1. Contributed paper
OPTO-ELECTRONICS REVIEW 11(3), 193–196 (2003)
Colour temperature estimation algorithm for digital images
– properties and convergence
K. WNUKOWICZ* and W. SKARBEK
Institute of Radioelectronics, Warsaw University of Technology,
15/19 Nowowiejska Str., 00-665 Warsaw, Poland
The paper presents an algorithm for estimation of temperature of image. Colour temperature is important, perceptual feature
describing colour and content of images. The main idea of the algorithm is to average pixel values of image, omitting the
values which have meaningless influence on perception of colour temperature. It is done in an iterative procedure. The con-
vergence of the procedure is discussed. The algorithm can be applied in image search/retrieval tasks and is proposed in the
MPEG-7 colour temperature descriptor for estimation of colour temperature of images.
Keywords: colour temperature, colour perception, image retrieval.
1. Introduction This article presents a colour temperature estimation al-
gorithm for image to represent general visual impression of
Colour temperature is one of the visual features essentially colour temperature a viewer has of the image. The impres-
influencing perception of colour by the human visual sys- sion depends on elements like image colour content, illumi-
tem. Categories such as hot, warm, moderate, and cool are nation of the scene while it was photographed, and to some
used for describing the felt temperature of the touched ob- extent on observation conditions. The procedure consists of
jects. The same categories can be considered in the case of two main steps. In the first step, the image average colour
colour temperature feeling by observer who is viewing col- value is computed by omitting pixels having poor influence
our scene or image. This feeling depends mostly on proper- on colour temperature impression. In the second step, the
ties of illumination of the viewed scene. Different kinds of colour temperature value is estimated for previously com-
illumination of the same scene gives different colour tem- puted colour, utilizing its chromaticity coordinate values. It
perature feelings, adequately to the illumination. For exam- is done by Robertson’s algorithm [1] which approximates
ple, natural daylight can have light in broad range of colour colour temperature by means of the fixed lines on uv chro-
temperature values depending on the time of the day as maticity diagram called isotemperature lines.
well as atmospheric and weather conditions which have an The estimated colour temperature of image can be clas-
influence on colour temperature perception in outdoor im- sified into one of subjective categories: hot, warm, moder-
ages. The view of the same landscape in various viewing ate, and cold. The whole range of colour temperature val-
conditions such as a sunny day at noon, cloudy sky or at ues should be divided into 4 sub-ranges. This task was ap-
twilight gives varied feelings of colour temperature. In the proached by conducting subjective experiments on a group
same way works artificial light – different light sources can of people who visually assessed test images with respect to
give different colour temperature feelings for the illumi- colour temperature feeling. The result of the assessment
nated scene. was used for partition objectively computed colour temper-
The concept of colour temperature is not explicitly re- ature values into the subjective categories [2].
lated to thermal temperature of the viewed objects. It is de- The estimated colour temperature could be applied for
rived from a relationship between the temperature of a hy- image indexing and searching engines and is proposed as a
pothetical object called black body and its appeared colour. basis for a new visual descriptor in MPEG-7 standard [3,4].
The colour chromaticity of black body just depends on
temperature of this body. Being based on this assumption 2. Procedure for estimation of temperature of
one can classify colours in the range from hot to cold ac- image
cording to its similarity to of colour black body in appro-
priate temperature. A basic definition of colour temperature can be stated as an
absolute temperature of the black body whose spectral dis-
tribution of radiance power is proportional to the given
*e-mail: stimulus. It means that the both radiations have the same
K.Wnukowicz@elka.pw.edu.pl
Opto-Electron. Rev., 11, no. 3, 2003 K. Wnukowicz 193

2. Colour temperature estimation algorithm for digital images – properties and convergence
Fig. 2. Isotemperature lines on the uv chromaticity diagram.
The estimation of colour temperature for the given col-
Fig. 1. Planck’s locus of black body on xy chromaticity diagram. our has the steps as follows:
• convert chromaticity coordinates from (xs,ys) to (us,vs)
(according to CIE 1960 UCS),
chromaticity values. The chromaticity of black body radia- • find two adjecent isotemperature lines, from collection
tion depends only on its temperature and is defined by of 31 isotemperature lines, which are neighbours to the
Planck’s formula [1]. It is convenient to depict this depend- point (us,vs) on the chromaticity diagram,
ency on a chromaticity diagram. Figure 1 shows the curved • compute value of colour temperature from the distance
line named Planck’s locus, corresponding to the chromatic- ratio between the point and both of the two adjacent
ity of a black body at the temperature changing from isotemperature lines.
2000 K (red colour) to 25000 K (blue colour).
Because of the fact that having the basic definition of 3. Calculation of the perceptional average
colour temperature it can be determined only for a small set chromaticity coordinates of image
of colours, a correlated colour temperature concept is intro-
duced. A correlated colour temperature is the temperature In the first stage of colour temperature estimation there are
of Planck’s black body whose perceived colour most computed the chromaticity coordinates of average colour
closely resembles that of the given stimulus. So, it is de- of image pixels related to human perception of colour tem-
fined rather in perceptual aspect. In practice, the term of perature. Pixels which have poor or meaningless influence
colour temperature is used also for correlated colour tem- on this perception are discarded during calculation. Firstly,
perature for shortness. The calculation of colour tempera- image pixels are converted into standard linear colour
ture is performed by use of the perceptually homogeneous space sRGB [5]. Equation
UV chromaticity diagram (CIE 1960). It is assumed that
if R(i, j ) £ 0.03928 ´ 2550
.
the colour temperature is constant along the lines which are
perpendicular to the Planck’s locus on this diagram
æ R(i, j ) ö
(Fig. 2). These short straight lines are called isotemperature RsRGB (i, j ) = ç ÷
lines. è 255 ´ 12.92 ø
The algorithm for calculation of the chromaticity coor- else (1)
dinates of image has its main steps as follows: 2 .4
• linearize image pixels: RGB –> sRGB, é R(i, j ) ù
ê 255 + 0.055 ú
• convert colour space sRGB –> XYZ, RsRGB (i, j ) = ê ú
• discard pixels with Y luminance value below threshold ê .
1055 ú
Tl, ë û
• iteratively average remaining pixels discarding the ones presents calculation of R colour component for most com-
with values above a threshold adapted after each itera- monly available images represented in the form suited to
tion, PC computer monitors. The G and B components are con-
• take chromaticity coordinates (xs,ys) of average colour verted in the same way. Parameters i and j indicate the
given in XYZ. pixel position in rows and columns respectively.
194 Opto-Electron. Rev., 11, no. 3, 2003 © 2003 COSiW SEP, Warsaw

3. Contributed paper
The obtained sRGB colour components are in the range pixels not indicated for discarding”. The averaging proce-
[0,1], what simplifies further computation. Next, pixel val- dure is carried out for all of the three colour components X,
ues are converted into XYZ colour space by multiplying the Y and Z. The f coefficient is a multiplier for the colour
conversion matrix M and the sRGB colour vectors component average value to obtain threshold above which
pixels are discarded. Its typical value is 3, what was ob-
é X (i, j ) ù é R(i, j ) ù tained in the subjective experiments [6].
ê Y (i, j ) ú = M ´ ê G(i, j ) ú , (2) The procedure for averaging image pixels was verified
ê ú ê ú on a test set of images. Typical number of iterations for the
ë Z (i, j ) û
ê ú êë B(i, j ) û
ú test images was in the range from 4 to 8 depending on the
where pixel value distributions in images. Maximum number of
é0.4124 0.3576 01805 ù
. iterations was above 20. The convergence of the averaging
M= ê 0.2126 07152 0.0722 ú
. procedure can be described as in Eq. (5).
ê ú
ë 0.0193 01192 0.9505û
ê . ú
Let A n = X n , K n = X n , and Sn is a sum of pixel val-
Black and near black colours do not impact signifi- ues in the set Xn, and n is the loop number
cantly colour temperature perception, so the dark pixels are
omitted from calculation. The auxiliary table p is a mask æ S ö
Sn = K n An ç An = n ÷
for marking discarded pixels. This is a matrix which has è Kn ø
the same dimensions as the image. If the mask value at the
specific position p(i,j) is 0 then the corresponding pixel in and
the image is omitted from further calculations. Tll is a
threshold for pixel discarding having its typical value 5%
S n = S n +1 + å x,
x Î Xn
of maximal component range. Only the luminance compo- x > fAn
nent Y is used for discarding dark pixels where
ì if Y (i, j ) < Tll then p(i, j ) = 0 K n A n = K n +1 A n +1 + åx ³
í . (3) x Î Xn
îelse p(i, j ) = 1 x > fAn
³ K n +1 A n +1 + fA n (K n - K n +1 ),
In the next step, the remaining pixels are iteratively av- A n (K n - fK n + fK n +1 ) ³ K n +1 A n +1, (5)
eraged. In this process, a threshold for indicating colours
standing out is assessed in each iteration and pixels exceed- é (1 - f )K n + fK n +1 ù
A n +1 £ A n ê ú =
ing the threshold are marked for omitting. The pixels dis- ë K n +1 û
carded here are too much different from the averaged mean
é K ù
value and represent self-luminous regions or objects [6] = A n ê f - ( f - 1) n ú .
ë K n +1 û
X Ts (0) = 0
An is the decreasing sequence if
loop
row - 1 col - 1 é Kn ù
1 ê f - ( f - 1) K ú £ 1,
Xa = å
row ´ col i = 0
å X (i, j), ë n +1 û
j =0
X Ts = f ´ X a (4) thus
if ( X Ts (t ) = X Ts (t - 1)) return X a é æ K n öù
ê ( f - 1)ç 1 - ÷ ú £ 0.
ì if X (i, j ) > X Ts then p(i, j ) = 0 ë è K n +1 ø û
í
îelse p(i, j ) = 1
end loop It is true because f >1 and Kn > = Kn+1, therefore 0 £ An+1 £
An. The sequence is convergent because it is not increasing
and is lower bounded.
In averaging procedure, Eq. (4), XTs(t) indicates the
The (xs,ys) chromaticity values are obtained from com-
threshold in the current loop t above which the pixels are
puted average colour as follows.
discarded. If the threshold value is the same as in the previ-
ous loop [XTs(t – 1)], it means that no pixels were discarded Xa
xs = ,
in that loop and the mean value Xa is returned. The compu- X a + Ya + Z a
tation of mean value Xa is done only for pixels which have (6)
Ya
corresponding mask value p(i, j) above 0. The same is for ys = .
expression row´cols. It intuitively means: “the number of X a + Ya + Z a
Opto-Electron. Rev., 11, no. 3, 2003 K. Wnukowicz 195

4. Colour temperature estimation algorithm for digital images – properties and convergence
4. Estimation of colour temperature of given proximated by a ratio of distances from the point to the
colour two adjacent isotemperature lines.
The formula for resulting colour temperature is given as
After computing the chromaticity coordinates of the aver-
age colour of image, its colour temperature can be esti- di
TRc = TRi + (TRi +1 - TRi ). (9)
mated. Firstly, the chromaticity coordinates need to be con- d i - d i +1
verted to (us,vs) coordinates according to the CIE
5. Conclusions
4x s
us =
-2x s + 12 y s + 3 In the article, the algorithm for estimation of colour tem-
(7)
6y s perature of image is presented. The purpose of the estima-
vs = tion is to render human visual perception of this colour fea-
-2x s + 12 y s + 3
ture in static images as well as in moving ones (video se-
quences). Thereby, it is a considerable feature of image for
Secondly, the line perpendicular to the Planck’s locus, application in image search and retrieval tasks. That is just
the crossing point (us,vs), must be determined on the dia- what was a need, and a motivation for its designing origin.
gram. The line in question is an isotemperature line for the MPEG-7, a standard for describing an image content, have
obtained averaged image colour. For this purpose, Robert- got a contribution, proposing a descriptor for visual content
son’s algorithm can be used [1], which utilizes 31 fixed browsing based on colour temperature. Other possible ap-
isotemperature lines given in the form of parameters gath- plication of the colour temperature feature may be conver-
ered in a table. The given isotemperature lines are within a sion of colour temperature of image. Users of multimedia
range from 1667 K to 100000 K, and they are specified by systems often have their personal preferences on colour
4 parameters: their colour temperatures Ti and geometrical temperature of viewed images. If the colour temperature of
locations on a diagram, which are tangents of an angle be- image is known as well as the user preference on it, conver-
tween the line and the horizontal direction ti and the point sion of image appearance can be easy done to conform to
of crossing the Planck’s locus given by (ui,vi) coordinates. user needs. Further, potentially beneficial domain is pho-
To find out an isotemperature line for the point (us,vs), the tography. Knowledge of the colour temperature of photo
two neighbouring adjacent fixed isotemperature lines image makes it possible to do an automatic conversion of
should be determined at first. It is done by calculating the it, just to meet user needs.
distances to all of the 31 given lines and picking two adja-
cent ones of which the ratio between the distances from the References
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196 Opto-Electron. Rev., 11, no. 3, 2003 © 2003 COSiW SEP, Warsaw