗ s ⊗ t,

incident rays increases. First, the number of captured images increases as the number of blocks N increases. Second, the SNRs of the captured images decreases as the sizeof each block decreases, because the radiance of each ray
also decreases.
Parallel method: To cope with the former limitation on
the number of captured images, we reduce the number of
captured images by generating multiple rays that do not interfere each other at the same time. Specifically, we makeuse of the fact that the 5 DoF lighting system generates redundant rays that do not arrive a scene, and then set thetransmittances of multiple blocks to 1 at the same time.
Figure 4 shows an example of the parallel method. Suppose that a scene of interest is located in front of the LC
panel and that at most a single ray among the 4 rays arrives the scene, which depends on the distance between thescreen and the LC panel, the number of required images isreduced from N × N to N × M where M = N/4 in thiscase. The parallel method sets one of the elements in s andmultiple elements in t to 1 and sets the other elements to
0. Note that the above parallelization is compatible with thefollowing multiplexing.
Multiplexed parallel method:
To cope with the latter limitation on the SNRs of the captured images, we make use of multiplexed illumination [19]that is a well-known technique for increasing SNRs without
increasing the number of captured images and measurement
time. Whereas the multiplexed naive method in Figure 5
requires N × N captured images, the multiplexed parallel
method in Figure 6 requires only N × M captured images.
The multiplexed parallel method captures those images un-(2)

where c, s, and t are described by using the S-matrices withthe sizes of L, N , and M respectively. The images taken
under the coded illumination are sequentially decoded byusing the inverses of the S-matrices in three steps.

3.3. Black offset removal
In general, a small amount of light is projected from a
projector and passes through a transmissive LC panel, eventhough we set the input to the projector and/or the transmittance of the LC panel to 0. Therefore, the images of a scene
illuminated by using the 5 DoF lighting system, which consists of a projector and a transmissive LC panel, are contaminated by the black offsets of the projector and the LC panel.
The contamination is serious because the offset due to each
black ray is small but the number of the rays is large. However, the way of removing the effects of the offsets causedby the two-layer setup is non-trivial, whereas the offsets ofa projector or an LC panel can be removed easily by image
subtraction.
Accordingly, we reveal how the black offsets of the projector and the LC panel propagate to the images captured
by using the two-layer setup, and then propose a method
for removing the effects of those offsets from them. Let us
denote the offsets of the projector and the LC panel by N -D
vectors δ and  respectively. Then, the actual intensities of
the N blocks of the rear-projection display s0 and the actual
transmittances of the N blocks of the LC panel t0 are given
by
s0
t0

= s + δ,= t + .

(3)
(4)

Substituting the above equations into the desired intensities
of N × N rays in eq.(1), we obtains ⊗ t = (s0 − δ) ⊗ (t0 − )
= s0 ⊗ t0 − δ ⊗ t0 − s0 ⊗  + δ ⊗ .

(5)
(6)

Therefore, we can remove the effects of the black offsets
by subtracting the two images captured when the input tothe projector is 0, i.e. δ ⊗ t0 and the transmittance of the LC
panel is 0, i.e. s0 ⊗  from the image captured under s0 ⊗ t0
and adding the image captured when both the input to theprojector and the transmittance of the LC panel are 0, i.e.
δ ⊗  to it. Thus, the number of required images becomesL × (N + 1) × (M + 1) in total.

3.4. Image synthesis under novel lighting
We synthesize an image of a scene under a novel lighting
environment by linearly combining the acquired images ofthe scene on the basis of the superposition principle of illumination. Specifically the novel image I is represented by alinear combination of the acquired images Blnm under the
ray with the l-th color and passing through the n-th blockon the screen and the m-th block on the LC panel as
I=

L X
N X
N
X

wlnm Blnm .

Figure 7. (a) an image of the first scene and the synthesized images
from the images acquired by using (b) the 5 DoF baseline methodand (c) our proposed method. Note that our method reduces thenumber of captured images and the required time for measurementby almost a quarter.

(7)

l=1 n=1 m=1Here, wlnm are the coefficients of the linear combinationand computed from a desired 5-D incident light field.

4. Experiments
We implemented the prototype of a two-layer 5 DoF
lighting system in Figure 2. We used a cooled CCD camera
BU-50C from BITRAN with a linear radiometric response
function for HDR image acquisition. We show the resultsof two scenes; one contains an aroma candle, a water gun,and marbles in a wineglass in Figure 7 (a), and the othercontains an empty glass bottle, a tennis ball, and a glass
bottle with olive oil in Figure 8 (a). We used two projectors
for a rear-projection projector: an EB-S04 from EPSON for
the first scene and an MS524 from BenQ for the second
scene. Until otherwise noted, we set L = 3, N = 63, and
M = 15 ' N/43 , for which the measurement time of our
proposed method was about 100 min.
In order to confirm the effectiveness of our proposed
method, we compared the following three methods.
• 5 DoF baseline method:
This method requires L × (N + 1) × (N + 1) images. We combine the multiplexed naive method forthe 4 DoF of the positions (x, y) and (u, v) in Figure 5
with the multiplexed color for the 1 DoF of the color,
3 The orders for which the Hadamard matrices exist are limited.

Figure 8. (a) an image of the second scene and the synthesizedimages from the images acquired by using (b) the 5 DoF baseline method and (c) our proposed method. Note that our method
reduces the number of captured images and the required time formeasurement by almost a quarter.

and take account of the black offsets. We consider theimages acquired by using this method and the images
synthesized from them as the ground truths.
• Our proposed method:
Our method requires L × (N + 1) × (M + 1) images.

Figure 9. The images of the first scene captured under (a)(b) cyan,(c)(d) magenta, and (e)(f) yellow illumination patterns (a)(c)(e)without and (b)(d)(f) with the offset removal. The pixel values of
the all images are scaled by the same factor for display purpose.

Figure 10. The synthesized images of the first scene under (a)(b)red, (c)(d) green, and (e)(f) blue nearby point light sources fromthe images acquired by using (a)(c)(e) the 4 DoF baseline methodand (b)(d)(f) our proposed 5 DoF method.

We combine the multiplexed parallel method for the 4
DoF of the positions (x, y) and (u, v) in Figure 6 withthe multiplexed color for the 1 DoF of the color, andtake the black offsets into consideration.

surement by almost a quarter. In Figure 8, we can see thatthe result for the second scene is similar to that of the firstscene. The PSNRs of the synthesized images in 16 bit byusing our method in Figure 7 and Figure 8 are 53.92 dB and
54.12 dB respectively. Those results show the effectivenessof our method.
Figure 9 shows the images of the first scene captured under (a)(b) cyan, (c)(d) magenta, and (e)(f) yellow illumination patterns (a)(c)(e) without and (b)(d)(f) with the offset
removal. We can clearly see that (a)(c)(e) the images without the offset removal are brighter than (b)(d)(f) those withthe offset removal. Therefore, the proposed method works
well for removing the offsets in the two-layer lighting system.
Figure 10 shows the synthesized images under (a)(b) red,(c)(d) green, and (e)(f) blue nearby point light sources fromthe images acquired by using (a)(c)(e) the 4 DoF baseline
method with white light sources and (b)(d)(f) our proposed
5 DoF method with RGB light sources. Hereafter, we set
L = 3, N = 127, and M = 31 ' N/4, for which themeasurement time of our method was about 430 min. We
synthesized the images under (a) red, (c) green, and (e) blue

• 4 DoF baseline method:
This method requires (N + 1) × (M + 1) images taken
under white light sources. We use the multiplexedparallel method for the 4 DoF of the positions (x, y)and (u, v) in Figure 6, and take the black offsets into
consideration. We synthesize the images under red,green, and blue light sources from the red, green, andblue channels of the acquired images under white lightsources.
Figure 7 shows (a) an image of the first scene, andthe synthesized images under a novel lighting environment
from the images acquired by using (b) the 5 DoF baseline
method and (c) our proposed method. Here, we assume awhite nearby point light source. We can see that (c) thesynthesized image by using our method is very similar to(b) the ground truth, even though our method reduces thenumber of captured images and the required time for mea-

Figure 11. The synthesized images of the second scene under(a)(b) red, (c)(d) green, and (e)(f) blue nearby point light sourcesfrom the images acquired by using (a)(c)(e) the 4 DoF baseline
method and (b)(d)(f) our proposed 5 DoF method.

Figure 12. The synthesized images of the second scene by using
our proposed method with various 5-D incident light fields.

5. Conclusion and future work
light sources from the red, green, and blue channels of theacquired images under white light sources. Comparing (e)and (f), we can see that our 5 DoF method can reproduce
the appearance of the water gun with fluorescent components, which absorb blue light and emit yellow light and red
light, whereas the 4 DoF baseline method cannot. Figure 11
shows that our 5 DoF method can reproduce the appearanceof the tennis ball with fluorescent components, whereas the
4 DoF baseline method cannot. Those results clearly showthat our 5 DoF method with the 1 DoF of the color is usefulfor synthesizing images of fluorescent materials.
Figure 1 and Figure 12 show the synthesized images ofthe first and the second scenes respectively by using our proposed method with various 5-D incident light fields. Here,
we assume (a)(b) a white light source and (c)(d)(e)(f) threelight sources with red, green, and blue colors. We can seethat our method can synthesize photo-realistic images in theframework of IBRL, in particular, the refraction due to thearoma candle in Figure 1 and the caustics due to the empty
glass bottle in Figure 12 are remarkable.

In this paper, we proposed a method for IBRL with 5-D
incident light fields by using a two-layer 5 DoF lighting system consisting of a rear-projection display and a transmissive LC panel. Our proposed method efficiently acquires
the required images by using coded illumination; it reduces
the number of captured images and the required time formeasurement, and enhances their SNRs. In addition, we
proposed a method for removing the effects of the black
offsets due to the projector and the LC panel in the twolayer setup. Through the experiments using the prototype
system, we confirmed that our method is useful for synthesizing photo-realistic images under 5-D incident light fields,
in particular, images of scenes with fluorescent materials.
The future work of this study includes the extension tomultispectral light sources [9, 6, 14] for increasing the resolution of color. It enables us to synthesize photo-realistic
images of scenes where wavelength-dependent phenomena
such as refraction, diffraction, interference, and scattering
are observed. The extension of the region of interest by using the larger lighting system or multiple lighting systems
is also one of the future directions of our study.

Acknowledgments
This work was partially supported by JSPS KAKENHI
Grant Numbers JP17H01766 and JP16H01676 and Support
Center for Advanced Telecommunications Technology Research (SCAT).

References[1] E. Adelson and J. Bergen. Computational Models of Visual
Processing, chapter The plenoptic function and the elementsof early vision, pages 3–20. MIT Press, 1991. 1[2] K. Barnard. Color constancy with fluorescent surfaces. In
Proc. CIC 1999, pages 257–261, 1999. 2[3] P. Debevec, T. Hawkins, C. Tchou, H.-P. Duiker, W. Sarokin,
and M. Sagar. Acquiring the reflectance field of a humanface. In Proc. ACM SIGGRAPH 2000, pages 145–156, 2000.
1[4] M. Fuchs, H. Lensch, V. Blanz, and H.-P. Seidel. Superresolution reflectance fields: synthesizing images for intermediate light directions. In Proc. EG 2007, pages 447–456, 2007.
1[5] A. Ghosh, S. Achutha, W. Heidrich, and M. O’Toole. BRDF
acquisition with basis illumination. In Proc. IEEE ICCV2007, pages 1–8, 2007. 2[6] K. Hirai, D. Irie, and T. Horiuchi. Multi-primary image projector using programmable spectral light source. Journal of
the Society for Information Display, 24(3):144–153, 2016. 7[7] M. Hirsch, G. Wetzstein, and R. Raskar. A compressive lightfield projection system. In Proc. ACM SIGGRAPH 2014,
page Article No.2, 2014. 2[8] M. Hullin, J. Hanika, B. Ajdin, H.-P. Seidel, J. Kautz, andH. Lensch. Acquisition and analysis of bispectral bidirectional reflectance and reradiation distribution functions. In
Proc. ACM SIGGRAPH 2010, page Article No.97, 2010. 2[9] I. Kauvar, S. Yang, L. Shi, I. McDowall, and G. Wetzstein.
Adaptive color display via perceptually-driven factored spectral projection. In Proc. ACM SIGGRAPH Asia 2015, page
Article No.165, 2015. 7[10] A. Lam, A. Subpa-Asa, I. Sato, T. Okabe, and Y. Sato. Spectral imaging using basis lights. In Proc. BMVC 2013, 2013.
2[11] D. Lanman, M. Hirsch, Y. Kim, and R. Raskar. Contentadaptive parallax barriers: optimizing dual-layer 3D displays
using low-rank light field factorization. In Proc. ACM SIGGRAPH Asia 2010, page Article No.163, 2010. 2, 3
[12] C. Liu and J. Gu. Discriminative illumination: per-pixel classification of raw materials based on optimal projections ofspectral BRDF. IEEE Trans. PAMI, 36(1):86–98, 2014. 2[13] W.-C. Ma, T. Hawkins, P. Peers, C.-F. Chabert, M. Weiss,and P. Debevec. Rapid acquisition of specular and diffuse
normal maps from polarized spherical gradient illumination,
2007. 2[14] K. Maeda and T. Okabe. Acquiring multispectral light transport using multi-primary DLP projector. In Proc. IPTA 2016,
pages 1–6, 2016. 7[15] V. Masselus, P. Peers, P. Dutré, and Y. Willems. Relighting with 4D incident light fields. In Proc. ACM SIGGRAPH
2003, pages 613–620, 2003. 2, 3
[16] S. Nayar, G. Krishnan, M. Grossberg, and R. Raskar. Fast
separation of direct and global components of a scene using high frequency illumination. In Proc. ACM SIGGRAPH
2006, pages 935–944, 2006. 2[17] J.-I. Park, M.-H. Lee, M. Grossberg, and S. Nayar. Multispectral imaging using multiplexed illumination. In Proc.
IEEE ICCV 2007, pages 1–8, 2007. 2[18] P. Peers, D. Mahajan, B. Lamond, A. Ghosh, W. Matusik,
R. Ramamoorthi, and P. Debevec. Compressive light transport sensing. ACM TOG, 28(1):Article No.3, 2009. 1[19] Y. Schechner, S. Nayar, and P. Belhumeur. A theory of multiplexed illumination. In Proc. IEEE ICCV 2003, pages 808–
815, 2003. 1, 2, 4[20] P. Sen and S. Darabi. Compressive dual photography. Computer Graphics Forum, 28(2):609–618, 2009. 1[21] N. Sloane, T. Fine, P. Phillips, and M. Harwit. Codes for
multiplex spectrometry. Applied Optics, 8(10):2103–2106,
1969. 4[22] S. Tominaga, T. Horiuchi, and T. Kamiyama. Spectral estimation of fluorescent objects using visible lights and an
imaging device. In Proc. CIC 2011, pages 352–356, 2011. 2[23] C. Wang and T. Okabe. Joint optimization of coded illumination and grayscale conversion for one-shot raw material
classification. In Proc. BMVC 2017, 2017. 2[24] J. Wang, Y. Dong, X. Tong, Z. Lin, and B. Guo. Kernel
Nyström method for light transport. In Proc. ACM SIGGRAPH 2009, page Article No.29, 2009. 1[25] G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar. Tensor
displays: compressive light field synthesis using multilayer
displays with directional backlighting. In Proc. ACM SIGGRAPH 2012, page Article No.80, 2012. 2[26] C. Zhang and I. Sato. Separating reflective and fluorescentcomponents of an image. In Proc. IEEE CVPR 2011, pages
185–192, 2011. 2[27] Z. Zhou, T. Yu, X. Qiu, R. Yang, and Q. Zhao. Light fieldprojection for lighting reproduction. In Proc. IEEE VR 2015,
pages 135–142, 2015. 3