colour space models for soil science

18
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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Page 1: Colour Space Models for Soil Science

www.elsevier.com/locate/geoderma

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

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

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).

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

006) 320–337

Page 2: Colour Space Models for Soil Science

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 321

non-contiguous slices presented as each page of the

colour book. Melville and Atkinson (1985) discussed

measurements of soil colour using the Munsell soil

colour charts and recommended the use of the CIE-

LAB system.

Soil colour is a continuous variable that varies in

the x, y and z spatial dimensions. It varies across the

landscape and it varies with depth. Vertical variation

in soil colour is used to distinguish different horizons

in a profile and provides an indirect measure of

important soil characteristics including drainage,

aeration, organic matter content and general fertility.

Soil colour is important in many systems of soil

classification. It is common practice for soil scientist

to use soil colour as a determinant of soil type (e.g.

red chromosol, brown kurosol (Isbell, 2002)), field

soil chemical, physical and biological properties (i.e.

soil quality and function) (e.g. Sanchez-Maranon et

al., 1997; Ben-Dor et al., 1997; Lindbo et al., 1998)

and the occurrence of soil processes (e.g gleying

(Van Huyssteen et al., 1997)). Properties such as

soil organic carbon content, iron content, soil water

content, and texture have been shown to have good

correlations with soil colour. Soils with dark surface

horizons are generally associated with high organic

matter contents, categorising them as fertile and

suitable for plant growth (Schulze et al., 1993).

Dark brown and black soils are also thought to

contain high levels of nitrogen, have good aeration

and drainage, and pose a low erosion risk. Generally,

the opposite is thought of light coloured soils. The

colour of iron containing soil minerals that undergo

oxidation and reduction reactions can provide useful

information on the hydrologic condition of a soil.

For example the occurrence of red haematite (a-

Fe2O3) in the soil profile suggests that the soil is

well-drained and has an aerobic environment while

the occurrence of yellow goethite (a-FeOOH)

implies the presence of a reduced soil environment.

Barron and Torrent (1986) looked at the influence of

iron oxides on soil colour. Soil colour can also be

used to qualitatively describe the moisture status of a

soil, for example, due to changes in the refractive

index dry soils are lighter in colour than wet soils.

Thompson and Bell (1996) used a colour index for

identifying hydric conditions in seasonally saturated

soil. Blavet et al. (2000) used soil colour (hue and

redness) to estimate the mean annual rate of soil

waterlogging. Therefore soil colour can be used for

rapid approximation of soil properties, their function

and condition.

The spatial variation of surface soil colour is

increasingly the subject of much remote sensing

research, as the spectral and spatial resolution of air-

borne and satellite imagery improves, and the cost of

images decreases (e.g. Escadafal et al., 1989; Matti-

kalli, 1997; Mathieu et al., 1998; Leone and Escada-

fal, 2001). Soil processes that affect surface soil may

be identified by colour differences (Escadafal, 1993),

hence surface soil colour has been used to categorise,

evaluate and map soils. De Jong (1992) looked at the

use of imaging spectroscopy to map erosion hazard in

the Mediterranean. Coleman et al. (1990) used the

Thematic Mapper (TM) to differentiate surface soils

and found significant correlations between radiance

data and organic matter, iron content, and particle size

distribution. Sanchez-Maranon et al. (1996) used soil

colour (hue, value and chroma) in their evaluation of

calcareous soils for reforestation in Sierra Nevada,

Spain. Francis and Schepers (1997) used soil colour

to devise a selected soil sampling scheme for the site-

specific management of soil nutrients.

The aims of this paper are threefold. (i) To describe

commonly used colour space models that have been

used to designate colour in three dimensional space

and the algorithms used for conversions between

them, (ii) to compare their representational qualities

and their relationship to the Munsell soil colour sys-

tem, and (iii) in a case study, to determine the colour

model(s) best suited for quantitative description of soil

colour and its relationship to soil organic carbon.

Before we delve into the work, we shall briefly

describe the main characteristics of the colour models

we considered.

1.1. Colour space models

Colour is a 3-dimensional psychophysical phenom-

enon. Colour is represented in colour space models

whereby individual colours are specified by points in

these spaces. There are many ways by which one can

measure colour. In this instance we will only refer to

those that attempt to create equal perceived colour

differences (e.g. the Munsell colour system) and

those that link the spectral profile of colours to the

basic units of colour perception, i.e. trichromatic col-

Page 3: Colour Space Models for Soil Science

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337322

orimetry (e.g. the RGB, CIE XYZ systems and their

derivatives). For details on the theories and models of

colorimetry, the reader is referred to, amongst many

others, Billmeyer and Saltzman (1981) and Wyszecki

and Stiles (1982).

1.1.1. Munsell HVC soil colour system

Soil colour is commonly described qualitatively

using Munsell soil colour charts and the three vari-

ables: hue, value and chroma (HVC). These three

variables describe a perceptual colour space and not

a quantitative measure of visible light. Hue is

denoted categorically by the letter abbreviation of

the colour of the spectrum (R for red, YR for

yellow-red, Y for yellow) preceded by numbers

from 0 to 10. Within each letter range, the hue

becomes more yellow and less red as the numbers

increase. Value is specified on a numerical scale

from 0 (absolute black) to 10 (absolute white).

Chroma is also described numerically beginning at

0 for neutral greys (the achromatic point) to a max-

imum value of 20, which is never approached with

soil. The system was designed to arrange colours

according to equal intervals of visual perception,

thus the primary advantage of the Munsell system

is its ease of interpretation. However, Munsell HVC

coordinates are psychosensory, based on subjective

perception and comparison and thus the system is

not uniform. The Munsell colour system is repre-

sented in Fig. 1a.

1.1.2. RGB

Colour in the RGB system is produced by any

additive or subtractive mixture of the spectra of the

three primary colours red (R), green (G) and blue

(B). Their corresponding monochromatic primary

stimuli occur at 700, 546 and 436 nm, respectively.

On a 8-bit digital system colour is quantified by

numeric tristimulus R, G, B values that range from

0 (darkness) to 255 (whiteness). Combinations of

R, G, B primaries can produce a gamut of (28)3

different colours (Wyszecki and Stiles, 1982). The

colour gamut of the system forms a cube compri-

sing orthogonal RGB Cartesian coordinates (Fig.

1b). Each colour is then represented by a point

on or in the cube. All grey colours are present in

the main diagonal from black (R =G =B =0) to

white (R =G =B =255).

1.1.3. CIE XYZ

In 1931 the Commission Internationale de l’Eclai-

rage (CIE) standardised colour order systems by spe-

cifying the light source, the observer and the

methodology used to derive the values for describing

colour (C.I.E. 1931). The XYZ colour system was

also accepted then and it has been used ever since.

In this system, Y represents the brightness (or lumi-

nance) of the colour, while X and Z are virtual (or not

physically realisable) components of the primary

spectra (Wyszecki and Stiles, 1982). The relationships

between XYZ and RGB systems are described in the

Methods section below. The system was designed to

produce non-negative tristimulus values for each col-

our. Often this system is used as the platform from

which other colour specifications are made and as

intermediaries for determining perceptually uniform

colour systems such as CIELAB or CIELUV.

1.1.3.1. CIE Yxy. The XYZ tristimulus values are

useful for defining a colour, but the results are not

easily visualised. To overcome this problem, CIE

defined a colour space in 1931 that depicts colour

into two dimensions; this is the CIE Yxy colour space.

The standardising equations are presented in the

Methods section below. The chromaticity co-ordi-

nates x and y are independent of luminance, Y, and

specify colour variations from blue to red and blue to

green, respectively. Thus colour is represented in an

xy chromaticity diagram (Fig. 1c). The CIE chroma-

ticity diagram has one major drawback in that there

is a discrepancy between perceived colour differences

and the actual spacing of colour in the system. Both

XYZ and Yxy systems are perceptually non-linear.

1.1.4. Helmholtz chromaticity

An alternative set of coordinates developed to

overcome the difficulties of the xy chromaticity coor-

dinates are the Helmholtz chromaticity coordinates;

kd, Pe and Y, which describe the dominant wave-

length, the purity of excitation and luminance, respec-

tively. The dominant wavelength of a colour correlates

approximately with the hue of the colour illuminated

by illuminant C. The purity of excitation, measured as

a percentage, correlates in an approximate way with

the saturation of the colour. The luminance refers to

the brightness of the colour and is scaled from 0%

(black) to 100% for a white object with a diffuse

Page 4: Colour Space Models for Soil Science

CHROMA

VALUE5R

5YR

5Y

5GY

5G5B

5PB purple-blue

blue

yellow-green

yellow

orangered

4 68

10

white

9

8

7

6

5

4

2

1

black

green

purple

5PHUE

HUE

RED

GREEN

BLUE

BLACK

WHITE

0

255

255

255

YELLOW

CYAN

MAGENTA

Red

Green

Blue

x

y

380

780

520

570

490

600

550

500

450

Purple

achromatic light

daylight

0

0.8 Pure wavelength locus (nm)

(a) (b)

(c) (d)

+a* +u* red

+b* +v*

yellow

-b* -v*

blue

-a* -u*

green

L*

0.8

Fig. 1. (a) The Munsell colour model represented by a cylindrical coordinate system. (b) The RGB model, (c) the CIE xy chromaticity diagram

(d) the CIELu*v* and CIELa*b* colour space model. (a) adapted from http://www.britanica.com/ (b � d) adapted from Wyszecki and Stiles

(1982).

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 323

reflectance of 1 in the visible range of the spectrum.

The equations defining the parameters of the Helm-

holtz chromaticity coordinates are given in the Meth-

ods section below.

1.1.5. CIELUV and CIELAB

The CIE in 1964 proposed the CIELUV system,

which attempts to overcome the perceptual non-line-

arity of the XYZ and Yxy. The CIELUV system is

obtained after the xy coordinates are transformed to a

uniform chromaticity scale (Wyszecki and Stiles,

1982). CIELAB is an approximately uniform colour

system. Its values are calculated by non-linear trans-

formations of XYZ. Common to both systems is L the

metric lightness function (representing brightness or

luminance) which ranges from 0 (black) to 100

(white); a* and b* and u* and v* the chromacity

coordinates represent opponent red–green scales (+a,

+u reds, �a, �u greens), and opponent blue–yellow

scales (+b, +v yellows, �b, �v blues) (Fig. 1d and e,

respectively). The equations defining these systems

are given in the Methods section below.

Page 5: Colour Space Models for Soil Science

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

Page 6: Colour Space Models for Soil Science

Red

Green

Blue

I

DW

CDW

x

y

S

S,

P

Fig. 2. CIE xy chromaticity diagram and calculation of Helmholz

coordinates. Adapted from Wyszecki and Stiles (1982).

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 325

kd (DW). The DW of a colour is defined as the

wavelength of the monochromatic stimulus that,

when mixed with a specified achromatic stimulus

(such as CIE standard illuminant C or D65), matches

the given stimulus in colour (Wyszecki and Stiles,

1982). From Fig. 2, it is the wavelength of the colour

of the visible spectrum whose chromaticity is on the

same straight line as the sample point (S) and the

achromatic point (I) (for illuminant C this point is

xw=0.3101; yw=0.3163). For non-spectral colour, i.e.

colours that do not appear in the visible spectrum, a

complementary dominant wavelength (CDW) is used

(Fig. 2). From Fig. 2, these colours are located in the

triangular area encompassed by I, Red and Blue. The

reason for this is that the DWof sample (SV), indicatedby the interception point (P) does not have a corre-

sponding wavelength. Thus the line from I to P is

extended backwards to determine the CDW (Fig. 2).

Dominant wavelengths for the Munsell colour chips

were calculated from a table produced by Judd (1933)

in Wyszecki and Stiles (1967) after computation of the

following ratios:

x� xw

y� ywand

y� yw

x� xw

The purity of excitation of a given colour is an

exactly defined ratio of distances in the xy chromati-

city diagram. It is the ratio of the distance between the

illuminant point (I) to the sample point (S) and that

form N to the spectrum locus DW (Fig. 2). The purity

of excitation may be calculated using:

Pe ¼x� xw

yb � ywor Pe ¼

y� yw

xb � xw

where x and y refer to the chromaticity coordinates,

xw and yw refer to the chromaticity coordinates of the

achromatic stimulus and xb and yb are the chromati-

city coordinates of the boundary colour stimulus

(Wyszecki and Stiles, 1982).

2.4. CIE XYZ to CIELAB and CIELUV

CIE XYZ tristimuli were standardised with values

corresponding to the D65 white point: X0=95.047,

Y0=100 and Z0=108.883. We then transformed the

standardised tristimuli to the CIELAB and CIELUV

Cartesian coordinate systems using the following

equations (CIE, 1978):

L ¼ 116� Y

Y0

� �13

� 16 forY

Y0

� �N0:008856

¼ 903:3� Y

Y0

� �otherwise

where L is the metric lightness function (or luminos-

ity), which is common to both CIELAB and CIELUV

models. The a* and b* chromacity coordinates were

derived using:

a* ¼ 500� X

X0

� �13

� Y

Y0

� �13

" #

b* ¼ 200� Y

Y0

� �13

� Z

Z0

� �13

" #

The u* and v* coordinates were derived using:

u* ¼ 13L� uV� unVð Þ

where

uV ¼ 4X

X þ 15Y þ 3Zð Þ ;unV ¼4X0

X0 þ 15Y0 þ 3Z0ð Þ and

v* ¼ 13L� v V� vnVð Þ

where

v V ¼ 9Y

X þ 15Y þ 3Zð Þ ; vnV ¼9Y0

X0 þ 15Y0 þ 3Z0ð Þ

Page 7: Colour Space Models for Soil Science

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337326

2.4.1. CIELCH

To facilitate visualisation of the colour within the

CIELAB spherical colour space, it can be transformed

into cylindrical coordinates to provide CIE hue (h*)

and chroma (c*) values, as follows:

h* ¼ arctanb*

a*

� �

c* ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia*ð Þ2 þ b*ð Þ2

q

The CIELCH system was designed to identify the

components of colour in terms of correlates of per-

ceived hue, chroma and lightness.

2.4.2. Redness index

We also computed a redness index (RI) introduced

by Barron and Torrent (1986) for the estimation of

haematite content in soils. It is based on the Kubelka–

Munk theory, which provides a good technique to

calculate the colour of haematite containing mixtures

(Barron and Torrent, 1986). In this instance we imple-

mented their index based on the CIELAB colour

space:

RI ¼L a*ð Þ2 þ b*ð Þ2� 0:5

d108:2

b*dL6

where RI is a simple multiplicative index in which

each variable is given an exponent. Barron and Tor-

rent (1986) tested various exponents until maximum

correlation was obtained between the RI and haema-

tite content.

2.5. CIE XYZ to RGB

To transform from CIE XYZ into RGB, we first

rescaled the XYZ tristimulus between 0 and 1 and

then performed the following three-by-three matrix

(A) transformation for illuminant D65 and 28 standardobserver (Wyszecki and Stiles, 1982):

R

G

B

2435¼ 3:240479 � 1:537150 � 0:498535� 0:969256 1:875992 0:0415560:055648 � 0:204043 1:057311

24

35d X

Y

Z

2435

2.5.1. RGB to CIE XYZ

For the inverse transform the R, G and B data were

also rescaled between 0 and 1 before transformation

into CIE XYZ using the following matrix (A�1) trans-

form (Wyszecki and Stiles, 1982):

X

Y

Z

24

35 ¼ 0:412453 0:357580 0:180423

0:212671 0715160 0:0721690:019334 0:119194 0:950227

24

35d R

G

B

24

35

where Y represents the luminance component of the

image and X and Z two additional components whose

spectral composition correspond to the colour match-

ing characteristics of human vision (CIE, 1986). In

XYZ, any colour is represented as a set of positive

values.

2.6. Decorrelation of RGB data

RGB data are highly correlated. To decorrelate the

tristimuli we transformed the RGB data into three

statistically independent components:

HRGB ¼2dGð Þ � R� B

4

IRGB ¼Rþ Gþ B

3;

SRGB ¼R� B

2;

where HRGB, IRGB and SRGB represent hue, light

intensity and chromatic information, respectively.

Fig. 3 summarises the order and manner in which

all the above transformations were made.

2.7. Case study: soil colour and its relationship to soil

organic carbon

2.7.1. Soil sampling and laboratory analyses

The soil used in this study comprises A-horizon

samples (0–20 cm), originating from Australia and

France. Forty-four soil samples were collected from

various locations in Victoria (13), South Australia (5),

Western Australia (15) and Tasmania (11). Seventy-

seven samples were collected from different locations

in NSW, Australia. Forty-five soil samples were col-

lected from various locations in Brittany, France. The

soils were selected to provide our study with a repre-

Page 8: Colour Space Models for Soil Science

Munsell HVC

CIE XYZ

RGB

DRGBHRGB, IRGB, CRGB

CIELa*b*

CIELc*h*

CIELu*v*RI

CIE xyY

Helmholtzλd, Pe, Y

Fig. 3. Colour space transformations (and back transformations)

starting from RGB and/or Munsell HVC tristimuli. Munsell HVC

and RGB systems are commonly used in soil science and remote

sensing studies as the starting colour systems used to describe soil

colour (e.g. RGB tristimuli are easily extracted from satellite

images; field measurements of soil colour using the Munsell soil

colour book). Broken lines represent non-linear transformations,

while unbroken lines represent linear transformations.

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 327

sentative range in soil colour. Once collected, the soil

was air-dried and ground to a size fraction b2 mm.

The soil analysis conducted is described in Table 1.

Fourteen soil OC and colour data were also used from

the Canadian study by Shields et al. (1968).

2.7.2. Soil sample preparation for colour

measurements

Approximately 20 cm3 portions of each ground,

air-dry sample were placed into 30 cm3 petri dishes

for soil colour measurements. The surface of the

samples was smoothed to ensure even micro topogra-

phy. Soil colour measurements were taken of each

sample in both dry and wet states. Wetting the sam-

ples involved spraying approximately 4 ml of deio-

nised water (depending on the air-dry water content)

as a fine mist onto the soil surface to achieve even

moistening without ponding. After adding 20% water

by volume, there were no apparent changes in colour.

Table 1

Laboratory methods of soil analyses

Soil property Technique

pHCa 1 :5 soil :0.01M CaCl2pHW 1:5 soil :H2O extract

Organic carbon dag/kg dichromate oxidation

combustion

Clay content dag/kg pipette

pipette

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)

Page 9: Colour Space Models for Soil Science

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.

Page 10: Colour Space Models for Soil Science

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

represent different levels of chroma.

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 329

Fig. 6 shows the relationships between Munsell H

and C vs. CIELAB a* and b* and CIELUV u* and v*

coordinates.

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 .7 .8x

(a) (b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

y

0 .1 .2 .3 .4x

Red

Green

Blue

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

Page 11: Colour Space Models for Soil Science

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

Page 12: Colour Space Models for Soil Science

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 =

green, B = blue, P = purple and R = red.

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 331

values of a* and u*. Hence, yellower Munsell hues

have a smaller range of +a* and +u* values than do

redder hues (Fig. 6a and c, respectively). Redder

Munsell hues have smaller ranges of CIELAB +b*

and CIELUV +v* values than do yellower hues (Fig.

2

3

4

5

6

7

8

Val

ue (

Mun

sell)

50 100 150 200 250R

2

3

4

5

6

7

8

Val

ue (

Mun

sell)

50 100G

5

10

15

20

25

Hue

ang

le (

Mun

sell)

-20 -10 0 10 20HRGB

2

3

4

5

6

7

8

Val

ue (

Mun

sell)

50 100IRG

(a)

(d)

(b)

(e)

Fig. 8. Scatterplots of relationships between (a–c) Munsell value (V) and RG

and chroma (C) vs. DRGB colour coordinates HRGB, IRGB and SRGB, respe

6b and d, respectively), as b* and v* describe yellow

hues with values of chroma extending out from the

achromatic point. The range of a*, b* and u*, v*

chromaticity coordinates increases with increasing

Munsell chroma (Fig. 6e–h). There was a perfect

150 200

2

3

4

5

6

7

8

Val

ue (

Mun

sell)

0 50 100 150 200B

150 200B

1

2

3

4

5

6

7

8

Chr

oma

(Mun

sell)

10 20 30 40 50 60 70SRGB

(c)

(f)

B colour coordinates and (d–f) between Munsell hue (H), value (V)

ctively. Different black markers represent different levels of chroma.

Page 13: Colour Space Models for Soil Science

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337332

relationship between Munsell value and the metric

lightness function L (Radj2 =0.99). Fig. 7 shows the

Munsell colour chart gamut as represented by the

CIELAB and CIELUV colour coordinates, highlight-

ing the range of the Munsell soil colour chips.

In a perfect match between the Munsell and CIE-

LAB and CIELUV systems, hue and chroma values

would form a more symmetrical and circular

dspiderwebT effect (Melville and Atkinson, 1985). In

Fig. 7, hue and chroma values are more symmetrical

in the CIELAB diagram (Fig. 7b) than in the CIELUV

diagram (Fig. 7c), thus CIELAB more closely repre-

sents the Munsell colour system. Fig. 8 illustrates the

relationship between Munsell coordinates and the

RGB and DRGB colour space models.

The main disadvantage of the RGB system for

describing soil colour is the high degree of correla-

tion and the high influence of illumination intensity

on each of the dimensions. Fig. 8a–c shows the

relationship between Munsell V and each of the R,

G and B coordinates, stressing the high influence

and proportionality of illumination on the RGB data.

0

50

100

150

200

250

R

0 50 100 150 200 250G

0

50

100

150

200

250

R

0 50 100

0

50

100

150

200

IRG

B

-50 0 50HRGB

-100

-50

0

50

100

SR

GB

-50 0HRG

(a)

(d) (e)

(b)

Fig. 9. The Munsell soil colour gamut (black markers) with relation to the e

colour system and the (d–f) DRGB colour system. Different black markers

represents the line of greys.

To eliminate this problem we de-correlated the RGB

model (DRGB) into coordinates that correlate well

with the more perceptual parameters of hue, value

and chroma, i.e. HRGB, IRGB, SRGB. The HRGB, IRGBand SRGB coordinates provide good approximations

to the Munsell H, V and C coordinates, respectively

(Fig. 8d–f). The DRGB colour model is more stable

with changes in illumination than the RGB model.

Fig. 9 shows the Munsell colour gamut as repre-

sented by the RGB and DRGB colour systems,

highlighting the range and configuration of the Mun-

sell soil colour chips in each of the colour space

models.

3.2. Case study: soil colour and its relationship to soil

organic carbon

The surface soil samples used in this study encom-

pass a wide geographic extent. This variation is

reflected in the wide ranging distributions of their

soil properties as well as in their perceived and quan-

tified soil colour measurements (Table 2).

150 200 250B

0

50

100

150

200

250

G

0 50 100 150 200 250B

50B

0

50

100

150

200

IRG

B

-100 -50 0 50 100SRGB

(c)

(f)

ntire colour gamut (light grey markers) represented by the (a–c) RGB

represent different levels of chroma. In (a), (b) and (c) the solid line

Page 14: Colour Space Models for Soil Science

Table 2

Statistics of soil organic carbon and colour parameters from differ-

ent colour space models

Mean Standard

Deviation

Median Range

OC dag/kg 1.80 1.37 1.39 0.00–8.90

SQRT. OC dag/kg 1.25 0.49 1.18 0.00–2.98

pHCa 5.95 1.33 5.99 3.66–9.73

Clay dag/kg 21.92 13.47 17.13 1.83–63.33

Munsell H8 19.2 2.70 20.00 12.5–22.50

Munsell V 3.38 0.70 3.00 2.00–5.00

Munsell C 2.98 1.16 3.00 1.00–6.00

H8 21.46 2.55 22.13 11.71–24.98

V 2.44 0.68 2.39 0.72–4.36

C 2.24 0.70 2.17 0.43–4.12

X 4.95 2.54 4.43 0.59–14.73

Y 4.74 2.53 4.14 0.57–14.11

Z 3.01 1.75 2.59 0.43–9.12

x 0.39 0.02 0.39 0.34–0.44

y 0.37 0.01 0.37 0.35–0.40

kd (nm) 582.61 2.55 582.82 573.30–589.02

Pe 37.46 8.38 37.07 16.58–55.83

L 24.68 7.40 24.12 5.15–44.39

a* 5.93 2.27 5.77 0.10–13.24

b* 11.75 3.67 11.39 2.75–21.66

u* 11.58 4.33 10.95 0.98–24.79

v* 10.66 3.96 10.31 1.60–21.72

c* 13.24 4.06 12.84 3.07–23.87

h* 1.10 0.12 1.09 0.87–1.54

R 72.76 18.68 73.39 22.00–127.24

G 55.29 16.32 53.18 16.00–99.29

B 41.21 13.63 40.09 12.00–79.00

HRGB �0.85 0.97 �0.97 �4.21–2.23IRGB 56.42 15.81 55.10 16.67–100.66

SRGB 15.78 4.93 15.30 3.00–29.13

RI 81.59 165.15 21.00 1.00–1056.50

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 333

The soil samples used in this study had a wide

range of soil OC and a representative range in soil

colour (Table 2). The average kd of the samples was

20

40

60

Cou

nt A

xis

0 1 2 3 4ΔE (wet)

m = 0.61σ = 1.02

Fig. 10. Histogram of colour differences (DE) between replicate wet and

standard deviation (r).

583 nm, ranging from 573 to 589 nm. The angular

Munsell H of our samples ranged from 12.5 (2.5YR)

to 22.5 (2.5Y), with Munsell V ranging from 2 to 5

units and Munsell C from 1 to 6 units. Although

Munsell colour chart measurements are the most com-

mon method used to describe soil colour, they are

prone to perceptual human errors. Colour differences

(DE) between replicate measurements were smaller

for wet Munsell determinations due to the homogeni-

sation of colour caused by wetting (Fig. 10).

The average difference between replicate dry

measurements was 2.3 colour difference units,

while for wet measurements it was 0.6 units. Preci-

sion was also lower for the dry measurements, as

shown by the standard deviation of the difference

between replicates (Fig. 10). The subjective nature of

the measurements, the need for more than one obser-

ver to estimate soil colour and the resulting lack of

precision is a major drawback of Munsell soil colour

measurements (Post et al., 1994). There are various

other studies suggesting the use of spectrophot-

ometers (e.g. Barrett, 2002) and digital cameras

(e.g. Viscarra Rossel et al., 2003) for rapid, quanti-

tative measurements of field soil colour.

3.3. Relationship between colour model parameters

and soil organic carbon (OC)

Rapid and accurate quantification of the spatial

distribution of soil OC is desirable in agriculture.

Conventional techniques to quantify soil OC are

expensive, time-consuming and on occasions inaccu-

rate (e.g. McCauley et al., 1993). Soil colour may be

used to quantify soil OC. There are a number of

studies reporting relationships between soil colour

10

20

30

Cou

nt A

xis

0 1 2 3 4 5 6ΔE (dry)

m = 2.33 σ = 1.58

dry Munsell soil colour measurements showing the mean (m) and

Page 15: Colour Space Models for Soil Science

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337334

and soil OC. Most of these deal with the Munsell

HVC system. For example, Franzmeier (1988)

reported relationships between soil organic matter

and Munsell value and chroma with R2 values of

b0.48. Schulze et al. (1993) reported a weak relation-

ship (R2=0.31) between wet Munsell value and soil

OC for soil with varying textural composition. Lindbo

et al. (1998) used a chroma meter to measure relation-

ships between soil colour, soil OC and hydromorphol-

ogy. They reported an R2 value of 0.63 for the

relationship between dry Munsell value and soil OC.

Konen et al. (2003) used a chroma meter to develop

relationships between soil colour, soil OC and texture.

They showed logarithmic relationships between

reflectance, Munsell value, Munsell chroma and soil

OC. The R2 values of their relationships ranged from

0.68 to 0.77. The basis for all of this work is the fact

that darker soil contains higher amounts of soil OC

than lighter coloured soil. This darkening of soil with

higher OC content is due to the effect of saturated

organic matter and to variations in composition and

Table 3

Correlations between soil organic carbon (OC) and soil colour parameters

OC (All n =180) OC (Australia n =44) OC

Munsell H �0.19 �0.47Munsell V �0.59 �0.46Munsell C �0.45 �0.26H �0.18 �0.43 �0V �0.72 �0.78 �0C �0.68 �0.70 �0X �0.79 �0.78 �0Y �0.77 �0.77 �0Z �0.69 �0.74 �0x �0.28 �0.41 �0y �0.45 �0.62 �0kd �0.05 0.09 �0Pe �0.35 �0.52 �0L �0.74 �0.79 �0a* �0.37 �0.44 �0b* �0.65 �0.71 �0u* �0.67 �0.68 �0v* �0.76 �0.75 �0c* �0.62 �0.68 �0h* �0.17 �0.39 �0R �0.79 �0.79 �0G �0.70 �0.77 �0B �0.59 �0.72 �0HRGB �0.04 �0.06 �0IRGB �0.72 �0.71 �0SRGB �0.68 �0.79 �0RI 0.30 0.62 0

quantity of black humic acid (Schulze et al., 1993).

Organic materials in soil contribute to soil colour

through the formation of organo-mineral complexes.

Correlations between soil OC and soil colour vari-

ables from the various colour systems examined are

shown in Table 3.

Organic carbon was also well correlated to the

lightness parameters of the different colour models,

and to a lesser extent to their chromaticity. Generally,

highest correlations were obtained for R of the RGB

and v* of the CIELUV models (Table 3). The R

coordinate of the RGB model showed the strongest

single parameter relationship to soil OC with a Radj2 of

0.66 (Fig. 11a). The reason for this may be that R

contains combined information on both brightness

and chromaticity. Thus measurements will also be

very sensitive to the lighting condition at the time of

measurements (see above).

The L and v* parameters of the CIELUV model

also showed good relationships, with Radj2 values of

0.56 and 0.52, respectively (Fig. 11b and c). Combin-

(NSW n =77) OC (France n =45) OC (Canada n =14)

�0.21�0.88�0.63

.41 0.12 �0.87

.68 �0.86 �0.84

.71 �0.85 �0.83

.68 �0.83 �0.84

.66 �0.83 �0.83

.52 �0.77 �0.70

.43 �0.65 �0.37

.64 �0.86 �0.57

.05 �0.32 0.51

.54 �0.74 �0.47

.70 �0.87 �0.87

.36 �0.68 �0.19

.72 �0.88 �0.81

.64 �0.82 �0.79

.75 �0.89 �0.91

.69 �0.85 �0.80

.36 0.03 �0.87

.75 �0.88 �0.90

.66 �0.86 �0.87

.50 �0.76 �0.72

.18 0.12 �0.77

.71 �0.86 �0.84

.68 �0.87 �0.84

.50 0.47 0.83

Page 16: Colour Space Models for Soil Science

0

0.5

1

1.5

2

2.5

3

20 40 60 80L + u* + v*

y = 5.677 – 1.167 log10 (L + u*+ v*)RMSE = √0.27 dag/kg

R2adj. = 0.68

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

u*

y = 3.117 – 0.790 log10 (u*)

RMSE = √0.34 dag/kgR2adj. = 0.52

0

0.5

1

1.5

2

2.5

3

10 20 30 40L

y = 4.843 – 1.139 log10(L)RMSE = √0.31 dag/kg

R2adj.= 0.56

0

0.5

1

1.5

2

2.5

3

SQ

RT

OC

dag

/kg

0 5 10 15 20v*

y = 3.317 – 0.905 log10 (v*)

RMSE = √0.30 dag/kg R2

adj.= 0.63

0

0.5

1

1.5

2

2.5

3

SQ

RT

OC

dag

/kg

20 40 60 80 100 120R

y = 7.304 – 1.425 log10 (R)RMSE = √0.28 dag/kg

R2adj. = 0.66

(a) (b) (c)

(d) (e)

Fig. 11. Relationships between soil OC and soil colour parameters from the RGB model: R, and the CIELUV model: L, u*, v* and combined

L +u*+v*. French data (!), Australian data (o), NSW data (+) and Canadian data (�). (n =180).

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337 335

ing the parameters of the CIELUV model improved

the relationship producing better Radj2 and RMSE

values (Fig. 11e). When we regressed soil OC as a

function of the tristimulus of each colour model, we

found that the Munsell HVC model produced the

weakest relationships and least accurate results

(Radj2 =0.36 and RMSE=0.62 dag C/kg soil), followed

by the CIE Yxy (Radj2 =0.54 and RMSE=0.57 dag C/

kg soil) and the Helmholtz coordinates kd, Pe, Y

(R2adj=0.56 and RMSE=0.57 dag C/kg soil). The

CIELCH model produced the strongest relationship

with an Radj2 . value of 0.67 and an RMSE of 0.51 dag

C/kg soil. There was no significant difference

(a =0.01) between the multiple linear regression pre-

dictions of soil OC using tristimuli of each of the

remaining colour models (Radj2 =0.66 and RMSE=

0.52 dag C/kg soil).

Using such relationships it may be possible to

differentiate surface soil OC content across the land-

scape based on soil colour. Similarly, they may be

used to characterise the within-field variation in soil

OC. The potential exists for the development of a

proximal don-the-goT soil colour sensor to provide

detailed information on the spatial variability of soil

OC. Soil colour, measured using such proximal as

well as remote sensors may also provide useful ancil-

lary information for the production of digital soil

maps (McBratney et al., 2003).

4. Conclusions

In this paper we described a number of colour

space models that may be used for quantitative

descriptions of soil colour and algorithms that may

be used to convert between them. We also compared

their representational qualities and evaluated them

against the more commonly used system for describ-

ing soil colour, the Munsell HVC system. Any of the

colour space models may potentially be used in soil

science. Munsell H showed good correlations to CIE

y, kd, h* and HRGB; Munsell V to the metric lightness

function L, CIE Y, R, G, and B and IRGB and Munsell

C to CIE x, Pe, a*, b*, u*, v* and c* and SRGB.

Page 17: Colour Space Models for Soil Science

R.A. Viscarra Rossel et al. / Geoderma 133 (2006) 320–337336

However, conjunctively the Munsell HVC parameters

were best correlated to the CIELCH and DRGB mod-

els and their respective parameters.

Soil colour alone is not a functional attribute of

soil, therefore in a case study, we evaluated the use-

fulness of each of the colour models studied by look-

ing at relationships between soil colour and soil

organic carbon. Organic carbon was correlated to

parameters from the various colour space models

that describe both the lightness of the colour and its

chroma.

Which colour model is best suited for descriptions

of soil colour? The answer depends 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 quanti-

tative, numerical or predictive analysis then colour

models that use Cartesian-type coordinate systems

will be more suitable. For predictions of soil OC,

the Munsell HVC system was the least suitable of

all of the models tested while the CIELUV and

CIELCH models were slightly more suitable than

other colour systems.

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