Separating Reflective and Fluorescent Components of an Image
Cherry Zhang
University of Waterloo
200 University Ave. West, Waterloo, Ontario, Canada
c23zhang@uwaterloo.ca

Imari Sato
National Institute of Informatics
2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan
imarik@nii.ac.jp, imarik@u-tokyo.ac.jp

Abstract
Traditionally researchers tend to exclude fluorescencefrom color appearance algorithms in computer vision andimage processing because of its complexity. In reality, fluorescence is a very common phenomenon observed in many
objects, from gems and corals, to different kinds of writing paper, and to our clothes. In this paper, we provide
detailed theories of fluorescence phenomenon. In particular, we show that the color appearance of fluorescence isunaffected by illumination in which it differs from ordinaryreflectance. Moreover, we show that the color appearanceof objects with reflective and fluorescent components can be
represented as a linear combination of the two components.
A linear model allows us to separate the two components
using images taken under two unknown illuminants using
independent component analysis(ICA). The effectiveness ofthe proposed method is demonstrated using digital imagesof various fluorescent objects.

Figure 1. Examples of fluorescent objects: gems and corals,
clothes, banana peel and fluorescent sheets.

objects, from gems and corals, to different kinds of writing
paper, and to our clothes(Figure 1). Therefore, computer
vision techniques or image synthesis algorithms concernedwith exact object color must take fluorescence into account.
By experimentation, we discovered that a composite object with both ordinary reflective and fluorescent component
has the color appearance that is the sum of the two components interact with illuminants differently. To handle thetwo components correctly, it is necessary to separate themfirst. This motivates us to develop a method for separating
fluorescence and reflectance. In essence, if we assume an
ordinary color camera has narrowband RGB responses, we
can show that the intensity of a pixel pc on the captured
image can be expressed as a linear contribution

1. Introduction
In the field of computer vision, recognizing objects andpatterns by their color has always been a difficult problem
because the color appearance of objects varies dramaticallywith surrounding illumination. Researchers in computational color constancy proposed many algorithms and models to discount the effect of illumination and recover the true
color of objects [1, 8, 4]. Researchers in image reproduction and realistic rendering strive to accurately predict thecolor of objects under arbitrary illuminants [11]. While thealgorithms and techniques compute color appearance differently, they share one common assumption: none of theobjects in the scene exhibit fluorescence. In reality, fluorescence is a very common phenomenon observed in many

pc = ac Rc + bc Fc ,where c = {R, G, B}, Rc and Fc represent ordinary reflective and fluorescent components at pc . ac and bc are coefficients computed from camera responses and illumination
185

that represent how they affect the color appearance of thesecomponents. Since we do not know the illumination under which p is taken, we need to solve for R and F from theonly known variable p. To make this hard problem solvable,
we assume that reflective and fluorescent components seenin an image are statistically independent. The assumption isreasonable because in the absence of image interpretation,
the spacial distribution of fluorescent component is uncorrelated with the spatial distribution of the reflective component. Based on the linear contribution model, we show thatgiven p for two images taken under different illuminants, R
and F can be effectively recovered using independent component analysis (ICA).
The contributions of our paper are

brief explanations of fluorescence, and extended spectral
rendering algorithms to take fluorescence into account [11].
Hullin et al. proposed new ways to model and render fluorescent objects by acquiring their bispectral bidirectionalreflectance and reradiation distribution functions (BRRDF)
and the results showed significant improvement in fluorescent object modeling [9]. Furthermore, Barnard proposed ways to improve color constancy algorithms to include spectral data of several fluorescent materials [3]. Although Barnard solved some problems of including fluorescent objects in color constancy algorithms, his work was
mainly based on experimental measurements. His paper
did not provide comprehensive models for fluorescent surfaces. In our paper, we extend Barnard’s research by providing more detailed theories and accurate models for fluorescence.
To accurately predict the appearance of composite objects with both reflective and fluorescent components, it isimportant to separate the two components. Research in natural science [15] shows necessary procedures for measuring color of fluorescent materials in the spectral domain using optical devices. For example, Haneishi and Kamimuraused spectral data taken under multiple light sources under known spectral distributions, for characterizing fluorescent samples [12]. Alterman et al. separated the appearanceof each fluorescent dye from a mixture by unmixing multiplexed images [2]. Nakajima and Tominaga used statisticsof fluorescent materials for estimating fluorescent components of a real material using multi-spectral images seen
under sunlight [13]. In the early stage of our research, we
successfully separated the components of fluorescent sheets
using spectral data captured by a spectrometer. The successful results motivated us to develop a more practical systemfor doing the separation using images taken by an ordinary
digital camera.
The computer vision community has several methods forseparating components of an image [14, 17]. Some algorithms separate specular reflections from diffuse reflections. Some algorithms separate non-correlated components of images. For example, Farid and Adelson proposeda method for separating a painting from the reflection ofan observer on the glass in front of the painting, using two
images [7]. We found that Farid and Adelson’s problem
closely resembles the fluorescence-separation problem weare interested in. Therefore, a similar approach based on
independent component analysis is used in our case for separating reflective and fluorescent components.

• providing a theory of fluorescent phenomenon,• showing that the color of fluorescent component is notaffected by the color of its illuminant, in which it differs from that of ordinary reflective component, and• proposing a method for separating reflective and fluorescent components using only two images taken under
different illuminants.
As far as we know, this is the first attempt to separate reflective and fluorescent components of an image taken under unknown illumination. The rest of the paper is structured as follows. Section 2 summarizes earlier research incolor constancy, color appearance and rendering algorithms
for fluorescent surfaces, as well as research in image separation. Section 3 presents the theories and experimental
results explaining how fluorescent surfaces interact with illuminants. Our algorithm and the results for separating ordinary reflective and fluorescent components of an image
are presented in Section 4 and 5. In the conclusion, we discuss issues and future directions of our research.

2. Related Work
The color appearance of non-fluorescent surfaces has always been the main focus of color-related computer visionalgorithms. For example, in computational color constancy,
researchers attempt to recover the “true color” of objects
under a reference illuminant [1, 8]. The true color is thenmodified to predict the appearance of objects under otherilluminants. Barnard et al. studied and compared existingcolor constancy algorithms by evaluating their performancewith a large set of test images [4]. Some of the test images
contain fluorescent objects, but all of the evaluated color
constancy algorithms treat them as ordinary objects.
Later on, researchers realized that assuming all objects
are non-fluorescent greatly limits on the accuracy of color
algorithms, because many objects around us exhibit fluorescence. In Johnson and Fairchild’s research, they provided

3. Properties of Fluorescent Surfaces
3.1. FluorescenceWe start by looking at what is fluorescence. Most typical fluorescent material absorbs light in the near ultravio186

Figure 2. Natural daylight and fluorescent lamp both have strong
UV and short-wavelength components.

let (UV) range from 200 nm to 380 nm, and re-emit visible
light in 380 nm to 720 nm. Some material absorbs shortwavelength visible light and re-emit longer-wavelength visible light. The first type of special UV lights are not required to observe fluorescence because many natural lighting conditions, such as daylight and cool fluorescent light,
have strong UV components (Figure 2). After decades ofstudies, researchers can explain fluorescence phenomenon
and two unique properties of fluorescent materials with concepts in quantum theory[6, 15]: fluorescent material always
emits light at longer wavelength than the absorbed light,
and the emission spectra of each fluorescent material always
have the same frequency distribution (e.g. shape) regardlessof the spectra of incident light.
Due to their unique properties, the appearance of fluorescent surfaces must be computed differently than reflective surfaces. The color of a reflective surface depends only
on the illuminant and its reflectance. For example, the observed spectrum of an ordinary reflective surface with reflectance R under illuminant I is

Figure 3. Measured excitation and emission spectra of fluorescentsheets. Top: Emission spectra for light source at different wavelength. Middle: Excitation(dotted) and emission(solid) spectra for
red-orange sheet. Bottom: Excitation(dotted) and emission(solid)
spectra for yellow sheet.

the frequency distribution and intensity of the emitted light.
Usually the emission spectrum is a function of wavelength
covering the visible range. The frequency distribution of
all emission spectra is constant, but the intensity varies.
Figure 3(Top) shows the measured emission spectra of a
red-orange fluorescent sheet. Each colored spectrum corresponds to the illuminant at a different wavelength, andhave the same frequency distribution as one another. Figure 3(Middle) shows the normalized1 excitation and emission spectra of the sheet. From the emission spectrum wecan see that the sheet appears reddish orange when it is illuminated with light in the range of 380 nm to 650 nm.
To obtain the observed spectrum of a pure fluorescentsurface, we must consider the sum of the contribution fromilluminant, excitation, and emission. Suppose the illuminant is I and its intensity at wavelength λi is I(λi ). Let
Ex and Em represent the normalized excitation and emission spectrum, respectively. Then the observed spectrum,

P (λ) = I(λ)R(λ),
where I(λ) is the intensity of the illuminant at wavelength
λ and R(λ) is the reflectance of the material at wavelength
λ. If we capture the object with a charge-coupled device(CCD) camera with three channels R,G and B, then thecolor of each pixel for each channel isZ
p = c̄(λ)I(λ)R(λ) dλ,(1)integrated over visible spectrum (380 nm to 720 nm), wherec̄(λ) = {r̄(λ), ḡ(λ), b̄(λ)} are the camera response curves
for each channel [16].
For a pure fluorescent surface, the observed spectrum
depends on the illuminant, the material’s excitation spectrum and emission spectrum. Excitation spectrum shows
how much energy from the illuminant is absorbed at eachwavelength. Thus it is a function of the wavelength of
the illuminant. For each wavelength in an excitation spectrum, there is a corresponding emission spectrum that shows

1 The spectral power distribution is normalized so that the minimum
intensity is 0 and the maximum intensity is 1.0187

P (λ, λi ), resulting from the illuminant at λi is
P (λ, λi )=I(λi )Ex0 (λi )Em(λ),

Ex(λi )
is the relative intensity of thewhere Ex0 (λi ) ≡ R Ex(λi ) dλi
excitation caused by the illuminant at wavelength λi . SinceI(λi )Ex0 (λi ) is a scalar, all P (λ, λi )’s have the same shapeas Em(λ). Considering illumination at all wavelengths,
the overall observed spectrum is computed by summing up
P (λ, λi )’s for all wavelength λi . i.e.

Z
P (λ) =(a) Measured spectra of the red-orange fluorescent sheet under illuminations
at different wavelength.

I(λi )Ex0 (λi ) dλi Em(λ).

The range of λi depends on the illuminant, and the range of
λ is the range of the observed light we wish to measure. Referring back to the example of red-orange fluorescent sheet,
Figure 3(Top) is the plot for P (λ, λi )’s.
If we capture the pure fluorescent surface with a CCD
camera, the color of the pixel for each channel isZp=I(λi )Ex0 (λi ) dλi(b) Illumination in the UV range: (c) Illumination in visible range:
observe fluorescence only.
observe both fluorescence and reflectance.

Zc̄(λ)Em(λ) dλ.

(2)

Many objects we see every day are neither pure reflective nor pure fluorescent; they are composites of ordinaryreflective and fluorescent components. Figure 4(a) shows
the overall change in the observed spectrum of such object.
Each colored line represents the observed spectrum corresponding to the illuminant at a particular wavelength. When
the wavelength of the illuminant falls in the UV range, orthe high-energy range of the object’s excitation spectrum,
fluorescent component dominates, thus we observe fluorescence only (Figure 4(b)). When the wavelength of the illuminant falls in the visible light range, we observe mixtureof fluorescence and reflectance (Figure 4(c)). When the illuminant is in the low-energy range of visible light and falls
outside of the excitation spectrum, fluorescence diminishes
and we only observe reflectance (Figure 4(d)).
Clearly, an object’s reflective and fluorescent components behave significantly differently. In the next section,
we will show a unique property of fluorescent component,
and present our findings on how it interacts with illuminantsdifferently from reflective component.

(d) Illumination in visible range andoutside of excitation range: observe
reflectance only.

Figure 4. Observed spectra of fluorescent sheet containing bothreflective and fluorescent components.

rial as
Z
X=
Z
Y =
Z
Z=

I(λi )Ex0 (λi ) dλi

Z

I(λi )Ex0 (λi ) dλi

Z

I(λi )Ex0 (λi ) dλiZx̄(λ)Em(λ) dλ,(3)ȳ(λ)Em(λ) dλ,(4)z̄(λ)Em(λ) dλ,(5)where x̄(λ), ȳ(λ), z̄(λ) are the CIE color matching functions. λ is integrated over visible light range 380 nm to
720 nm. LetZ
X0 = x̄(λ)Em(λ) dλ,Z
Y0 = ȳ(λ)Em(λ) dλ,Z
Z0 = z̄(λ)Em(λ) dλ

3.2. Constant Chromaticity
The most intriguing property of fluorescence we discovered is that it has constant color, or chromaticity, under mostilluminants. The proof of this property follows naturally
from Equation 2 in the previous section.
By replacing the camera response functions c̄(λ), we cancompute the CIE tristimulus values of the fluorescent mate188

Z

be the reference tristimulus values of the normalized emission spectrum Em. Substituting X0 , Y0 and Z0 into Equations 3 to 5,
R we have X = kX0 , Y = kY0 , and Z = kZ0
with k = I(λi )Ex0 (λi ) dλi . Note that k is a scalar andits value depends on the intensity of the illuminant and theexcitation spectrum of the material.
Now define reference chromaticity as
x0 =

+

Y0
X0
and y0 =.
X0 + Y0 + Z0
X0 + Y0 + Z0

X
kX0=
= x0 .
X +Y +Z
kX0 + kY0 + kZ0

Similarly, y = y0 . Thus the chromaticity of the fluorescentmaterial is independent of both the illuminant and excitation
spectrum; it only depends on the emission spectrum.
We verified our findings with carefully designed experiments. The results are shown in A PPENDIX. In summary,the color appearance of reflective component varies with illumination dramatically, whereas the appearance of fluorescent component stays constant except for intensity. In thenext section, we propose a method for separating ordinaryreflective and fluorescent components, in which the only inputs required are two images of objects taken under two
illuminants.

where pji is the j th pixel value for ith illumination, Rj
and Emj are the ordinary reflectance and fluorescenceat the Rj th pixel, ri (λn ) = c̄(λn )Ii (λn ), and fi (λn ) =c̄(λn ) Ii (λi )Ex0 (λi ) dλi . Let Pn = Mn Sn be the shortform of the matrix equation above. We call Pn the input matrix, Mn the mixing matrix, and Sn the signal matrix. If we input Pn to ICA 2 , ICA will first estimate Mn ,and Sn is computed as Mn−1 Pn . To obtain the image with
only reflective component, we combine Rj (λn ) in Sn for
n = {R, G, B}. Similarly to obtain the image with only
fluorescent component, we combine Emj (λn ) in Sn .

4. Separating Reflective and Fluorescent Components of an Image
4.1. The Model
When we take an image of composite objects withboth ordinary reflective and fluorescent components usinga CCD camera, the color of each pixel p on the final image for each channel c = {R, G, B} is the sum of the pixel
color for reflective component pO and fluorescent component pF . i.e. p = pO + pF . Substitute in Equation 1 and 2
for pO and pF , we haveZp =c̄(λ)I(λ)R(λ) dλZ+

I(λi )Ex0 (λi ) dλi

4.2. Ambiguities of ICA
Even though ICA works well for solving our problem,
it imposes two ambiguities. First, we cannot determine the“order” of the independent components R and Em. In otherwords, we do not know which resulting component is forfluorescence and which is for reflectance. The reason is thatboth mixing matrix and signal matrix are unknown; for thesame set of data Pn , ICA could recover the pair Mn and Sn
as either




r1 f1
Rj
Mn =
, Sn =
,
r2 f2
Emj

Z
c̄(λ)Em(λ) dλ(6)

We assume that the responses of a CCD camera havefairly narrow bandwidth, that is, light goes through the camera at a particular wavelength to reach the sensor [5]. The
narrowband assumption is often used in color constancy algorithms, so we can simplify Equation 6 as
pn

=

(7)

where λn for n = {R, G, B} is set to be the wavelength ofeach R,G,B channel of the camera.
Now for each channel, p is represented as a linear combination of the reflective component R and fluorescent component Em. Both R and Em are unknown to us. The spectral distribution of the illuminant under which p is taken, isalso unknown. To tackle the problem of blindly separating
R and Em from the only known variable p, we make theassumption that the two components are independent. This
assumption is reasonable since in our case, the spatial distribution of fluorescent component provides no predictionof the spacial distribution of the ordinary reflective components; we expect no correlation between images of thetwo components. Based on this assumption and Equation 7,
we solve the blind separation problem by applying independent component analysis (ICA) [10] to images of the objects
taken under different illuminants.
Since ICA requires the number of measurements to begreater than or equal to the number of independent components, we take images p1 and p2 of a fluorescent object under two distinct illuminants I1 and I2 . Formulate the problem based on Equation 7 for each n = {R, G, B} channel
as
 j
 


p1 (λn )r1 (λn ) f1 (λn )Rj (λn )=,r2 (λn ) f2 (λn )Emj (λn )pj2 (λn )Then the chromaticity of the object under an arbitrary illuminant becomesx=I(λi )Ex0 (λi ) dλi c̄(λn )Em(λn ),c̄(λn )I(λn )R(λn )2 We used the FastICA package in MATLAB in our experiments.

189

put images as
dj =q(xj1 − xj2 )2 + (y1j − y2j )2 .

In Section 3, we showed that dj is very small if j shows
the brightness of fluorescent component. Let sj1 and sj2 be
the recovered intensities at the j th pixel in the two images
computed by ICA. Normalize them as(sj )2(sj )2jjs0 1 = P 1 i 2 , s0 2 = P 2 i 2 .
i (s1 )i (s2 )
Then multiply the relative intensities by the chromaticity
difference dj , and sum over all pixels
X j
X j
t1 =
s0 1 dj , t2 =s0 2 dj .
j

If t1 is smaller than t2 , then the image represented by s1
is the fluorescent component. Otherwise the image represented by s1 is the fluorescent component. Intuitively, ifj
the j th pixel contains the fluorescent component, s0 willjbe big but d is small. Therefore, the overall t value forimage with fluorescent component is always smaller. This
technique assumes that the objects have much stronger fluorescent component than ordinary reflective component.

Figure 5. Top: colored sheets under white illuminant. Middle: colored sheets under green and pink illuminants. Bottom: fluorescentsheets seen under UV light.

4.2.2

or


r2
r1

f2
f1




, Sn =

Emj
Rj


.

j

Em0 (λn ) = sn ∗ c̄(λn )/f1 .

The second ambiguity is “scaling”. ICA recovers the mixing matrix within a scale factor of the true mixing matrix.
In other words, we cannot compute the absolute intensityof the pixels for each component. Again, the reason is thatboth Mn and Sn are unknown; any multipliers in Mn canbe canceled out by dividing the same scalars in Sn . i.e.



 

r1 /α f1 /β
αRj
r1 f1
Rj
=
r2 f2
Emj
r2 /α f2 /β
βEmj
4.2.1

Solving the “scaling” problem

In the Rmixing matrix, the integral part of scalar f1 (λn ) =c̄(λn ) Ii (λi )Ex0 (λi ) dλi depends only on the spectral
distribution of the illuminant and excitation of the fluorescent component and thus must be the same among all RGB
channels. This fact can be used for solving the scaling
ambiguity of fluorescent component if c̄(λn ) are known.
For each n = {R, G, B}, we scale the computed sn by
f1 /c̄(λn ). i.e.

Figure 6. Recovered fluorescent and reflective components using
images taken under green and pink illuminants

Mn =

j

j

Em0 (λn )’s estimate the relative intensities in RGB channels and provide the necessary color balance in the final image for fluorescent component. While in theory, this solution works for a scene consists of one type of fluorescentsurface where f1 is uniform for the entire image, it works
fine for scenes with multiple types of fluorescent surfaces inour experiments shown in Figure 6. In the case of multiple
types of fluorescent surfaces, we may have better solutions,and we will investigate the issue more in the future.
To achieve correct color balance for the reflective components, we look for or include a reference patch with whitereflectance in the input images. The recovered images for
RGB channels are combined in a way such that the whitepatch remains white in the reflectance-only image. If we

Solving the “ordering” ambiguity

We solve the ordering ambiguity by using the unique property of fluorescent component. Let xji and yij represent thex,y-chromaticity of the j th pixel in the ith image. Computethe chromaticity difference at the j th pixel between two in190

have a material of known fluorescence such as white paper with bluish fluorescence, we can utilize the known fluorescence for achieving correct color balance of fluorescentcomponent.
(a) Ground truth (seen under white light) and input images.

5. Results and Analysis
We tested our method with images taken with an ordinary CCD camera. The first scene is an image made withcolor sheets. The sheets contain different amount of fluorescence and reflectance (Figure 5 Top). The top two flowers are made of fluorescent sheets that appear bright yellow
and bright red-orange under white light. The flower in the
middle and the leaves are made of dark red and dark green
non-fluorescent sheets. The background is made of nonreflective light purple sheet.
We first recovered fluorescent and reflective components
using images taken under a green illuminant and a pink
illuminant (Figure 5 Middle). The recovered fluorescentcomponent (Figure 6 Left) shows that the color of fluorescent component of the yellow fluorescent sheet is in fact
green. In Section 3, we showed the measured emission
spectrum of the sheet (Figure 3 Bottom), which suggeststhat the color of the fluorescent component is green. Furthermore, we took images of the fluorescent flowers under
UV light, which provided “ground truth” for the color of thefluorescent components (Figure 5 Bottom). Our recovered
appearance agrees with experimental results, as well as the“ground truth”. The dark red and dark green sheets usedin making the scene have ordinary reflectance only since
the color of the middle flower and the leaves in the recovered reflective component (Figure 6 Right) is the same as
the color seen under white light. It is also worth noting thatthe yellow fluorescent flower appears to be orange in therecovered image for reflective component. Combining theorange color with the green color in the fluorescent component gives the flower its final yellow appearance. Moreover,
the red-orange fluorescent sheet has much stronger fluorescence compare to the yellow fluorescent sheet. Therefore,
its color appearance is almost all contributed by the fluorescent component.
Our method is effective on scenes with complex color
patterns, and scenes consist of objects as well. Figure 7 consists of two fluorescent sheets on top of a nonfluorescent background image with complex color patterns.
Our method succeeded in identifying the green and redorange color of the fluorescent sheets. The recovered image
for fluorescent component (Figure 7(b) Left) does not show
the background image at all, which clearly demonstrates thecorrectness and effectiveness of our method. Figure 8 are
the recovered results for a scene consists of objects. The
fluorescent sticks and non-fluorescent jar are separated into
two images. The color of the sticks (Figure 8(b)) matcheswith the ground truth (Figure 8(c)).

(b) Recovered images.

Figure 7. Fluorescent objects on top of reflective image with complex color patterns.

(a) Ground truth (seen under white light) and input images.

(b) Recovered images.

(c) Fluorescent sticks seen under UV light.

Figure 8. Examples of real fluorescent objects.

6. Discussions and Conclusions
We explained the difference in appearance between fluorescence and reflectance and proposed a method for separating fluorescent and reflective components of objects using images captured under two illuminants. Three issues
are worth further attention. First, the intensity of fluorescence varies proportionally to the illuminant; we may beable to use this property to infer information about the illuminant. Secondly, we assume that for an image, there isno correlation between the spatial distributions of reflective
and fluorescent components. In the future, we will explore
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Figure 9. Surfaces with ordinary reflectance and fluorescence.

(a) CIE standard daylights.

(b) CIE standard indoor lights.

Figure 10. Illuminants used in the experiments.

Figure 11. x-chromaticity(top) and y-chromaticity(bottom) of fluorescent and ordinary reflective surfaces under various illuminants. Left: fluorescent surfaces vs illuminants. Right: reflective
surfaces vs. illuminants.

statistical evidence to support the assumption. Thirdly, theproposed separation method assumes that a CCD camera
has narrowband responses. Even though this assumption ismade by many color constancy algorithms, it remains controversial. It is worth studying the effectiveness of the proposed method without making the narrowband assumption.
Overall, this paper presented ideas pioneering a new direction of research in computer vision and image processing.
A PPENDIX: Appearance of Ordinary Reflectance andFluorescence under Various Illuminants
The changes in color of eight fluorescent and nonfluorescent surfaces (Figure 9) were examined under standard daylight and indoor illumination. Figure 10 shows the
spectra of the illuminant, which cover a wide range of illumination conditions. The x,y-chromaticity vs illuminants
plots (Figure 11) clearly show that surfaces with strong
a fluorescent component are more prone to illumination
changes. The x-chromaticity of fluorescent yellow sheet
varies more because it contains a stronger reflective component compare to fluorescent red-orange sheet. The appearance of surfaces with only reflective component varies
greatly with illumination.
192