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Edge-Based Color Constancy
Joost van de Weijer, Theo Gevers, and Arjan Gijsenij

Abstract—Color constancy is the ability to measure colors ofobjects independent of the color of the light source. A well-known
color constancy method is based on the gray-world assumption
which assumes that the average reflectance of surfaces in the worldis achromatic. In this paper, we propose a new hypothesis for color
constancy namely the gray-edge hypothesis, which assumes thatthe average edge difference in a scene is achromatic. Based on
this hypothesis, we propose an algorithm for color constancy.
Contrary to existing color constancy algorithms, which are computed from the zero-order structure of images, our method isbased on the derivative structure of images. Furthermore, we propose a framework which unifies a variety of known (gray-world,
max-RGB, Minkowski norm) and the newly proposed gray-edge
and higher order gray-edge algorithms. The quality of the various
instantiations of the framework is tested and compared to thestate-of-the-art color constancy methods on two large data sets ofimages recording objects under a large number of different lightsources. The experiments show that the proposed color constancy
algorithms obtain comparable results as the state-of-the-art color
constancy methods with the merit of being computationally more
efficient.
Index Terms—Color constancy, object recognition, photometricinvariance.

I. INTRODUCTIONCOLOR constancy is the ability to recognize colors of objects independent of the color of the light source [1]. Obtaining color constancy is of importance for many computer vision applications, such as image retrieval, image classification,color object recognition, and object tracking [2]–[4].
Approaches to this problem can be divided into two groups.
For the first group, the aim is to represent images by features
which are invariant with respect to the light source, for example
within the context of image retrieval. Such invariant representation have been proposed by Funt and Finlayson [5], Gevers
and Smeulders [2], Geusebroek et al. [6], and Van de Weijer andSchmid [7]. For these methods, the actual estimation of the lightsource is not necessary. For the second group of approaches, theaim is to correct images for deviations from a canonical lightsource. Contrary to methods in the first group, solutions to thisproblem do estimate the color of the light source, be it explicitly
or implicitly. Methods, either propose a light source estimation,

Manuscript received August 7, 2006; revised May 3, 2007. This work was
supported by the Marie Curie European Fellowship Program of the Commission of the European Union. The associate editor coordinating the review ofthis manuscript and approving it for publication was Dr. Gabriel Marcu.
J. van de Weijer is with the LEAR team, INRIA Rhone-Alpes, 38330 Montbonnot, France, (e-mail: joost.van-de-weijer@inrialpes.fr).
T. Gevers and A. Gijsenij are with the Faculty of Science, University of Amsterdam, 1098 SJ Amsterdam, The Netherlands (e-mail: gevers@science.uva.nl;
gijsenij@science.uva.nl).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIP.2007.901808

after which the image is corrected [8]–[11], or they directly estimate the color corrected image [1], [12], after which the lightsource can be derived. If desired, illuminant invariant features
can subsequently be derived from the corrected image. In thispaper, we look at color constancy approaches of the second
group, i.e., methods from which a light source corrected image
can be computed.
One of the most successful color constancy methods is gamut
mapping proposed by Forsyth [1]. The method is based on theobservation that only a limited set of RGB values can be observed under a given illuminant. The set of all possible RGB
values for the canonical illuminant, typically a white illuminant,is called the canonical gamut. This canonical gamut is provento be a convex hull in RGB space. The algorithm computes
what transformations map an observed gamut into the canonical gamut. From these transformations, the illuminant color isderived. The gamut mapping algorithm provides among the best
results in color constancy experiments [3]. Finlayson et al. [12]improve the gamut mapping algorithm by restricting the transformations to be plausible, meaning that only illuminants areallowed which correspond to existing illuminants. This adaptation of the gamut algorithm, called GCIE for gamut constrained
illumination estimation, was shown to outperform the standard
gamut algorithm. Further approaches to color constancy include
probabilistic approaches [10] and learning-based methods [11].
A framework which unifies multiple color constancy algorithms
together is presented by Finlayson and Hordley [9]. They propose to estimate the illuminant from the correlation of the image
data, and the prior knowledge about which colors appear undera certain light.
Although the above-described algorithms arrive at reasonable color constancy accuracy, a drawback is that they are basedon complex algorithms and all require an image data set withknown light sources for calibration. In this paper, we will focus
on color constancy based on less complex color constancy
algorithms. To this end, fast algorithms are considered which
are based on low-level image features, such as max-RGB andgray-world. Max-RGB is a simple and fast color constancy
algorithm which estimates the light source color from the maximum response of the different color channels [13]. Anotherwell-known simple color constancy method is based on thegray-world hypothesis [8], which assumes that the averagereflectance in the scene is achromatic. If the images under evaluation are part of a coherent image data base, Gershon et al. [14]showed that assuming the average of a scene to be equal to theaverage reflectance of the database, improves the results overthe standard gray-world method. As an example, they mention
forest pictures full of green colors. In this case, most color
constancy methods will predict light sources biased towards thegreen color. The database-compensated gray-world algorithm
resolves this problem. These low-level methods are widely in

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use, even in digital consumer cameras, due to their very low
computational costs, i.e., taking the maximum (max-RGB) or
average pixel values (gray-world).
Low-level approaches regained further interest recently
after Finlayson and Trezzi [15] showed that only with minor
adaptations results are obtained which are similar to thoseof complex color constancy algorithms. In fact, they showedthat the max-RGB method and the gray-world method canbe interpreted as the same algorithm applied with different
instantiations of the error function. The max-RGB method is
Minkowski norm andshown to be equal to applying thegray-world is equal to using thenorm. They further showthat the best color constancy results are obtained with thenorm. Although these simple color constancy algorithms
are slightly outperformed by more elaborate methods, e.g.,gamut mapping, they perform surprisingly well while they areconceptually simpler (for an extensive evaluation of multiple
color constancy methods, see [3], [15], and [16]).
In this paper, we pursue this line of color constancy basedon low-level image features. First, we propose the gray-edge
hypothesis, which assumes that the average edge differencein the scene is achromatic. The method is based on the observation that the distribution of color derivatives exhibits thelargest variation in the light source direction. The Minkowski
norm of these derivatives is used to approximate this direction.
The method is further extended to also include higher orderderivatives. To our knowledge, this is the first work in whichcolor constancy based on image derivatives is pursued. Finally,
we propose a new framework of color constancy based on
low-level image features which includes the known algorithms(gray-world, max-RGB, shades of gray) and the newly proposed gray-edge and higher order gray-edge algorithms.
This paper is organized as follows. In Section II, color constancy based on the gray-world and the max-RGB hypothesis isdiscussed. In Section III, we propose the gray-edge hypothesis,
which estimates the illuminant color based on the distributionof the color derivatives. We further extend the color constancy
framework of Finlayson and Trezzi [15] to also include color
constancy methods derived from the gray-edge hypothesis. We
further extend it with a parameter to regulate the amount oflocal averaging. Section IV, contains experiments on two large
databases of images. Section V contains a discussion of results
and indications for future research. Section VI finishes with concluding remarks.

source color, or its projection on the RGB-kernels(2)given the image values, where is the spatial coordinate in
the image. The task of color constancy is not attainable without
further assumptions.
Buchsbaum [8] proposes the gray-world hypothesis whichassumes that the average reflectance in a scene is achromatic.
In the original work, the hypothesis is used to derive that the
average reflectance for the short-wave, middle-wave and longwave regions is equal. Here, we employ a stronger definition of
the achromatic reflectance of a scene (as also used in [15])(3)which avoids to make further assumptions. Buchsbaum [8], forexample, needed to make further assumptions on the basis functions for the camera sensitivities, the surface reflectances, andthe light source spectra. The constant is between 0 for no reflectance (black) and 1 for total reflectance (white) of the incident light, and the integral is over the domain of the scene. For
such a scene with achromatic reflectance, it holds that the reflected color is equal to the color of the light source, since
(4)
(5)
(6)
where we applied the theorem of Fubini to exchange the orderof integration. The normalized light source color is computedwith.
Another popular color constancy method is called max-RGB[17]. It is based on the assumption that the reflectance which isachieved for each of the three channels is equal(7)
where theoperation is executed on the separate channels(8)

II. GRAY-WORLD HYPOTHESISThe image values,
are dependent on the light source
length, the surface reflectancefunctions, for a Lambertian surface, where is the waveand the camera sensitivity(1)
where is the visible spectrum and bold fonts are applied forvectors. We assume that the scene is illuminated by a single lightsource. The goal of color constancy is to estimate the light

This method is sometimes explained as being derived from thewhite-patch hypothesis. Since a white patch reflects all the incident light, its position in the image can be found by searchingfor the maximum RGB values. It should be noted, however, thatthe max-RGB methods does not require the maxima of the separate channels to be on the same location; hence, it also obtains correct illuminant estimation results when the maximum
reflectance is equal for the three channels.
Recently, Finlayson and Trezzi [15] showed that the grayworld and the max-RGB algorithm are two different instantiations of a more general color constancy algorithm based on the

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VAN DE WEIJER et al.: EDGE-BASED COLOR CONSTANCY

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Minkowski norm. Their method is called shades of gray and iscomputed by(9)For, the equation is equal to the gray-world assumption.
, it is equal to color constancy by max-RGB. They
For
investigated the performance of the illuminant estimation as afunction of the Minkowski norm and found that the best results.
are obtained with a Minkowski norm with
A similar approach has been proposed by Barnard [18] toselect the appropriate transformation from the feasible set oftransformations computed with Gamut mapping method. In theoriginal work, Forsyth [1] proposed to take the transformation
belonging to the gamut with the maximum volume. Instead,
Barnard [18] considered various exponentials of the geometricmean of the transformation vector to select the best transformation from the feasible set. He showed that by varying the exponential, the selection criterion changes from taking the averageover all transformation to the maximum volume heuristic. Likein the case of the shades of gray method, intermediate exponentials were shown to obtain better results.
As a final extension of the gray-world algorithm, we consider local averaging. The norm computation, as given by (9),is a global averaging operation, which ignores the important
local correlation between pixels. This local correlation can beused to reduce the influence of noise. Local smoothing as apreprocessing step was proven to be beneficial for color constancy algorithms, as discussed in Barnard’s study [3]. To exploit this local correlation, we introduce a local smoothing with, with standard deviation
a Gaussian filter,
(10)
where

.

derivative distribution of images forms a relatively regular, ellipsoid-like shape, of which the long axis coincides with the lightsource color [20]. In Fig. 1, the color derivative distribution isdepicted for three images. The color derivatives are rotated tothe opponent color space as follows:(15)

coincides with the white light
In the opponent color space,direction. For the scene under white light (the leftmost picture),
the distribution of the derivatives are centered along thei.e., the white-light axis. Once we change the color of the lightsource, as in the second and third picture, the distribution of thecolor derivatives no longer align with the white-light axis. In
other words, color constancy based on the gray-edge assumption can be interpreted as skewing the color derivative distribuorientation.
tion such that the average derivative is in the
Similar to the gray-world based color constancy, thegray-edge hypothesis can also be adapted to incorporate the
Minkowski norm
(16)
Color constancy based on this equation assumes that the th
Minkowski norm of the derivative of the reflectance in a scene, theis achromatic. We distinguish two special cases. For
illuminant is derived by a normal averaging operation over the, the illuminant is comderivatives of the channels. For
puted from the maximum derivative in the scene. The resemblance between the color constancy derivation from the grayworld and gray-edge hypothesis is apparent. Both methods canbe combined in a single framework of color constancy methods
based on low-level image features derived from the following
general hypothesis:

III. GRAY-EDGE HYPOTHESISAs an alternative to the gray-world hypothesis, we propose
the gray-edge hypothesis: the average of the reflectance differences in a scene is achromatic(11)
The subscript indicates the spatial derivative at scale . With
the gray-edge assumption, the light source color can be computed from the average color derivative in the image given by
(12)
(13)
(14)
. The graywhereedge hypothesis originates from the observation that the color(17)
has been incorporated into the constant
The division by. Next to the already discussed hypotheses (gray-world, maxRGB, Minkowski norm, and the newly proposed gray-edge), it
is obvious that this framework also includes higher order-based
color constancy. High-order derivatives have correspondenceswith the center-surround mechanism of the human eyes for color
constancy such as exploited in the well-known center-surroundretinex algorithm [21]. The influence of the color intensities
could be weighted according to their distance to the center of thereceptive field generally calculated by a difference of Gaussianfunctions.
The illuminant estimation of (17) describes a framework
for low-level based illuminant estimation. This framework
produces different estimations for the illuminant color basedon three variables.
1) The order of the image structure is the parameter determining if the method is a gray-world or a gray-edge algorithm. The gray-world methods are based on the RGB

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Fig. 1. Three acquisitions of the same scene under different light sources [19]. In the bottom row, the color derivative distributions are shown, where the axes are
the opponent color derivatives and the surfaces indicate derivative values with equal occurrence and darker surfaces indicating a more dense distribution. Note theshift of the orientation of the distribution of the derivatives with the changing of the light source.

TABLE IOVERVIEW OF THE DIFFERENT ILLUMINANT ESTIMATIONS METHODS TOGETHER WITH THEIRHYPOTHESES. THESE ILLUMINANT ESTIMATIONS ARE ALL INSTANTIATIONS OF (17)values, whereas the gray-edge methods are based on thespatial derivatives of order . In this paper, we will investigate higher order-based color constancy up to order.
which determines the relative2) The Minkowski norm
weights of the multiple measurements from which thefinal illuminant color is estimated. A high Minkowski
norm emphasizes larger measurements whereas a low
Minkowski norm equally distributes weights among themeasurements.
3) The scale of the local measurements as denoted by . For
first- or higher order estimation, this local scale is combined with the differentiation operation computed with theGaussian derivative. For zero-order gray-world methods,
this local scale is imposed by a Gaussian smoothing operation.
An overview of the instantiations of the illuminant estimation
given by the framework of (17), which are considered in thispaper, is given in Table I.

An advantage of the color constancy methods based on (17)is that they are all based on low computational demanding operations. In fact, the th Minkowski norm of (smoothed) RGB
values or derivatives can be computed extremely fast (even realtime on dedicated hardware). Furthermore, the method does not
require an image database taken under a known light source forcalibration as is necessary for more complex color constancy
methods such as color gamut mapping, and color by correlation[1], [15].
IV. EXPERIMENTS
In the previous section, a general formulation for color illuminant estimation has been proposed based on low-level image
features. In this section, the performance is tested for various
parameter settings on a set of colorful objects in a controlledindoor setting, and on a real-world data set containing mainly
outdoor scenes. For both data sets, the illuminant color of thescene is provided as additional information (i.e., ground-truth).

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Fig. 2. Examples of the images in data set [19].

For evaluation, the angular error between the estimated lightsource and the actual light source is used as an error measure(18)

TABLE IIMEDIAN ANGULAR ERROR (DEGREES) ON INDOOR IMAGE
DATA SET FOR VARIOUS COLOR CONSTANCY METHODS

indicates a normalized vector. For the three data
where thesets tested here, we report the median angular error, which isconsidered appropriate to assess the performance of color constancy algorithms [22].
A. Controlled Indoor Image Set
First, the proposed algorithms are tested on a large data setof colorful objects under different light sources [19]. The set
consists of images taken under 11 varying light sources of 30
different scenes containing both matte and specular objects (seeexamples in Fig. 2). Several images where found to be unusable,
resulting in a data set of 321 images. Results of other color constancy algorithms on this standard data set are available in [3],[12], [15], and [22].
In Table II, the results of multiple methods are summarized.
Let us first consider the results obtained by the gray-world
and its performance as a function of the Minkowski norm andlocal smoothing. Both parameters significantly improve theperformance. For the zero-order instantiation, only varying the
Minkowski norm reduces the error from 7.0 for gray-world, to
3.7 for a Minkowski norm equal to 7. A further increase in performance of 15%, to an error of 3.2 , is obtained by combining
and a Minkowski norma simple local smoothing with). The illuminant estimations basedof 11 (indicated byon the gray-edge hypothesis, both the first and second-order,
exhibit similar behavior. Again, a significant drop in the error is
obtained by an appropriate choice of the Minkowski norm andlocal smoothing. The best results, an error of 2.7 , is obtainedwith the second-order gray-edge method.
In Fig. 3, the median error is given as a function of the
Minkowski norm and local smoothing for the indoor image set.
These figures show that a small local scale or a low Minkowski
norm perform significantly less. The performance increases byaugmenting the Minkowski norm and the local scale. The performance quickly levels off to a plateau where the performancechanges little. In Table III, we have indicated for which regionsof parameter settings a comparable performance, i.e., within
10% of the the optimal, is obtained.
Results of more complex color constancy methods, such as
gamut mapping, neural network algorithm, and color-by-correlation, have been reported in literature for the images in group A[3], [12], [22]. These results have been also included in Table II.
The more complex algorithms obtained comparable results tothe ones we reported. Only the CGIE algorithms obtains better

TABLE III
PARAMETER SETTINGS FOR WHICH THE PERFORMANCE REMAINS
WITHIN 10% OF OPTIMAL PERFORMANCE AS GIVEN IN TABLE II

results with an error of 1.3 . However, it should be noted that
this algorithm uses the 11 illuminants which where used during
the image acquisition as prior knowledge. If this prior knowledge is put aside, the performance drops to an error of 2.6(GCIE Version 3, 87 lights).
B. Real-World Image Set
Next, the color constancy algorithms are tested on a databasepresented by Ciurea and Funt [23]. The database contains 11 000
images extracted from 2 h of digital video. Both indoor and outdoor scenes from a wide variety of locations are represented (seeFig. 5). A small gray sphere was mounted onto the video camera,
appearing for all the images in the right bottom corner of the images. The sphere is exploited to estimate the illuminant color in
the scene. This color illuminant estimation is available with the
database and is used as a ground truth in this experiment. The
original images were extracted from 15 different film clips taken
at different locations. Because of the high correlation between
the images in the database, the experiments are performed ona subset of 150 randomly chosen images containing ten images
from each of the 15 video clips. The pixels in the right bottom

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Fig. 3. Median angular error of the general gray-world, first-order, and second-order gray-edge method as a function of the Minkowski norm and local smoothing.
The angular error axis is inverted for visualization purposes.

Fig. 4. Examples of the images from the real-world data set [23].

Fig. 5. Color constancy results of gray-world, general gray-world, gray-edge, and second-order gray-edge on real-world data set. The angular error is indicatedin the right bottom corner. The first row depicts a failure of the edge-based approaches, whereas the gray-world methods give acceptable results. The second andthird rows show examples where the gray-world methods fail and the gray-edge methods obtain superior results.

corner, which contains the gray sphere, are excluded from thecolor constancy computation.
The results on the real-world data set are summarized inTable IV. Again, an appropriate choice of the parameters
significantly improves the results. Interestingly, the gray-edge
performs best on this set of real-world images. It improves
the color constancy results with about 40% compared to the
Max-RGB.

In Fig. 5, corrected images based on gray-world and grayedge methods are given for the real-world set. We applied the
optimal parameters as given in Table IV. We often found a highcorrelation between the two edge-based methods. However, theestimations based on the gray-world and the two edge-based
methods differ often. For example, in row one of Fig. 5, theedge-based methods fail and their estimation of the light source
is too blue, whereas the general gray-world obtains acceptable

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VAN DE WEIJER et al.: EDGE-BASED COLOR CONSTANCYTABLE IVMEDIAN ANGULAR ERROR (DEGREES) FOR VARIOUS COLORCONSTANCY METHODS ON REAL-WORLD IMAGE SET

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Further work also includes searching for more elaborate ways
to combine the low-level building blocks proposed in this paper.
Can we find ways to decide what method is expected to perform
best on a particular image? Furthermore, we believe that automatic estimation of the parameters separately per image, insteadof for the whole data set, will improve the color constancy results, possibly within a learning context, such as proposed by
Cardei et al. [11]. Another interesting research direction would
be to constrain the possible illuminants to be physically feasible
as is done in [12].
VI. CONCLUSION

results. The second row shows an example where the large blue
sky results in an light source estimation which is much too
blue for the gray-world methods. The edge-based methods obtain better results for this image. The last row shows an example where the second-order gray-edge method outperforms
the other methods.
V. DISCUSSION
In the previous experiments, we have demonstrated that the
proposed color constancy algorithms obtain comparable results
to more complex color constancy algorithms. However, the optimal parameter setting vary for the different data sets. Important to note is the difference in the Minkowski norm for theedge-based methods. On the real-world set, a Minkowski normof one is optimal whereas for the indoor sets a higher Minkowski
norm between 6 and 15 is optimal. This is probably causedby the black background present in the indoor scenes. For theedge-based methods, the illumination estimate is computed byaveraging the edge differences in a scene. Depending on the
Minkowski norm, more weight is given to prominent edges. For
the edge-based methods, the fact that the background in the images of sets A and B is black, significantly increases the chancethat the highest edge in the image is black-white. This explains
why a high Minkowski norm for these data sets is preferred. Incase of the real-world data, the chance that the highest edge-response is caused by a black-white edge is smaller and consequently it is advantageous to take multiple measurements in
the image into account. This is reflected in a lower Minkowski
norm.
The proposed gray-edge algorithm can be obtained from thegray-world algorithm by simply exchanging the RGB values forthe spatial image derivatives. The zero-order image structure,
which provides the building stones for the gray-world method,is replaced by the higher order image structure. In the case of
the gray world, the change to higher orders proved beneficial
and the gray-edge methods outperform the gray-world methods.
To our knowledge this paper is the first to propose color constancy derived from image derivatives. Methods such as Gamut
mapping, neural network based color constancy and color bycorrelation are all based on the zero-order structure of images.
However, there is no restriction which prevents them from using
the higher order structure of images, and it would be interesting
to see how these methods performed once based on the derivatives of images, or based on both zero-order and higher order
structure of images.

In this paper, we have investigated edge-based color constancy. The method is derived from the gray-edge hypothesis
which assumes that the average edge difference in a scene isachromatic. In contrast to existing methods, which are based on
zero-order structure of the image, our method is based on thehigher order structure of images. Furthermore, we introduce aframework of color constancy based on low-level image features
which includes the known algorithms (gray-world, max-RGB,
Minkowski norm) as well as the newly proposed gray-edge andhigher order gray-edge algorithms. The quality of the various instantiations of the framework is tested on two large data sets ofimages recording objects under a large number of different lightsources. The experimental results show that the newly proposed
simple color constancy algorithms obtain similar results as more
complex state-of-the-art color constancy methods. Furthermore,
the results show that color constancy based on the gray-edge
hypothesis obtains better results than those obtained with thegray-world method for real-world images.
ACKNOWLEDGMENT
The authors would like to thank F. Ciurea for providing thereal-world database.
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Joost van de Weijer received the M.Sc. degree
in applied physics from the Delft University ofTechnology, Delft, The Netherlands, in 1998, and the
Ph.D. degree in computer science from the University of Amsterdam, Amsterdam, The Netherlands, in
2005.
He is currently a Marie Curie Intra-European
Fellow with the LEAR team, INRIA Rhone-Alpes,
France. His research interests include color constancy,
object recognition, color image processing, color
naming, and machine learning for computer vision.

Theo Gevers is an Associate Professor of computerscience at the University of Amsterdam, Amsterdam,
The Netherlands, and an ICREA Research Professor
at the Computer Vision Center (UAB), Barcelona,
Spain. At the University of Amsterdam, he is a
Teaching Director of the M.Sc. degree program in artificial intelligence. He has published more than 100
papers on color image processing, image retrieval,and computer vision. His main research interests
are in the fundamentals of content-based image
retrieval, color image processing, and computer
vision specifically in the theoretical foundation of geometric and photometricinvariants.
Dr. Gevers is the Chair of the Internet Imaging Conference (SPIE 2005 and2006) and Multimedia Content Access: Algorithms and Systems (SPIE 2008),
and coorganizer of the First International Workshop on Image Databases andMulti Media Search (1996), the International Conference on Visual Information Systems (1999, 2005), and the Conference on Multimedia and Expo (ICME
2005). He is the Guest Editor of the International Journal of Computer Vision
special issue on content-based image retrieval and the Computer Vision andImage Understanding special issue on color for image indexing and retrieval.
Further, he is a Lecturer for postdoctoral courses given at various major conferences (CVPR, ICCV, ICPR, ICIP, SPIE, and CGIV).

Arjan Gijsenij received the M.Sc. degree in computer science from the University of Groningen,
Groningen, The Netherlands, in 2005. Currently,
he is pursuing the Ph.D. degree at the University of
Amsterdam, Amsterdam, The Netherlands.
His research interests include computer vision,(color) image processing, and statistical patternrecognition. His current research focuses on color
constancy algorithms.

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