Colour space models for soil science R.A. Viscarra Rossel a, * , B. Minasny a , P. Roudier a,b , A.B. McBratney a a Australian Centre for Precision Agriculture, The University of Sydney, NSW 2006, Australia b ENSAM, AgroMontpellier, 34060 Montpellier Cedex 01, France Received 26 August 2004; received in revised form 5 July 2005; accepted 27 July 2005 Available online 15 September 2005 Abstract Soil colour is an important soil property. It is frequently used by soil scientists for the identification and classification of soil. It is also used as an indicator of field soil physical, chemical and biological properties as well as of the occurrence of soil processes. Measurements of soil colour are commonly made using the Munsell soil colour charts. A number of other colour space models, that overcome some of the limitations of the Munsell HVC system exist and may be used to more aptly describe soil colour. We looked at nine colour space models and a redness index: Munsell HVC, RGB, decorrelated RGB (DRGB), CIE XYZ, CIE Yxy, CIELAB, CIELUV, CIELHC, and Helmoltz chromaticity coordinates. The aims of this paper are to (i) describe the algorithms used for transformations between these colour space models, (ii) compare their representational qualities and their relationships to the Munsell soil colour system, and (iii) in a case study, determine the model best suited to describe the relationship between soil colour and soil organic carbon. The type of colour model to use will depend on the purpose. For example, if soil colour is being used for merely descriptive purposes, then the Munsell HVC system will remain appropriate; if it is being used for numerical statistical or predictive analysis, as in our case study, then colour models that use Cartesian-type coordinate systems will be more useful. Of these, the CIELUV and CIELCH models appear to be more suitable for predictions of soil organic carbon. D 2005 Elsevier B.V. All rights reserved. Keywords: Soil colour; Munsell soil colour; CIE; RGB; Helmholtz chromaticity coordinates; Soil organic carbon 1. Introduction Soil colour has long been used for soil identifica- tion and qualitative determinations of soil character- istics (e.g. Webster and Butler, 1976). The reason is that various soil components exhibit spectral response in the visible range of the electromagnetic spectrum, between wavelengths 400 and 700 nm. Soil colour is commonly and widely measured using a Munsell soil colour chart (Munsell Color Company, 1975). It is intuitively designed to reflect our perception of colour and its variations. It is a useful system for categorical qualifications of soil colour, however it does not lend itself for numerical and statistical analysis as the Munsell colour space is divided into a series of 0016-7061/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.geoderma.2005.07.017 * Corresponding author. Tel.: +61 2 9351 5813; fax: +61 2 9351 3706. E-mail address: [email protected](R.A. Viscarra Rossel). Geoderma 133 (2006) 320 – 337 www.elsevier.com/locate/geoderma
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Geoderma 133 (2
Colour space models for soil science
R.A. Viscarra Rossel a,*, B. Minasny a, P. Roudier a,b, A.B. McBratney a
a Australian Centre for Precision Agriculture, The University of Sydney, NSW 2006, Australiab ENSAM, AgroMontpellier, 34060 Montpellier Cedex 01, France
Received 26 August 2004; received in revised form 5 July 2005; accepted 27 July 2005
Available online 15 September 2005
Abstract
Soil colour is an important soil property. It is frequently used by soil scientists for the identification and classification of soil.
It is also used as an indicator of field soil physical, chemical and biological properties as well as of the occurrence of soil
processes. Measurements of soil colour are commonly made using the Munsell soil colour charts. A number of other colour
space models, that overcome some of the limitations of the Munsell HVC system exist and may be used to more aptly describe
soil colour. We looked at nine colour space models and a redness index: Munsell HVC, RGB, decorrelated RGB (DRGB), CIE
XYZ, CIE Yxy, CIELAB, CIELUV, CIELHC, and Helmoltz chromaticity coordinates. The aims of this paper are to (i) describe
the algorithms used for transformations between these colour space models, (ii) compare their representational qualities and
their relationships to the Munsell soil colour system, and (iii) in a case study, determine the model best suited to describe the
relationship between soil colour and soil organic carbon. The type of colour model to use will depend on the purpose. For
example, if soil colour is being used for merely descriptive purposes, then the Munsell HVC system will remain appropriate; if
it is being used for numerical statistical or predictive analysis, as in our case study, then colour models that use Cartesian-type
coordinate systems will be more useful. Of these, the CIELUV and CIELCH models appear to be more suitable for predictions
R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337324
2. Methods
Munsell soil colour charts have appropriately
chosen chips that encompass the possible range
of soil colours. Hence, colour chips from the
Munsell soil colour book (Munsell Color Company,
1994), corresponding to value, chroma combina-
tions for hues between 5R and 5Y inclusive,
were used as a proxy for soil colour and as the
source for the transformations between colour
space models.
2.1. Munsell HVC to CIE XYZ
To transform from Munsell HVC to CIE XYZ,
we used a neural network. To model this transfor-
mation, we used XYZ values (that correspond to
the Munsell soil colour chips) derived from the
Munsell Conversion program Version 6.41 (http://
www.gretagmacbeth.com). Values of Munsell Hue
were converted to angle according to Munsell’s nota-
tion (ranging from 0 to 100). The notation is divided
into 100 steps of equal visual change in hue, with 5
at the beginning (5R) and 100 at the end (10RP). We
found that network with 4 hidden nodes modelled
this transformation adequately.
2.1.1. CIE XYZ to Munsell HVC
The algorithm used for the back transformation
from CIE XYZ to Munsell HVC is based on that by
Miyahara and Yoshida (1988). We modified the algo-
rithm and made it more appropriate for soil colour by
fitting the following relationships to the rescaled CIE
XYZ values. First a non-linear process transform was
performed as follows:
f Xcð Þ ¼ 11:559X13c � 1:695
f Yð Þ ¼ 11:396Y13 � 1:610
f Zð Þ ¼ 11:510Z13c � 1:691
where Xc=1.020X and Zc=0.487Z. Then:
H1 ¼ f Xcð Þ � f Yð Þ
H2 ¼ 0:4 f Zcð Þ � f Yð Þð Þ:
S1 and S2 are then calculated for the correction of
the uniformity of colour components as follows:
S1 ¼ 8:398þ 0:832dcoshð ÞH1
S2 ¼ � 6:102� 1:323dcoshð ÞH2
where h =tan�1(H2 /H1). H, V and C are then
defined as:
H ¼�����tan�1 S2
S1
� �� 100
2p
�����V ¼ f Yð Þ
C ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS21 þ S22
q:
The modified coefficients on the above equations
were found so that they minimize the colour differ-
ence between the true Munsell soil colour chart sam-
ples and predicted values (Godlove, 1951):
DE ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2C1C2 � 1� cos
2p100
DH
� �� �þ DCð Þ2þ 4DVð Þ2
s
where C1 and C2 are the chroma units of the two
colour measurements separated by DC chroma units,
DH hue units and DV value units. The equation
accounts for the perceived difference in the magnitude
of value and chroma scales, as well as for the angular
separation of hue.
2.2. CIE XYZ to Yxy
The CIE chromaticity coordinate values are calcu-
lated by normalising X and Y using the following
equations:
x ¼ X
X þ Y þ Zð Þ y ¼ Y
X þ Y þ Zð Þ
where x and y values lie between 0 and 1. Usually
only x and y are given, because z=1�x�y.
2.3. CIE xy chromaticity to Helmholtz chromaticity
coordinates
Any colour, when plotted on the CIE xy diagram
may be specified in terms of its dominant wavelength
Samples were left for 1 h before colour measurements
to minimise glistening and reduce specular reflection
and other measurement inconsistencies. These sam-
ples were used for both Munsell and spectrometric
measurements of soil colour.
2.7.3. Munsell measurements of soil colour
Soil colour was measured using the Munsell col-
our book (Munsell Color Company, 1994). Measure-
ments were performed under diffuse natural daylight
lighting conditions. The colour difference between
the replicate observations (of both dry and wet mea-
surements) was calculated using the equation derived
by Godlove (1951). The equation accounts for the
perceived difference in the magnitude of value and
chroma scales, as well as for the angular separation
of hue.
2.7.4. Spectrometric measurements of soil colour
The spectral reflectance of the Australian soil sam-
ples was measured using an ultraviolet-visible-near
infrared spectrometer (Varian Cary 500) equipped
with a diffuse reflectance accessory, with a spectral
range of 350–2500 nm. In this instrument, samples are
placed in a dark enclosure before measurements. The
French samples were scanned with a FieldSpec visi-
ble-near infrared spectrometer with a spectral range of
700–1300 nm. The scanner fibre-optic probe was
placed in an enclosure 0.1 m above the sample and
two halogen lamps illuminated the samples from 458angles. The optics of the instrument was set to 108 and10 spectra were collected and averaged for every
sample. In both instances, a white reference block
supplied with each spectrometer was used to calibrate
the instruments. Spectra were collected directly from
the soil surface of each sample at 2 nm intervals. The
reflectance data in the ranges between 450–520 nm,
520–600 nm and 630–690 nm corresponding to the
Location Reference
Australia White (1969)
France AFNOR (1996)
Australia Based on Walkley and Black (1934)
France AFNOR (1996)
Australia Rayment and Higginson (1992)
France AFNOR (1996)
R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337328
red, green and blue Landsat bands 1, 2 and 3, respec-
tively, were averaged and multiplied by 255 to get the
8-bit pixel colour encoding. These RGB values were
transformed to the other colour space models
described previously using ColoSol, software devel-
oped to perform both single tristimulus transforma-
tions and multiple colour space transformations in an
ASCII text file (Viscarra Rossel, 2004). We started
with RGB colour because in soil science and remote
sensing studies these are commonly used as the start-
ing colour systems, e.g. RGB tristimuli are easily
extracted from satellite images.
2.7.5. Relationship between soil colour and soil
organic carbon (OC)
The soil OC data was positively skewed, hence it
was normalised using a square root transform. We then
correlated colour parameters of the different colour
models to soil OC contents. Based on these, relation-
ships were derived between soil OC and selected
colour parameters. We regressed soil OC (using multi-
ple linear regression) as a function of the tristimuli
values of each colour model, i.e. soil OC= f(tristimuli,
e.g. L, u*, v*). To quantify the accuracy of the rela-
tionships, we used the adjusted coefficient of determi-
nation (Radj2 ) and cross-validated (Efron and Tibrishani,
1993) root mean squared error (RMSE).
3. Results
Three hundred and seventy two Munsell soil colour
chips were used in the colour space transformations.
The CIE XYZ system served as a platform from where
the various other colour space transformations were
executed (see Fig. 3). The neural network estimates of
CIE XYZ from Munsell HVC data were accurate.
There were no concerns with over-fitting or biasedness
of predictions as we always remain within the range of
the Munsell soil colour data. Remember that this step
was introduced to computerise the transformation from
Munsell HVC to CIE XYZ. The reverse transforma-
tion using the modified Miyahara and Yoshida (1988)
algorithm was also accurate. The average difference
between the estimated Munsell values and those from
the Munsell soil colour chart was 0.27 units. Highest
errors occurred for 5R at chroma values of 6 to 8. We
will now compare the resulting transformations and
explore the relationships between the Munsell HVC
system and the various other transformed colour space
models.
3.1. Relationships between Munsell HVC and other
colour space models for soil
The median angular hue of the Munsell soil colour
chip data was 158, corresponding to a Munsell hue of
5YR. Munsell value ranged from 2 to 8, while chroma
ranged from 1 to 8 units and was positively skewed.
Fig. 4(a and b) presents the relationships between
Munsell H and C vs. CIE x and CIE y chromaticities,
while Fig. 4(c and d) shows the relationships between
Munsell H and C vs. the Helmholtz coordinates kd
and Pe.
Redder hues (Munsell H) show to have a smaller
range in CIE y chromaticity than yellower hues (Fig.
4a). Low Munsell C values have a smaller range in
CIE x chromaticity than more saturated Munsell C
values (Fig. 4b). This apparent non-uniformity in the
distribution in CIE y chromaticity for corresponding
Munsell hues, illustrates the non-uniformity of the
CIE xy system. Unlike the Munsell HVC system,
which has colour samples that are perceptually equi-
distant, the CIE xy system is perceptually non-uni-
form, giving greater bias to the yellow and green
colour gamut (Fig. 1c shows the CIE xy diagram).
The Helmholtz coordinates kd and Pe were correlated
to Munsell H and C parameters, respectively (Fig. 4c
and d). Low Munsell C values have a smaller range in
Pe values than more saturated Munsell C values (Fig.
4d). There is good correlation between CIE x and Pe
parameters (cf. Fig. 4b and d). The average kd for the
Munsell soil colours was 590 nm with a range of 575
to 615 nm. Yellow Munsell hues have wavelength in
the range from 574 to 585 nm, red Munsell hues have
wavelengths in the range from 590 to 615 nm and
yellow-red hues have wavelengths from approxi-
mately 580 to 600 nm (Fig. 4c).
Fig. 5 shows the Munsell soil colour chart gamut as
represented by the CIE xy chromaticity coordinates
and the Helmholtz coordinates.
Generally, the CIE x chromaticity coordinate was
well correlated to parameters of the various colour
space models that describe the chromaticity of the
samples, while the CIE y coordinate was better corre-
lated to parameters describing their hue.
1
2
3
4
5
6
7
8
Chr
oma
(Mun
sell)
.35 .4 .45 .5 .55 .6x
0.3
0.35
0.4
0.45
y
5 10 15 20 25Hue angle (Munsell)
(a)
(c)
(b)
(d)
1
2
3
4
5
6
7
8
Chr
oma
(Mun
sell)
0 20 40 60 80 100Pe (%)
5
10
15
20
25
Hue
ang
le (
Mun
sell)
580 590 600 610
λd (nm)
Fig. 4. Scatterplots of relationships between Munsell vs. CIE xy and Helmholtz coordinates: (a) Munsell hue (H) vs. CIE y, (b) CIE x vs.
Munsell chroma (C), (c) dominant wavelength kd vs. Munsell H and (d) purity of excitation (i.e. saturation) Pe vs. Munsell C. Different markers
Fig. 5. The Munsell soil colour chart gamut as represented by (a) CIE xy
colour gamut. Different markers represent different levels of chroma. (b) H
Pe (%).
CIELAB +a* and CIELUV +u* coordinates
describe red Munsell hues with values of chroma
ranging from zero for the achromatic point to positive
(c)
.5 .6 .7
615 nm 600 nm
590 nm
574 nm
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
y
0 .1 .2 .3 .4 .5 .6 .7x
2040
60
90 %
chromaticity coordinates. Black markers represent the Munsell soil
elmholz dominant wavelength kd (nm) and (c) Helmholz saturation
5
10
15
20
25
Hue
ang
le (
Mun
sell)
0 10 20 30 40 50 60
v*
1
2
3
4
5
6
7
8
Chr
oma
(Mun
sell)
0 10 20 30 40 50 60v*
1
2
3
4
5
6
7
8
Chr
oma
(Mun
sell)
10 20 30 40 50 60u*
1
2
3
4
5
6
7
8
Chr
oma
(Mun
sell)
0 10 20 30 40 50 60b*
1
2
3
4
5
6
7
8
Chr
oma
(Mun
sell)
0 10 20 30 a*
5
10
15
20
25
Hue
ang
le (
Mun
sell)
10 20 30 40 50 60
u*
5
10
15
20
25
Hue
ang
le (
Mun
sell)
0 10 20 30 40 50 60 b*
5
10
15
20
25
Hue
ang
le (
Mun
sell)
0 10 20 30 a*
(a)
(e)
(b)
(f)
(c)
(g)
(d)
(h)
Fig. 6. Scatterplots of relationships between (a–d) Munsell hue (H) and (e–h) Munsell chroma (C) vs. CIE a* b* and CIE u* v* c rdinates. Different markers represent different
levels of chroma.
R.A.Visca
rraRossel
etal./Geoderm
a133(2006)320–337
330
70
70
oo
0
10
20
30
40
50
60
70
80
90
100
L
(a)
-100
-50
0
50
100
-100 -50 0 50 100 150
u- u+
v+
v-
(c)
R
YR
Y
G
GY
BG
B PB
RP
P -50
0
50
100
-50 0 50
R
YR
Y
G
GY
BG
B PB
RP
P
a+a-
b-
b+(b)
Fig. 7. Munsell soil colour gamut (shaded area in (a) and black markers in (b) and (c)) with relation to the entire colour gamut (light grey
markers) represented by the CIELa*b* and CIELu*v* colour systems. (a) Shows the lightness function L, (b) a plot of a* vs. b* and (c) a plot
of u* vs. v*. Different black markers in (b) and (c) represent different levels of chroma. Letters represent Munsell hue coding: Y = yellow, G =