Blue Shift Assumption: Improving Illumination Estimation Accuracy for

Single Image from Unknown Source

Nikola Bani

c and Sven Lon

cari

Image Processing Group, Department of Electronic Systems and Information Processing,

Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, Croatia

Keywords:

Chromaticity, Color Constancy, Blue, Illumination Estimation, White Balancing.

Abstract:

Color constancy methods for removing the inﬂuence of illumination on object colors are divided into statistics-

based and learning-based ones. The latter have low illumination estimation error, but only on images taken

with the same sensor and in similar conditions as the ones used during training. For an image taken with an

unknown sensor, a statistics-based method will often give higher accuracy than an untrained or speciﬁcally

trained learning-based method because of its simpler assumptions not bounded to any speciﬁc sensor. The

accuracy of a statistics-based method also depends on its parameter values, but for an image from an unknown

source these values can be tuned only blindly. In this paper the blue shift assumption is proposed, which acts

as a heuristic for choosing the optimal parameter values in such cases. It is based on real-world illumination

statistics coupled with the results of a subjective user study and its application outperforms blind tuning in

terms of accuracy. The source code is available at http://www.fer.unizg.hr/ipg/resources/color constancy/.

1 INTRODUCTION

Color constancy enables the human visual system to

recognize object colors even under various illumina-

tion (Ebner, 2007). Digital cameras also implement

some form of computational color constancy (Kim

et al., 2012). It ﬁrst estimates the scene illumina-

tion and then it corrects the colors through chromatic

adaptation (Gijsenij et al., 2011). The image forma-

tion model commonly used for illumination estima-

tion and written under Lambertian assumption is (Gi-

jsenij et al., 2011)

(x) =

I(λ, x)R(λ, x)ρ

(λ)dλ (1)

where c ∈ {R, G, B} is a color channel of the image

f, x is a given image pixel, λ is the wavelength of the

light, ω is the visible spectrum, I(λ, x) is the spec-

tral distribution of the light source, R(λ, x) is the sur-

face reﬂectance, and ρ

(λ) is the camera sensitivity

of color channel c. Removing x from I(λ, x) by as-

suming uniform illumination simpliﬁes the problem

so that observed light source is then

e =









I(λ)ρ(λ)dλ. (2)

A successful chromatic adaptation requires only

the direction of e (Barnard et al., 2002). How-

ever, since both I(λ) and ρ(λ) are unknown and

only f is given, calculating e is an ill-posed prob-

lem, which is solved by introducing various as-

sumptions. Over time this gave rise to two main

groups of illumiantion estimation methods. In the

ﬁrst group are low-level statistics-based methods such

as White-patch (Land, 1977; Funt and Shi, 2010)

and its improvements (Bani

c and Lon

cari

c, 2013;

Bani

c and Lon

cari

c, 2014a; Bani

c and Lon

cari

2014b), Gray-world (Buchsbaum, 1980), Shades-of-

Gray (Finlayson and Trezzi, 2004), Grey-Edge (1st

and 2nd order) (Van De Weijer et al., 2007). The sec-

ond group consists of learning-based methods such

as gamut mapping (Finlayson et al., 2006), nat-

ural image statistics (Gijsenij and Gevers, 2007),

spatio-spectral learning (Chakrabarti et al., 2012),

simplifying the illumination solution space in vari-

ous ways (Bani

c and Lon

cari

c, 2015a; Bani

c and

Lon

cari

c, 2015b; Bani

c and Lon

cari

c, 2015b; Bani

and Lon

cari

c, 2017), using color/edge moments (Fin-

layson, 2013), regression trees with simple features

from color distribution statistics (Cheng et al., 2015),

spatial localization (Barron, 2015; Barron and Tsai,

2017), using various convolutional neural network ar-

chitectures (Bianco et al., 2015; Shi et al., 2016; Hu

et al., 2017; Qiu et al., 2018).

Bani

c, N. and Lon

cari

c, S.

Blue Shift Assumption: Improving Illumination Estimation Accuracy for Single Image from Unknown Source.

DOI: 10.5220/0007394101910197

In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 191-197

ISBN: 978-989-758-354-4

191

The most recent learning-based methods outper-

form the statistics-based ones by far and in some cases

the estimation error can only be attributed to violation

of uniform illumination assumption or wrong ground-

truth illumination (Zakizadeh et al., 2015). Neverthe-

less, learning-based methods work so accurately only

for images taken with the same sensor and in similar

conditions as the ones used in the training dataset. For

images taken with another sensor they will usually fail

because different sensor characteristics described by

ρ(λ) were present during image formation (Bani

c and

Lon

cari

c, 2017). Thus, for a single image in the wild

from an unknown source learning-based methods will

usually not be useful. In cases like this statistics-

based methods will often be more accurate because

of their simpler assumptions not bounded to any spe-

ciﬁc sensor. The accuracy of statistics-based methods

also depends on their parameter values, but for a sin-

gle image from an unknown source these values can

be tuned only blindly. In this paper the blue shift as-

sumption is proposed, which acts as a heuristic for

choosing the optimal parameter values in such cases.

It is based on real-world illumination statistics cou-

pled with the results of a subjective user study and it

is more accurate then blind tuning.

The paper is structured as follows: Section 2 gives

the motivation for making a new assumption, in Sec-

tion 3 the so called blue shift assumption is proposed,

Section 4 contains the experimental results, and Sec-

tion 5 concludes the paper.

2 MOTIVATION

2.1 Real-world Observations

As mentioned in the introduction, assumptions are

needed to handle the illumination estimation prob-

lem. While learning-based methods try to extract ad-

ditional information about images to obtain more ac-

curate illumination estimations, such learning is not

possible when only a single image from an unknown

source is given and in such cases statistics based

methods should be preferred. Most of these methods

also have parameters whose values affect the accu-

racy, but without having any other images from the

same source, it is hard to automatically tell which

parameter values will give the most accurate result.

One of the solutions is to look for additional proper-

ties that are usually encountered in natural images. If

the basic statistics of illuminations that inﬂuence nat-

ural images are observed, some general patterns can

be observed. For example, by looking at the red chro-

maticities of systematically measured real-world illu-

mination colors as shown in Fig. 1, it can be seen that

the majority of them is centered around lower values.

From theoretical aspect this could mean that the real-

world illumination or at least the illumination in im-

ages of scenes mostly taken by people tends to have

lower red chromaticity values i.e. higher blue chro-

maticity values because of the strong linear connec-

tion between the two (Bani

c and Lon

cari

c, 2015a).

The root cause for this asymmetry can be found in

the fact that most of images are taken in outdoor con-

ditions. For example, in the GreyBall dataset (Ciurea

and Funt, 2003) that contains 11346 images roughly

57% of them were taken outdoor, for the eight NUS

datasets (Cheng et al., 2014) this amounts to roughly

74%, while for RAISE, the challenging real-world

image dataset (Dang-Nguyen et al., 2015), this goes

over 85%. Namely, in outdoor conditions the most

common two illumination sources are the sun and the

light scattered across the sky with the latter one hav-

ing more blue chromaticity and less red chromaticity

almost by deﬁnition. In practice this means that the

scene illumination of taken images will generally tend

to be shifted more to the blue.

Figure 1: The red chromaticity distribution of the ground-

truth illuminations from the GreyBall dataset (Ciurea and

Funt, 2003).

2.2 Numerical Observations

Since illumination estimations of statistics-based

methods appear ”to correlate roughly with the ac-

tual illuminant” (Finlayson, 2013) i.e. ”they oc-

cupy roughly the same region in the chromatic-

ity plane” (Bani

c and Lon

cari

c, 2017), this further

means that this empirical information could be ap-

plied to illumination estimations. For example, when

a statistics-based method produces different results

for various parameter values and it has to be decided

which one to select as the ﬁnal one without having any

other information, the ones shifted more to the blue

should on average probably be preferred. To check to

what degree illumination estimations correlate to the

actual ground-truth illumination with respect to the

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

192

being shifted more or less to the blue, it is enough to

perform simple counting of illumination estimations

given by chosen methods where the red chromatic-

ity is less than the red chromaticity of the ground-

truth. Probably the best known statistics-based meth-

ods with at least one parameter are Shades-of-Gray,

General Gray-World, 1st-order Gray-Edge, and 2nd-

order Gray-Edge. All of these methods have the

Minkowski norm p parameter, while all but Shades-

of-Gray additionally have the σ parameter for Gaus-

sian smoothing. For the purpose of counting the pa-

rameter values were constrained to p ∈ {1, . . . , 10}

and σ ∈ {1, 2, 3}. If for all combinations of these pa-

rameter values every of the mentioned methods is ap-

plied to each image in the Cube dataset (Bani

c and

Lon

cari

c, 2017), eight NUS datasets (Cheng et al.,

2014), and the GreyBall dataset (Ciurea and Funt,

2003), the percentages of the illumination estimations

whose red chromaticity is less than the red chromatic-

ity of the ground-truth illumination for a given image

are given in Table 1. It can be seen that across meth-

ods and datasets in most cases illumination estima-

tions are on average shifted too much to the red.

3 THE PROPOSED ASSUMPTION

3.1 Statement

The previous section boils down to the following two

observations: 1) real-world images are taken under il-

lumination that is on average shifted more to the blue,

and 2) most commonly used statistics-based illumina-

tion estimation methods give illumination estimations

that are on average shifted more to the red.

Based on these two observations, the so called

blue shift assumption can be proposed: among sev-

eral candidate illumination estimations for a given

image, the ones with the lower red chromaticity are

more accurate. It has to be stressed again that this

is only an assumption like e.g. the Gray-World as-

sumption that assumes the average scene reﬂectance

to be achromatic. Such and similar assumptions are

often violated, but as as explained in the introduction,

they are still required because of the ill-posed nature

of the illumination estimation problem. The blue shift

assumption is applied to existing illumination estima-

tions, which means that it can be used only in com-

bination with other assumptions used by the methods

that initially created these illumination estimations.

3.2 Application

The simplest application of the proposed blue shift

assumption to a set of illumination estimations would

be to choose the one with the lowest red chromatic-

ity. However, empirically it has been found out that

it is better to take the illumination estimation with

the second lowest red chromaticity. This founding

can be atrributed to the fact that the lowest red chro-

maticity has a higher probability of being an outlier

and should therefore be avoided. Additionally, when

inspecting cases where there was no signiﬁcant out-

lying, the difference between the lowest and second

lowest red chromaticity was not found to be signiﬁ-

cantly high. All this justiﬁes taking the second low-

est red chromaticity in order to avoid potential out-

liers. The formal notation of the described procedure

is given in Algorithm 1.

Algorithm 1: Blue shift assumption.

Input: estimation chromaticities E =

(1)

, . . . , e

(n)

}

Output: assumed optimal illumination estima-

tion e

∗

1: r = min

(i)

 smallest red chromaticity

2: m = argmin

(i)

|r < e

(i)

}  index of second

smallest

3: e

∗

← e

(m)

3.3 Subjective Error Assessment

When the application of the blue shift assumption

mistakenly increases the angular error, the resulting

chromatically adapted image will by deﬁnition tend

to be subjectively warmer than an average image with

the same illumination estimation error. This is be-

cause the red component will be reduced, which in

turn will result in less reduction of the redish illumi-

nation inﬂuence and thus subjectively warmer images.

A recent user study has shown ”that when the illumi-

nations are distinct, there is a preference for the out-

door illumination to be corrected resulting in warmer

ﬁnal result” (Cheng et al., 2016). In other words

even if the application of the blue shift assumption

increases the error, subjectively it is still more accept-

able than a colder result with the same angular error as

can be seen in Figure 2. However, as can be predicted

by the results shown in Table 1, a more usual effect of

the blue shift assumption application will be to choose

the illumination estimation that is less shifted to the

blue than other illumination estimations produced by

a given method for various parameter values.

Blue Shift Assumption: Improving Illumination Estimation Accuracy for Single Image from Unknown Source

193

Table 1: Percentages of the illumination estimations whose red chromaticity is less than the red chromaticity of the ground-

truth illumination.

Cube dataset NUS datasets GreyBall dataset

Shades-of-Gray 27% 38.76% 35.38%

General Gray-World 29.99% 44.48% 34.13%

1st-order Gray-Edge 34.76% 38% 50.32%

2nd-order Gray-Edge 32.86% 34.24% 50.72%

(a) (b) (c)

Figure 2: The effect of red and blue illumination shift-

ing based on the application of the blue shift assumption

to the results of the Shades-of-Gray method (Finlayson

and Trezzi, 2004) to one of the images from the NUS

datasets (Cheng et al., 2014): (a) chromatic adaptation with

the result of application of the blue shift assumption and

an angular error of 11.56

◦

, (b) chromatic adaptation with

ground-truth illumination, and c) chromatic adaptation with

the illumination of the same angular error of 11.56

◦

as in

a), but with the opposite i.e. red shifting.

4 EXPERIMENTAL RESULTS

4.1 Experimental Setup

The validity of the blue shift assumption was tested on

the Cube dataset (Bani

c and Lon

cari

c, 2017) and eight

linear NUS datasets (Cheng et al., 2014) because they

all have linear images in accordance with Eq. 1. The

ColorChecker dataset was not used because it has

been shown on several occasions (Lynch et al., 2013;

Finlayson et al., 2017) that it has a public record of

biased and wrong usage. Additionally, the GreyBall

dataset has also not been used for two reasons. The

ﬁrst one is that it contains non-linear images. The

second reasons is that it was used to observe the regu-

larity that serves as the basis for the blue shift assump-

tion, so it may be biased to use it for testing the va-

lidity of the assumptions. Among various estimation

accuracy measures (Gijsenij et al., 2009; Finlayson

and Zakizadeh, 2014; Bani

c and Lon

cari

c, 2015a) the

most commonly used one is the angle between the il-

lumination estimation vector and the ground-truth il-

lumination i.e. the angular error. When describing

the angular errors on a dataset by a single statistic,

the median angular error is considered to be the best

choice (Hordley and Finlayson, 2004) due to the prop-

erties of angular error distribution.

4.2 Baseline Methods

The blue shift assumption is supposed to be used in

cases when there is only a single image available i.e.

when there are no other training images. In such

circumstances practically no learning-based method

can be either trained or used. As for the statistics-

based methods, their parameter values can also not be

checked on other images to see which ones should

be preferred. A simple baseline method for a sin-

gle image in this case is to simply average the results

obtained for various parameter values without giving

preference to any of them. It is also interesting to see

what errors are produced by ideally ﬁxed parameter

values for a given dataset. While this is deﬁnitely un-

fair because of the advantage of the knowledge of the

whole dataset, for comparison purposes it is useful to

see how far or close the from such errors is the appli-

cation of the blue shift assumption.

Figure 3: Combining the results of the Shades-of-Gray

method on NUS datasets for various upper limits on p.

4.3 Accuracy

The tested statistics-based methods with at least

one parameter were as earlier Shades-of-Gray, Gen-

eral Gray-World, 1st-order Gray-Edge, and 2nd-order

Gray-Edge. The parameter values were also con-

strained in the same way. Table 2 shows the angu-

lar errors obtained by the baseline methods and the

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

194

Table 2: Combined angular errors on the linear images of the Cube dataset (Bani

c and Lon

cari

c, 2017) and eight NUS

datasets (Cheng et al., 2014) (lower is better). The used format is the same as in (Barron and Tsai, 2017).

Algorithm

Cube dataset NUS datasets

Mean Med. Tri.

Best

25%

Worst

25%

Avg. Mean Med. Tri.

Best

25%

Worst

25%

Avg.

Shades-of-Gray (Finlayson and Trezzi, 2004)

Averaged baseline 2.65 1.91 2.07 0.42 6.18 1.94 3.65 2.95 3.16 0.95 7.46 3.00

Ideally ﬁxed

parameters

2.55 1.72 1.90 0.38 6.14 1.81 3.44 2.61 2.78 0.83 7.42 2.74

Blue shift assumption 2.18 1.51 1.66 0.36 5.16 1.59 3.82 2.73 2.92 0.91 8.67 2.99

General Gray-World (Barnard et al., 2002)

Averaged baseline 2.60 1.75 1.93 0.39 6.22 1.84 3.16 2.35 2.53 0.70 6.90 2.47

Ideally ﬁxed

parameters

2.47 1.56 1.77 0.37 6.15 1.73 3.28 2.43 2.58 0.70 7.34 2.53

Blue shift assumption 2.15 1.44 1.59 0.35 5.20 1.55 3.40 2.58 2.71 0.81 7.48 2.70

1st-order Gray-Edge (Van De Weijer et al., 2007)

Averaged baseline 2.43 1.63 1.83 0.49 5.72 1.82 3.38 2.55 2.74 0.89 7.26 2.74

Ideally ﬁxed

parameters

2.40 1.52 1.76 0.45 5.78 1.76 3.07 2.11 2.33 0.70 7.05 2.37

Blue shift assumption 2.07 1.43 1.59 0.49 4.68 1.61 3.44 2.42 2.60 0.84 7.84 2.70

2nd-order Gray-Edge (Van De Weijer et al., 2007)

Averaged baseline 2.70 1.93 2.12 0.74 5.97 2.18 3.83 3.00 3.18 1.17 7.90 3.20

Ideally ﬁxed

parameters

2.43 1.53 1.77 0.46 5.83 1.77 3.11 2.28 2.42 0.78 6.91 2.47

Blue shift assumption 2.25 1.68 1.82 0.53 4.90 1.78 3.88 2.63 2.84 0.92 9.03 3.00

blue shift assumption on linear images of the Cube

dataset and eight NUS datasets. In all but one case the

blue shift assumption leads to higher accuracy than

the simple averaged baseline method. As for the ide-

ally ﬁxed parameters, on NUS datasets they always

give lower errors and on the Cube dataset only once.

An additional property of the blue shift assumption is

that it is more stable than the simple averaged baseline

method. Namely, as the number of possible parameter

values increases, the accuracy of the averaged result

tends to decrease, while the one of the blue shift as-

sumption remains much more stable. In Fig. 3 this is

shown for the results of applying the Shades-of-Gray

method to the NUS datasets. There is another impor-

tant thing to be observed in Table 2, namely the fact

that for supposedly more accurate methods the blue

shift assumption also results in higher estimation ac-

curacy. For example in terms of median angular er-

ror on both the Cube and the NUS datasets the blue

shift assumption gives higher accuracy for 1st-order

Gray-Edge than for General Gray-World and it also

gives higher accuracy for General Gray-World than

for Shades-of-Gray.

When the blue shift assumption is applied to non-

linear images, the positive effect is visible to a lesser

extent as can be seen on the results for the non-linear

images of the GreyBall dataset (Ciurea and Funt,

2003) shown in Table 3. Here the blue shift assump-

tion leads to higher accuracy than the simple averaged

baseline method in half of the cases. The main dif-

ference between these images and the images from

the Cube and NUS datasets is that the images in the

GreyBall dataset are non-linear, which practically al-

ways leads to higher errors in illumination estimation

accuracy for a given method (Gijsenij et al., 2011; Gi-

jsenij et al., 2018). This shows how increased estima-

tion errors also lead to inefﬁciency of the blue shift

assumption. Something similar could also have been

observed in Table 2 for linear images where the blue

shift assumption was shown to be less efﬁcient when

applied to results of less accurate methods.

4.4 Discussion

The experimental results clearly show the beneﬁts of

the blue shift assumption over the simple averaged

baseline method. In addition to being more accurate,

this assumption is also more stable when the number

of illumination estimations to be combined changes.

The blue shift assumption failed to outperform the

averaged baseline only for the General Gray-World

method on the NUS datasets. It is also interesting to

note that in many cases the blue shift assumption out-

performs the results obtained by using ideally ﬁxed

parameters, which shows the beneﬁts of the assump-

tion’s dynamical parameter values adjustment. The

cases for which the blue shift assumption fails are the

ones where all underlying illumination estimations

are already erroneously shifted to the blue or where

they are all very close to the ground-truth illumina-

tion. Nevertheless, as explained previously in more

detail in Section 3.3, the resulting errors are relatively

acceptable.

Blue Shift Assumption: Improving Illumination Estimation Accuracy for Single Image from Unknown Source

195

Table 3: Angular errors on the non-linear images of the GreyBall dataset (Ciurea and Funt, 2003) (lower is better). The used

format is the same as in (Barron and Tsai, 2017).

Algorithm Mean Med. Tri.

Best

25%

Worst

25%

Avg.

Shades-of-Gray (Finlayson and Trezzi, 2004)

Averaged baseline 6.23 5.37 5.58 1.74 12.20 5.25

Ideally ﬁxed parameters 6.11 5.28 5.48 1.75 11.88 5.17

Blue shift assumption 6.29 5.40 5.62 1.72 12.35 5.27

General Gray-World (Barnard et al., 2002)

Averaged baseline 6.50 5.58 5.81 1.78 12.76 5.44

Ideally ﬁxed parameters 6.24 5.37 5.60 1.76 12.16 5.26

Blue shift assumption 6.49 5.51 5.79 1.73 12.83 5.40

1st-order Gray-Edge (Van De Weijer et al., 2007)

Averaged baseline 6.50 5.58 5.81 1.78 12.76 5.44

Ideally ﬁxed parameters 6.24 5.37 5.60 1.76 12.16 5.26

Blue shift assumption 6.49 5.51 5.79 1.73 12.83 5.40

2nd-order Gray-Edge (Van De Weijer et al., 2007)

Averaged baseline 6.82 5.15 5.71 1.43 14.73 5.31

Ideally ﬁxed parameters 6.10 4.85 5.28 1.64 12.42 5.02

Blue shift assumption 7.88 5.80 6.49 1.51 17.54 6.01

5 CONCLUSIONS

The so called blue shift assumption has been proposed

to increase the accuracy of statistics-based methods

for the case when there is only one image given from

an unknown sensor. It was experimentally shown

to outperform the simple averaging baseline method

when no preference is given to any of the parameter

values of a chosen statistics-based method. The re-

sults of a user study can additionally be used to show

that even in failure cases the blue shift assumption

produces results that are subjectively more acceptable

than average failure cases. In future some better out-

lier removal strategies in the blue shift assumption

will be researched to further increase the accuracy.

Another direction will be to look for some other sim-

ilar properties that can be used when only on a single

image is given.

ACKNOWLEDGEMENT

This work has been supported by the Croatian Science

Foundation under Project IP-06-2016-2092.

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