Graphic technology — Image quality evaluation methods for printed matter — Part 11: Colour gamut analysis

This document defines procedures to measure and compare the colour gamuts of RGB and CMYK printing processes. It is not applicable to other printing processes.

Technologie graphique — Méthodes d'évaluation de la qualité d'image pour les imprimés Analyse de la gamme des couleurs — Partie 11: Analyse de la gamme des couleurs

Grafična tehnologija - Metode ocenjevanja kakovosti slike za tiskovine - 11. del: Analiza barvne lestvice

General Information

Status
Published
Publication Date
04-Apr-2022
Current Stage
6060 - International Standard published
Start Date
05-Apr-2022
Due Date
21-Jul-2023
Completion Date
05-Apr-2022

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TECHNICAL ISO/TS
SPECIFICATION 18621-11
Second edition
2022-04
Graphic technology — Image
quality evaluation methods for
printed matter —
Part 11:
Colour gamut analysis
Technologie graphique — Méthodes d'évaluation de la qualité
d'image pour les imprimés —
Partie 11: Analyse de la gamme des couleurs
Reference number
ISO/TS 18621-11:2022(E)
© ISO 2022
---------------------- Page: 1 ----------------------
ISO/TS 18621-11:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
© ISO 2022 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TS 18621-11:2022(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction .................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Describing a colour gamut .........................................................................................................................................................................2

4.1 General ........................................................................................................................................................................................................... 2

4.2 Requirements of a gamut boundary description ..................................................................................................... 2

4.3 Device gamut and usable gamut ............................................................................................................................................. 3

4.4 Procedures for describing a colour gamut ..................................................................................................................... 3

4.4.1 General ........................................................................................................................................................................................ 3

4.4.2 Procedure for describing the colour gamut of a reproduction system based

on its ICC profile .................................................................................................................................................................. 4

4.4.3 Procedure for describing the device gamut of a reproduction system based

on its characterization model ................................................................................................................................. 5

4.4.4 Procedure for describing the device gamut of a reproduction system based

on measurement of a printed gamut target ............................................................................................... 5

4.4.5 Procedure for describing the device gamut of a reproduction system based

on characterization data ............................................................................................................................................. 5

5 Computing the volume of a colour reproduction gamut ............................................................................................ 6

5.1 General ........................................................................................................................................................................................................... 6

5.2 Volume of a single gamut ............................................................................................................................................................... 6

5.2.1 Volume calculation ........................................................................................................................................................... 6

5.2.2 Verifying the volume calculation ......................................................................................................................... 7

5.3 Volume of the intersection of two gamuts ..................................................................................................................... 8

5.3.1 General ........................................................................................................................................................................................ 8

5.3.2 Determining if a coordinate is inside or outside a gamut .............................................................. 8

6 Comparing colour gamuts ..........................................................................................................................................................................9

6.1 General ........................................................................................................................................................................................................... 9

6.2 GCI ...................................................................................................................................................................................................................... 9

6.3 Gamut coverage ...................................................................................................................................................................................... 9

6.4 Out-of-gamut volume proportion ........................................................................................................................................... 9

7 Encoding and communicating a colour gamut description .................................................................................... 9

Annex A (informative) Images for use in determining the gamut boundary of RGB and

CMYK printing processes .........................................................................................................................................................................11

Annex B (informative) Gamut volumes for a set of reference profiles .........................................................................12

Annex C (informative) Errors in triangulation ......................................................................................................................................13

Annex D (normative) Media-relative colour gamuts .......................................................................................................................15

Bibliography .............................................................................................................................................................................................................................16

iii
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ISO/TS 18621-11:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 130, Graphic technology.

This second edition cancels and replaces the first edition (ISO/TS 18621-11:2019), which has been

technically revised.
The main changes are as follows:
— Formula (1) has been corrected;
— requirements for conformance were clarified throughout;
— the list of example gamut volumes in Table B.1 has been revised.
A list of all parts in the ISO 18621 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
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ISO/TS 18621-11:2022(E)
Introduction

The colour gamut that can be achieved by a reproduction system is an important attribute. It enables

users to compare the colour reproduction capabilities of different printing systems and to determine

whether one system can simulate all the colours available in another. This document describes

procedures to define and compare colour gamuts.

Given a set of coordinates known to lie on the surface of a colour gamut, the volume of the gamut can

be determined by segmenting the gamut into a series of tetrahedra, computing the volume of each

tetrahedron and summing the results. For a reproduction process with three colour components, a

colour will lie on the surface if it satisfies the condition that at least one component has a value of 0

or 1, where 1 represents the maximum amount of the colour component. However, printing processes

usually have four or more colour components (e.g. Cyan, Magenta, Yellow and Black in four-colour

process printing), and determining which coordinates lie on the gamut boundary cannot be done solely

from the relative amounts of the colour components. For CMYK processes, in almost all cases, the Black

colorant extends the gamut below the gamut vertex at each hue angle. This makes it possible to identify

a set of coordinates which are expected to lie on the gamut surface from the relative colorant amounts

and the coordinates of the two- and three-colour overprints. For processes with more than four colour

components, some knowledge of the colorimetry of a sample of colours from the colour data encoding is

needed in order to determine which colours lie on the boundary.

For these reasons, coordinates on the surface of the gamut of RGB and CMYK printing processes can be

determined by printing a test chart with suitable colorant combinations, and measuring the colours;

while for other printing processes, it is necessary to model the colorant-to-colorimetry relationship in

order to identify colours on the gamut boundary. (RGB here refers to the input signal and supports the

common situation where the printer driver accepts RGB instead of CMYK.)
© ISO 2022 – All rights reserved
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TECHNICAL SPECIFICATION ISO/TS 18621-11:2022(E)
Graphic technology — Image quality evaluation methods
for printed matter —
Part 11:
Colour gamut analysis

IMPORTANT — The electronic file of this document contains colours which are considered to be

useful for the correct understanding of the document. Users should therefore consider printing

this document using a colour printer.
1 Scope

This document defines procedures to measure and compare the colour gamuts of RGB and CMYK

printing processes.
It is not applicable to other printing processes.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 13655, Graphic technology — Spectral measurement and colorimetric computation for graphic arts

images

ISO 15076-1, Image technology colour management — Architecture, profile format and data structure —

Part 1: Based on ICC.1:2010
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www. iso. org/o bp
— IEC Electropedia: available at https:// www.e lectropedia. org/
3.1
colour gamut

range of colours that can be reproduced by an output device on a given medium, represented in a CIE-

based colour space

Note 1 to entry: The CIE colour space for representation of colour gamuts is normally CIELAB.

3.2
gamut vertex

coordinate in a CIE-based colour space which represents a point on a colour gamut (3.1) surface and

which is used in defining the surface of the gamut
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ISO/TS 18621-11:2022(E)
3.3
gamut face

planar sub-division of the colour gamut (3.1) surface formed by three or more coplanar gamut face edges

(3.4)

Note 1 to entry: The colour gamut of most output devices can be described in terms of a set of gamut faces that

completely enclose all the colours that can be reproduced by the device, with no gaps or overlaps.

Note 2 to entry: In this document, gamut faces are defined as having three gamut vertices.

3.4
gamut face edge
line connecting two adjacent vertices of a gamut face (3.3)

Note 1 to entry: In a continuous gamut surface, each gamut face edge is shared by two gamut faces.

3.5
characterization model

mathematical model that converts between coordinates in a device colour encoding and a CIE-based

colour space
3.6
device gamut

range of colours that corresponds to all possible combinations of colour channels of the device within

the device data encoding, when printed on a substrate
3.7
usable gamut

subset of the device gamut (3.6) that corresponds to the set of combinations of colour channels of the

device in practical use, when reproduced on an output medium

Note 1 to entry: The usable gamut of an output device is normally smaller than the device gamut owing to

practical limitations in the combinations of colour channels. Most CMYK devices cannot produce a print in which

all channels are set to the maximum. The usable gamut is applicable when the gamut to be determined is that of

the system when used as part of a reproduction workflow, using an ICC profile to convert to output channels;

while the device gamut is applicable when the gamut to be determined is that of the reproduction device

independently of the profile and its colour separation method.

Note 2 to entry: In practice, some printers do not allow all possible combinations of ink to be printed, and an ink-

limiting procedure is applied automatically in the printer. Where this is done, this "ink-limited" mode of printing

still should be considered to be the "device gamut".
4 Describing a colour gamut
4.1 General

The colour gamut of a reproduction system is a volume in 3D colour space. It shall be mathematically

described as a closed set of triangular faces on the surface of the gamut which completely encloses the

gamut volume.
4.2 Requirements of a gamut boundary description

Each face should be defined by three colorimetric coordinates, and the set of faces shall be defined

in such a way that it encloses the volume of the gamut without gaps or overlaps. The surface shall be

encoded as an nx3 array of vertices (in which there are n vertices and each row represents the colour

space coordinates of a gamut vertex) and an mx3 face array of indices into the vertices array (where

there are m faces and each row of the array identifies the three row numbers in the vertex array which

correspond to a gamut face). Each gamut vertex shall be described as a CIELAB L*, a*, b* value computed

from spectral reflectance or tristimulus values according to ISO 13655, and when this is done it shall

be stated which ISO 13655 measurement mode applies to the data. If the colour space used to describe

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ISO/TS 18621-11:2022(E)

the gamut vertices is not CIELAB computed according to ISO 13655, details of the colour space used

(including the CIE colorimetric observer and illuminant) shall be reported as metadata associated with

the gamut description. Where it is desired that the gamut description or comparison is media-relative,

CIELAB L*, a*, b* coordinates shall be scaled as described in Annex D.

In order to satisfy the requirement to enclose the gamut volume without gaps or overlaps, the following

conditions shall be met.

a) The three indices identifying each face shall identify vertices in clockwise order, when viewed from

the exterior of the volume.
b) Each gamut face edge shall be common to two gamut faces.

CIELAB L*, a*, b* computed according to ISO 13655 should be used where it is important to be able to

compare colour gamuts or where the gamut is derived from an ICC profile.

It is acknowledged that CIELAB is an approximately perceptually uniform colour space. The CIELAB

space over-predicts perceived chroma at higher values of C* chroma, and hence at the gamut boundary,

and this affects the gamut size.

Determining a set of faces that meet the conditions listed above from an arbitrary set of vertices is non-

trivial. For this reason, this document provides a set of well-spaced coordinates in device space, and an

associated triangulation. Full details of these data are given in Annex A.
4.3 Device gamut and usable gamut

The device gamut can be determined either from the characterization model (usually represented by

an ICC profile) or by direct measurement of colours that lie on the gamut boundary. To compute the

usable gamut, an additional step is required in which the device coordinates are restricted to those

available in the reproduction workflow. If an ICC profile is used to define the usable gamut, CIELAB

gamut surface coordinates in the device gamut can be transformed to device coordinates and then back

to CIELAB coordinates to obtain the usable gamut.

NOTE In some cases, the device or its driver can limit the range of colorant combinations, regardless of

whether an ICC profile is used.

The procedure in 4.4 should be used for determining the gamut boundary vertex and face arrays. If a

different procedure is used, it shall be stated when communicating the gamut boundary description

which procedure was used to determine the gamut vertices, and whether the device gamut or usable

gamut is described.
4.4 Procedures for describing a colour gamut
4.4.1 General

One of the following procedures should be used to describe the colour gamut of a reproduction system.

NOTE 1 In most cases, results obtained from these procedures, using the set of well-spaced coordinates in

[2]

device space described in this document, give very similar results . Certain factors affect the reproducibility of

the gamut description, such as when the black in a toner-based printer results in a lower L* value than any of the

other colorant combinations.

NOTE 2 An ICC profile is a convenient means of converting data between the device data encoding and

the corresponding colorimetry, and it defines the colour gamut available in a workflow based on ICC profile

conversions. Other methods of obtaining colorimetric values for coordinates on the gamut surface, such as direct

measurement or a characterization model, is also used.
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ISO/TS 18621-11:2022(E)

4.4.2 Procedure for describing the colour gamut of a reproduction system based on its ICC

profile

The following procedure should be used to compute the faces and vertices of a gamut boundary

description from an ICC profile for the reproduction system. The procedure is applicable to RGB and

CMYK devices.

Where used, the ICC profile shall be created according to ISO 15076-1, from characterization data

representing the printing process whose gamut is to be described. This method estimates the gamut of

the device represented by the profile, and depending on the accuracy of the AToB1 tag and the BToA1

tag of the profile this estimate might or might not itself be accurate. The accuracy of AToB1 and BToA1

tags shall be reported.

To maintain accuracy, the precision of data used for both device coordinates and CIELAB coordinates

shall be 16 bits or greater.

1) Generate an image whose pixels represent a set of device coordinates on the gamut boundary of the

encoding. The image should be arranged so that the ratio of the relative colorant amounts varies in

the horizontal direction, and the total colorant amount varies in the vertical direction. The white

point and black point are repeated across the first and last rows in the coordinate array. Annex A

gives details of images for this purpose for RGB and CMYK reproduction systems.

2) Convert the image in step 1) to CIELAB using an ICC profile for the reproduction medium, selecting

the ICC-Absolute Colorimetric rendering intent.

The values calculated following step 2) are the gamut vertices of the device gamut for RGB and

CMYK systems. These are also the usable gamut of an RGB reproduction system.

3) To obtain the usable gamut of a reproduction system, convert the CIELAB coordinates back to

device coordinates and then back to PCS CIELAB coordinates, in both cases using the ICC-Absolute

Colorimetric rendering intent. This step is necessary to ensure that only colorant values that are

permitted by the colour separation model are represented in the gamut description.

4) The CIELAB coordinates for each patch from step 3) are read row-wise and arranged as an m × n × 3

array to form the vertex array where m is the number of columns in the test image and n is the

number of rows.

5) To construct the face array for this data, start with the upper left device coordinate and move

clockwise to the two coordinates in the next row, as shown in Figure 1. The first row of the faces

list is therefore [1, m+2, m+1]. The next row in the faces list is [1, 2, m+2]. Continue to move through

the device coordinates until the face list is fully populated with one row per face.

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ISO/TS 18621-11:2022(E)
Key
a m pixels
b n pixels
Figure 1 — Triangulation of gamut target image

4.4.3 Procedure for describing the device gamut of a reproduction system based on its

characterization model

The following procedure can be used to compute the faces and vertices of a gamut boundary description

of a reproduction system using its characterization model.

1) From the device data in the test chart described in step 1) of 4.4.2, compute CIELAB values for each

colour patch using the characterization model.
2) Follow steps 4) to 5) from 4.4.2 to obtain the face and vertex list.

4.4.4 Procedure for describing the device gamut of a reproduction system based on

measurement of a printed gamut target

The following procedure can be used to derive the faces and vertices of a gamut boundary description

of a reproduction system using computations based on direct measurement of printed specimens.

1) Print the test chart described in step 1) of 4.4.2 on the printer without colour management and

measure the printed patches.

NOTE In order to determine the printer gamut independently on any ICC profile, colour management is

not applied.
2) Follow steps 4) to 5) from 4.4.2 to obtain the face and vertex list.

4.4.5 Procedure for describing the device gamut of a reproduction system based on

characterization data

The following procedure can be used to compute the faces and vertices of a gamut boundary description

of a reproduction system from characterization data.

1) Select the characterization data set which represents the device, using a test chart such as that

[1]
described in ISO 12642-1 .
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ISO/TS 18621-11:2022(E)
[3], [4], [5]

2) Use the alpha shapes method to determine the set of connected faces which enclose the

coordinates in step 1).

An alpha shapes radius of 40 is recommended. Since the radius depends on sampling size and

distribution, other values may be optimal for a given data set. Alpha shapes may generate an error

depending on the chosen radius.

NOTE The face list returned by the alpha shapes method will be different from that obtained by the

procedure in 4.4.3 and 4.4.4, but the volume calculated from these data according to Clause 5 has been found to

be in good agreement. See Reference [2] for more details.
5 Computing the volume of a colour reproduction gamut
5.1 General
The volume of colour reproduction gamuts shall be defined as follows.
5.2 Volume of a single gamut
5.2.1 Volume calculation
The gamut volume shall be calculated as shown below.

1) Define a point at the approximate centre of the gamut volume, whose CIELAB coordinates are the

average of the coordinates of the white and black point of the gamut.

2) Add this point to the set of points defining each gamut face to form a set of tetrahedra spanning the

gamut volume.

3) For each tetrahedron in turn, let the four vertices be p , p , and p (corresponding to the planar face

1 2 3

on the gamut boundary) and p (the approximate gamut centroid), as shown in Figure 2. If each

vertex p , etc is represented by its CIELAB L*, a* and b* coordinates, the (signed) volume of each

tetrahedron should then be computed using the scalar triple product shown in Formula (1):

 
ab⋅×c
V =− (1)
where
ap=−p
bp=−p
cp=−p
The ‘·’ and ‘ × ’ symbols denote dot product and cross product, respectively.
4) Sum the volumes of all the tetrahedra to obtain the total gamut volume.
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ISO/TS 18621-11:2022(E)
Key
1 gamut face p , p , p viewed from outside
1 2 3
2 fixed point p at approximate gamut centre

Figure 2 — Tetrahedron formed from single gamut face defined by vertices p and fixed point

1-3

NOTE 1 The sign of the scalar triple product in Formula (1) depends on the winding order of the planar face,

and in the clock-wise order defined, as shown in Figure 2, it is negative.

NOTE 2 If the scalar triple product is positive for a given tetrahedron, this might indicate a "fold" in the colour

gamut. See Annex C for more details.

The volume shall be reported as the number of "cubic CIELAB units", i.e. the number of hexahedra with

sides of 1,0 in the dimensions of CIELAB L*, a* and b*.
5.2.2 Verifying the volume calculation

If the conditions in 4.2 are met, the procedure in 5.2.1 will result in an accurate estimate of the gamut

volume. An additional check can be performed by computing the solid angle of each tetrahedron and

summing them. If the faces of the gamut surface correctly enclose the volume, the resulting value will

be equal to the solid angle of a sphere, i.e. 4π steradians.

NOTE A method of calculating the solid angle of a tetrahedron is given in Reference [6].

For guidance, the gamut volumes calculated from a set of reference profiles is provided in Annex B. This

can be used to verify the correctness of the procedure used.

In practice it can be difficult to satisfy the conditions in 4.2 for every face in a gamut. It is recommended

that the total solid angle is reported with the estimated volume. The volume associated with the number

of incorrectly-oriented faces should also be calculated and reported.

When the target image method is used to calculate the gamut surface the gamut volume shall be

reported as:
Gamut volume = 123456 (32)

where the figure in parentheses indicates the maximum error in the calculation. If this value is greater

...

ISO/TC 130 N 4680
ISO/TS PRF 18621-11:20212022(E)
ISO/TC 130/JWG 14
Date: 2021-11-26
Secretariat: SAC

Graphic technology — Image quality evaluation methods for printed matter — Part 11: Colour gamut

analysis
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ISO/TS 18621-11:2022(E)
© ISO 2019, 2022Published in Switzerland

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or

utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or

posting on the internet or an intranet, without prior written permission. Permission can be requested

from either ISO at the address below or ISO’s member body in the country of the requester.

ISO copyright office
CP 401 • Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. + Phone: +41 22 749 01 11
Fax + 41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerlandwww.iso.org
ii © ISO 2019 – All rights reserved
ii © ISO 2022 – All rights reserved
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ISO/TS 18621-11:2022(E)
Contents
Foreword 5
Introduction 6
1 Scope 7
2 Normative references 7
3 Terms and definitions 7
4 Describing a colour gamut 8
4.1 General 8
4.2 Requirements of a gamut boundary description 8
4.3 Device gamut and usable gamut 9
4.4 Procedures for describing a colour gamut 9

4.4.1 Procedure for describing the colour gamut of a reproduction system based on its ICC profile

4.4.2 Procedure for describing the device colour gamut of a reproduction system based on its

characterization model 10

4.4.3 Procedure for describing the device colour gamut of a reproduction system based on

measurement of a printed gamut target 11

4.4.4 Procedure for describing the device colour gamut of a reproduction system based on

characterization data 11
5 Computing the volume of a colour reproduction gamut 11
5.1 Volume of a single gamut 11
5.1.1 Volume calculation 11
5.1.2 Verifying the volume calculation 12
5.2 Volume of the intersection of two gamuts 12
5.2.1 Triangulated intersection 13
5.2.2 Voxel-based intersection 13
6 Comparing colour gamuts 13
6.1 GCI 14
6.2 Gamut coverage 14
6.3 Out-of-gamut 14
7 Encoding and communicating a colour gamut description 15

Annex A (normative) Images for use in determining the gamut boundary of RGB and CMYK printing processes

16
A.1 Gamut Boundary image 16
A.2 Gamut Boundary image triangulation 16
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ISO/TS 18621-11:2022(E)
Annex B (informative) Gamut volumes for a set of reference profiles 18
Annex C (informative) Errors in triangulation 20
C.1 Identification and impact 20
Annex D (normative) Media-relative colour gamuts 22
Bibliography 23
Foreword vi
Introduction vii
1 Scope 1
2 Normative references 1
3 Terms and definitions 1
4 Describing a colour gamut 2
4.1 General 2
4.2 Requirements of a gamut boundary description 2
4.3 Device gamut and usable gamut 3
4.4 Procedures for describing a colour gamut 3
4.4.1 General 3

4.4.2 Procedure for describing the colour gamut of a reproduction system based on its ICC profile

4.4.3 Procedure for describing the device gamut of a reproduction system based on its

characterization model 5

4.4.4 Procedure for describing the device gamut of a reproduction system based on measurement

of a printed gamut target 5

4.4.5 Procedure for describing the device gamut of a reproduction system based on

characterization data 6
5 Computing the volume of a colour reproduction gamut 6
5.1 General 6
5.2 Volume of a single gamut 6
5.2.1 Volume calculation 6
5.2.2 Verifying the volume calculation 8
5.3 Volume of the intersection of two gamuts 8
5.3.1 General 8
5.3.2 Determining if a coordinate is inside or outside a gamut 9
6 Comparing colour gamuts 9
6.1 General 9
6.2 GCI 9
6.3 Gamut coverage 9
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ISO/TS 18621-11:2022(E)
6.4 Out-of-gamut volume proportion 10
7 Encoding and communicating a colour gamut description 10

Annex A (informative) Images for use in determining the gamut boundary of RGB and CMYK printing

processes 11
Annex B (informative) Gamut volumes for a set of reference profiles 13
Annex C (informative) Errors in triangulation 14
Annex D (normative) Media-relative colour gamuts 16
Bibliography 17
© ISO 2022 – All rights reserved v
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ISO/TS 18621-11:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work. ISO

collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directiveswww.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any

patent rights identified during the development of the document will be in the Introduction and/or on

the ISO list of patent declarations received (see www.iso.org/patentswww.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the World

Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see
www.iso.org/iso/foreword.html), see www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 130, Graphic technology.

This second edition cancels and replaces the first edition (ISO/TS 18621-11:2019), which has been

technically revised.
The main changes are as follows:
— Formula (1) has been corrected;
— requirements for conformance were clarified throughout;
— the list of example gamut volumes in Table B.1 has been revised.
A list of all parts in the ISO 18621 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at
www.iso.org/members.htmlwww.iso.org/members.html.
vi © ISO 2019 – All rights reserved
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ISO/TS 18621-11:2022(E)
Introduction

The colour gamut that can be achieved by a reproduction system is an important attribute. It enables users

to compare the colour reproduction capabilities of different printing systems and to determine whether one

system can simulate all the colours available in another. This document describes procedures to define and

compare colour gamuts.

Given a set of coordinates known to lie on the surface of a colour gamut, the volume of the gamut can be

determined by segmenting the gamut into a series of tetrahedra, computing the volume of each tetrahedron

and summing the results. For a reproduction process with three colour components, a colour will lie on the

surface if it satisfies the condition that at least one component has a value of 0 or 1, where 1 represents the

maximum amount of the colour component. However, printing processes usually have four or more colour

components (e.g. Cyan, Magenta, Yellow and Black in four-colour process printing), and determining which

coordinates lie on the gamut boundary cannot be done solely from the relative amounts of the colour

components. For CMYK processes, in almost all cases, the Black colorant extends the gamut below the gamut

vertex at each hue angle. This makes it possible to identify a set of coordinates which are expected to lie on

the gamut surface from the relative colorant amounts and the coordinates of the two- and three-colour

overprints. For processes with more than four colour components, some knowledge of the colorimetry of a

sample of colours from the colour data encoding is needed in order to determine which colours lie on the

boundary.

For these reasons, coordinates on the surface of the gamut of RGB and CMYK printing processes can be

determined by printing a test chart with suitable colorant combinations, and measuring the colours; while

for other printing processes, it is necessary to model the colorant-to-colorimetry relationship in order to

identify colours on the gamut boundary. (RGB here refers to the input signal and supports the common

situation where the printer driver accepts RGB instead of CMYK.)
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TECHNICAL SPECIFICATION ISO/TS 18621-11:2021 2022(E)
Graphic technology — - Image quality evaluation methods for printed
matter — — Part 11: Colour gamut analysis

IMPORTANT — The electronic file of this document contains colours which are considered to be useful

for the correct understanding of the document. Users should therefore consider printing this document

using a colour printer.
Scope

This document defines procedures to measure and compare the colour gamuts of RGB and CMYK printing

processes.
It is not applicable to other printing processes.
Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

ISO 15076-1, Image technology colour management — Architecture, profile format and data structure —

Part 1: Based on ICC.1:2010

ISO 12642-1, Graphic technology — Input data for characterization of four-colour process printing — Part

1: Initial data set

ISO 13655, Graphic technology — Spectral measurement and colorimetric computation for graphic arts

images

ISO 15076-1, Image technology colour management — Architecture, profile format and data structure —

Part 1: Based on ICC.1:2010
Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https://www.iso.org/obphttps://www.iso.org/obp

— IEC Electropedia: available at http://www.electropedia.org/https://www.electropedia.org/

3.1
colour gamut

range of colours that can be reproduced by an output device on a given medium, represented in a CIE-

based colour space

Note 1 to entry: The CIE colour space for representation of colour gamuts is normally CIELAB.

3.2
gamut vertex
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ISO/TS 18621-11:20212022(E)

coordinate in a CIE-based colour space which represents a point on a colour gamut (3.1) surface and

which is used in defining the surface of the gamut
3.3
gamut face

planar sub-division of the colour gamut (3.1) surface formed by three or more coplanar gamut face edges

(3.4)

Note 1 to entry: The colour gamut of most output devices can be described in terms of a set of gamut faces that

completely enclose all the colours that can be reproduced by the device, with no gaps or overlaps.

Note 2 to entry: In this document, gamut faces are defined as having three gamut vertices.

3.4
gamut face edge
line connecting two adjacent vertices of a gamut face (3.3)

Note 1 to entry: In a continuous gamut surface, each gamut face edge is shared by two gamut faces.

3.5
characterization model

mathematical model that converts between coordinates in a device colour encoding and a CIE-based

colour space
3.6
device gamut

range of colours that corresponds to all possible combinations of colour channels of the device within the

device data encoding, when printed on a substrate
3.7
usable gamut

subset of the device gamut (3.6) that corresponds to the set of combinations of colour channels of the

device in practical use, when reproduced on an output medium

Note 1 to entry: The usable gamut of an output device is normally smaller than the device gamut owing to practical

limitations in the combinations of colour channels. Most CMYK devices cannot produce a print in which all channels

are set to the maximum. The usable gamut is applicable when the gamut to be determined is that of the system when

used as part of a reproduction workflow, using an ICC profile to convert to output channels; while the device gamut

is applicable when the gamut to be determined is that of the reproduction device independently of the profile and

its colour separation method.

Note 2 to entry: In practice, some printers do not allow all possible combinations of ink to be printed, and an ink-

limiting procedure is applied automatically in the printer. Where this is done, this "ink-limited" mode of printing

still should be considered to be the "device gamut".
Describing a colour gamut
General

The colour gamut of a reproduction system is a volume in 3D colour space. It shall be mathematically

described as a closed set of triangular faces on the surface of the gamut which completely encloses the

gamut volume.
Requirements of a gamut boundary description

Each face should be defined by three colorimetric coordinates, and the set of faces shall be defined in such a

way that it encloses the volume of the gamut without gaps or overlaps. The surface shall be encoded as an

nx3 array of vertices (in which there are n vertices and each row represents the colour space coordinates of

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ISO/TS 18621-11:20212022(E)

a gamut vertex) and an mx3 face array of indices into the vertices array (where there are m faces and each

row of the array identifies the three row numbers in the vertex array which correspond to a gamut face).

Each gamut vertex shall be described as a CIELAB L*, a*, b* value computed from spectral reflectance or

tristimulus values according to ISO 13655, and when this is done it shall be stated which ISO 13655

measurement mode applies to the data. If the colour space used to describe the gamut vertices is not CIELAB

computed according to ISO 13655, details of the colour space used (including the CIE colorimetric observer

and illuminant) shall be reported as metadata associated with the gamut description. Where it is desired

that the gamut description or comparison is media-relative, CIELAB L*, a*, b* coordinates shall be scaled as

described in Annex D.

In order to satisfy the requirement to enclose the gamut volume without gaps or overlaps, the following

conditions shall be met.

ia) The three indices identifying each face shall identify vertices in clockwise order, when viewed from

the exterior of the volume.
iib) Each gamut face edge shall be common to two gamut faces.

CIELAB L*, a*, b* computed according to ISO 13655 should be used where it is important to be able to

compare colour gamuts or where the gamut is derived from an ICC profile.

It is acknowledged that CIELAB is an approximately perceptually uniform colour space. The CIELAB space

over-predicts perceived chroma at higher values of C* chroma, and hence at the gamut boundary, and this

affects the gamut size.

Determining a set of faces that meet the conditions listed above from an arbitrary set of vertices is non-

trivial. For this reason, this document provides a set of well-spaced coordinates in device space, and an

associated triangulation. Full details of these data are given in Annex A.
Device gamut and usable gamut

The device gamut can be determined either from the characterization model (usually represented by an ICC

profile) or by direct measurement of colours that lie on the gamut boundary. To compute the usable gamut,

an additional step is required in which the device coordinates are restricted to those available in the

reproduction workflow. If an ICC profile is used to define the usable gamut, CIELAB gamut surface

coordinates in the device gamut can be transformed to device coordinates and then back to CIELAB

coordinates to obtain the usable gamut.

NOTE In some cases, the device or its driver can limit the range of colorant combinations, regardless of whether

an ICC profile is used.

The procedure in 4.4 should be used for determining the gamut boundary vertex and face arrays. If a

different procedure is used, it shall be stated when communicating the gamut boundary description which

procedure was used to determine the gamut vertices, and whether the device gamut or usable gamut is

described.
Procedures for describing a colour gamut
General

One of the following procedures should be used to describe the colour gamut of a reproduction system.

NOTE 1 In most cases, results obtained from these procedures, using the set of well-spaced coordinates in device

[12]

space described in this document, give very similar results . Certain factors affect the reproducibility of the gamut

description, such as when the black in a toner-based printer results in a lower L* value than any of the other colorant

combinations.
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ISO/TS 18621-11:20212022(E)

NOTE 2 An ICC profile is a convenient means of converting data between the device data encoding and the

corresponding colorimetry, and it defines the colour gamut available in a workflow based on ICC profile

conversions. Other methods of obtaining colorimetric values for coordinates on the gamut surface, such as direct

measurement or a characterization model, is also used.

Procedure for describing the colour gamut of a reproduction system based on its ICC profile

The following procedure should be used to compute the faces and vertices of a gamut boundary description

from an ICC profile for the reproduction system. The procedure is applicable to RGB and CMYK devices.

Where used, the ICC profile shall be created according to ISO 15076-1, from characterization data

representing the printing process whose gamut is to be described. This method estimates the gamut of the

device represented by the profile, and depending on the accuracy of the AToB1 tag and the BToA1 tag of the

profile this estimate maymight or maymight not itself be accurate. The accuracy of AToB1 and BToA1 tags

shall be reported.

To maintain accuracy, the precision of data used for both device coordinates and CIELAB coordinates shall be

16 bits or greater.

1) Generate an image whose pixels represent a set of device coordinates on the gamut boundary of the

encoding. The image should be arranged so that the ratio of the relative colorant amounts varies in

the horizontal direction, and the total colorant amount varies in the vertical direction. The white

point and black point are repeated across the first and last rows in the coordinate array. Annex A

gives details of images for this purpose for RGB and CMYK reproduction systems.

2) Convert the image in step 1) to CIELAB using an ICC profile for the reproduction medium, selecting

the ICC-Absolute Colorimetric rendering intent.

The values calculated following step 2) are the gamut vertices of the device gamut for RGB and CMYK

systems. These are also the usable gamut of an RGB reproduction system.

3) To obtain the usable gamut of a reproduction system, convert the CIELAB coordinates back to device

coordinates and then back to PCS CIELAB coordinates, in both cases using the ICC-Absolute

Colorimetric rendering intent. This step is necessary to ensure that only colorant values that are

permitted by the colour separation model are represented in the gamut description.

4) The CIELAB coordinates for each patch from step 3) are read row-wise and arranged as an m × n × 3

array to form the vertex array where m is the number of columns in the test image and n is the

number of rows.

5) To construct the face array for this data, start with the upper left device coordinate and move

clockwise to the two coordinates in the next row, as shown in Figure 1. The first row of the faces list

is therefore [1, m+2, m+1]. The next row in the faces list is [1, 2, m+2]. Continue to move through the

device coordinates until the face list is fully populated with one row per face.
4 © ISO 2019 – All rights reserved
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ISO/TS 18621-11:20212022(E)
Key
a m pixels
b n pixels
Figure 1 — Triangulation of gamut target image

Procedure for describing the device gamut of a reproduction system based on its characterization

model

The following procedure can be used to compute the faces and vertices of a gamut boundary description of a

reproduction system using its characterization model.

1) From the device data in the test chart described in step 1) of 4.4.2, compute CIELAB values for each

colour patch using the cha
...

TECHNICAL ISO/TS
SPECIFICATION 18621-11
Second edition
Graphic technology - Image quality
evaluation methods for printed
matter —
Part 11:
Colour gamut analysis
Technologie graphique — Méthodes d'évaluation de la qualité
d'image pour les imprimés —
Partie 11: Analyse de la gamme des couleurs
Member bodies are requested to consult relevant national interests in ISO/IEC

JTC 1/SC 28,ISO/TC 42 before casting their ballot to the e-Balloting application.

PROOF/ÉPREUVE
Reference number
ISO/TS 18621-11:2022(E)
© ISO 2022
---------------------- Page: 1 ----------------------
ISO/TS 18621-11:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
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ISO/TS 18621-11:2022(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction .................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Describing a colour gamut .........................................................................................................................................................................2

4.1 General ........................................................................................................................................................................................................... 2

4.2 Requirements of a gamut boundary description ..................................................................................................... 2

4.3 Device gamut and usable gamut ............................................................................................................................................. 3

4.4 Procedures for describing a colour gamut ..................................................................................................................... 3

4.4.1 General ........................................................................................................................................................................................ 3

4.4.2 Procedure for describing the colour gamut of a reproduction system based

on its ICC profile .................................................................................................................................................................. 4

4.4.3 Procedure for describing the device gamut of a reproduction system based

on its characterization model ................................................................................................................................. 5

4.4.4 Procedure for describing the device gamut of a reproduction system based

on measurement of a printed gamut target ............................................................................................... 5

4.4.5 Procedure for describing the device gamut of a reproduction system based

on characterization data ............................................................................................................................................. 5

5 Computing the volume of a colour reproduction gamut ............................................................................................ 6

5.1 General ........................................................................................................................................................................................................... 6

5.2 Volume of a single gamut ............................................................................................................................................................... 6

5.2.1 Volume calculation ........................................................................................................................................................... 6

5.2.2 Verifying the volume calculation ......................................................................................................................... 7

5.3 Volume of the intersection of two gamuts ..................................................................................................................... 8

5.3.1 General ........................................................................................................................................................................................ 8

5.3.2 Determining if a coordinate is inside or outside a gamut .............................................................. 8

6 Comparing colour gamuts ..........................................................................................................................................................................9

6.1 General ........................................................................................................................................................................................................... 9

6.2 GCI ...................................................................................................................................................................................................................... 9

6.3 Gamut coverage ...................................................................................................................................................................................... 9

6.4 Out-of-gamut volume proportion ........................................................................................................................................... 9

7 Encoding and communicating a colour gamut description .................................................................................... 9

Annex A (informative) Images for use in determining the gamut boundary of RGB and

CMYK printing processes .........................................................................................................................................................................11

Annex B (informative) Gamut volumes for a set of reference profiles .........................................................................12

Annex C (informative) Errors in triangulation ......................................................................................................................................13

Annex D (normative) Media-relative colour gamuts .......................................................................................................................15

Bibliography .............................................................................................................................................................................................................................16

iii
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ISO/TS 18621-11:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to

the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see

www.iso.org/iso/foreword.html.

This document was prepared by Technical Committee ISO/TC 130, Graphic technology.

This second edition cancels and replaces the first edition (ISO/TS 18621-11:2019), which has been

technically revised.
The main changes are as follows:
— Formula (1) has been corrected;
— requirements for conformance were clarified throughout;
— the list of example gamut volumes in Table B.1 has been revised.
A list of all parts in the ISO 18621 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
PROOF/ÉPREUVE © ISO 2022 – All rights reserved
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ISO/TS 18621-11:2022(E)
Introduction

The colour gamut that can be achieved by a reproduction system is an important attribute. It enables

users to compare the colour reproduction capabilities of different printing systems and to determine

whether one system can simulate all the colours available in another. This document describes

procedures to define and compare colour gamuts.

Given a set of coordinates known to lie on the surface of a colour gamut, the volume of the gamut can

be determined by segmenting the gamut into a series of tetrahedra, computing the volume of each

tetrahedron and summing the results. For a reproduction process with three colour components, a

colour will lie on the surface if it satisfies the condition that at least one component has a value of 0

or 1, where 1 represents the maximum amount of the colour component. However, printing processes

usually have four or more colour components (e.g. Cyan, Magenta, Yellow and Black in four-colour

process printing), and determining which coordinates lie on the gamut boundary cannot be done solely

from the relative amounts of the colour components. For CMYK processes, in almost all cases, the Black

colorant extends the gamut below the gamut vertex at each hue angle. This makes it possible to identify

a set of coordinates which are expected to lie on the gamut surface from the relative colorant amounts

and the coordinates of the two- and three-colour overprints. For processes with more than four colour

components, some knowledge of the colorimetry of a sample of colours from the colour data encoding is

needed in order to determine which colours lie on the boundary.

For these reasons, coordinates on the surface of the gamut of RGB and CMYK printing processes can be

determined by printing a test chart with suitable colorant combinations, and measuring the colours;

while for other printing processes, it is necessary to model the colorant-to-colorimetry relationship in

order to identify colours on the gamut boundary. (RGB here refers to the input signal and supports the

common situation where the printer driver accepts RGB instead of CMYK.)
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TECHNICAL SPECIFICATION ISO/TS 18621-11:2022(E)
Graphic technology - Image quality evaluation methods for
printed matter —
Part 11:
Colour gamut analysis

IMPORTANT — The electronic file of this document contains colours which are considered to be

useful for the correct understanding of the document. Users should therefore consider printing

this document using a colour printer.
1 Scope

This document defines procedures to measure and compare the colour gamuts of RGB and CMYK

printing processes.
It is not applicable to other printing processes.
2 Normative references

The following documents are referred to in the text in such a way that some or all of their content

constitutes requirements of this document. For dated references, only the edition cited applies. For

undated references, the latest edition of the referenced document (including any amendments) applies.

ISO 13655, Graphic technology — Spectral measurement and colorimetric computation for graphic arts

images

ISO 15076-1, Image technology colour management — Architecture, profile format and data structure —

Part 1: Based on ICC.1:2010
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
colour gamut

range of colours that can be reproduced by an output device on a given medium, represented in a CIE-

based colour space

Note 1 to entry: The CIE colour space for representation of colour gamuts is normally CIELAB.

3.2
gamut vertex

coordinate in a CIE-based colour space which represents a point on a colour gamut (3.1) surface and

which is used in defining the surface of the gamut
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ISO/TS 18621-11:2022(E)
3.3
gamut face

planar sub-division of the colour gamut (3.1) surface formed by three or more coplanar gamut face edges

(3.4)

Note 1 to entry: The colour gamut of most output devices can be described in terms of a set of gamut faces that

completely enclose all the colours that can be reproduced by the device, with no gaps or overlaps.

Note 2 to entry: In this document, gamut faces are defined as having three gamut vertices.

3.4
gamut face edge
line connecting two adjacent vertices of a gamut face (3.3)

Note 1 to entry: In a continuous gamut surface, each gamut face edge is shared by two gamut faces.

3.5
characterization model

mathematical model that converts between coordinates in a device colour encoding and a CIE-based

colour space
3.6
device gamut

range of colours that corresponds to all possible combinations of colour channels of the device within

the device data encoding, when printed on a substrate
3.7
usable gamut

subset of the device gamut (3.6) that corresponds to the set of combinations of colour channels of the

device in practical use, when reproduced on an output medium

Note 1 to entry: The usable gamut of an output device is normally smaller than the device gamut owing to

practical limitations in the combinations of colour channels. Most CMYK devices cannot produce a print in which

all channels are set to the maximum. The usable gamut is applicable when the gamut to be determined is that of

the system when used as part of a reproduction workflow, using an ICC profile to convert to output channels;

while the device gamut is applicable when the gamut to be determined is that of the reproduction device

independently of the profile and its colour separation method.

Note 2 to entry: In practice, some printers do not allow all possible combinations of ink to be printed, and an ink-

limiting procedure is applied automatically in the printer. Where this is done, this "ink-limited" mode of printing

still should be considered to be the "device gamut".
4 Describing a colour gamut
4.1 General

The colour gamut of a reproduction system is a volume in 3D colour space. It shall be mathematically

described as a closed set of triangular faces on the surface of the gamut which completely encloses the

gamut volume.
4.2 Requirements of a gamut boundary description

Each face should be defined by three colorimetric coordinates, and the set of faces shall be defined

in such a way that it encloses the volume of the gamut without gaps or overlaps. The surface shall be

encoded as an nx3 array of vertices (in which there are n vertices and each row represents the colour

space coordinates of a gamut vertex) and an mx3 face array of indices into the vertices array (where

there are m faces and each row of the array identifies the three row numbers in the vertex array which

correspond to a gamut face). Each gamut vertex shall be described as a CIELAB L*, a*, b* value computed

from spectral reflectance or tristimulus values according to ISO 13655, and when this is done it shall

be stated which ISO 13655 measurement mode applies to the data. If the colour space used to describe

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ISO/TS 18621-11:2022(E)

the gamut vertices is not CIELAB computed according to ISO 13655, details of the colour space used

(including the CIE colorimetric observer and illuminant) shall be reported as metadata associated with

the gamut description. Where it is desired that the gamut description or comparison is media-relative,

CIELAB L*, a*, b* coordinates shall be scaled as described in Annex D.

In order to satisfy the requirement to enclose the gamut volume without gaps or overlaps, the following

conditions shall be met.

a) The three indices identifying each face shall identify vertices in clockwise order, when viewed from

the exterior of the volume.
b) Each gamut face edge shall be common to two gamut faces.

CIELAB L*, a*, b* computed according to ISO 13655 should be used where it is important to be able to

compare colour gamuts or where the gamut is derived from an ICC profile.

It is acknowledged that CIELAB is an approximately perceptually uniform colour space. The CIELAB

space over-predicts perceived chroma at higher values of C* chroma, and hence at the gamut boundary,

and this affects the gamut size.

Determining a set of faces that meet the conditions listed above from an arbitrary set of vertices is non-

trivial. For this reason, this document provides a set of well-spaced coordinates in device space, and an

associated triangulation. Full details of these data are given in Annex A.
4.3 Device gamut and usable gamut

The device gamut can be determined either from the characterization model (usually represented by

an ICC profile) or by direct measurement of colours that lie on the gamut boundary. To compute the

usable gamut, an additional step is required in which the device coordinates are restricted to those

available in the reproduction workflow. If an ICC profile is used to define the usable gamut, CIELAB

gamut surface coordinates in the device gamut can be transformed to device coordinates and then back

to CIELAB coordinates to obtain the usable gamut.

NOTE In some cases, the device or its driver can limit the range of colorant combinations, regardless of

whether an ICC profile is used.

The procedure in 4.4 should be used for determining the gamut boundary vertex and face arrays. If a

different procedure is used, it shall be stated when communicating the gamut boundary description

which procedure was used to determine the gamut vertices, and whether the device gamut or usable

gamut is described.
4.4 Procedures for describing a colour gamut
4.4.1 General

One of the following procedures should be used to describe the colour gamut of a reproduction system.

NOTE 1 In most cases, results obtained from these procedures, using the set of well-spaced coordinates in

[2]

device space described in this document, give very similar results . Certain factors affect the reproducibility of

the gamut description, such as when the black in a toner-based printer results in a lower L* value than any of the

other colorant combinations.

NOTE 2 An ICC profile is a convenient means of converting data between the device data encoding and

the corresponding colorimetry, and it defines the colour gamut available in a workflow based on ICC profile

conversions. Other methods of obtaining colorimetric values for coordinates on the gamut surface, such as direct

measurement or a characterization model, is also used.
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4.4.2 Procedure for describing the colour gamut of a reproduction system based on its ICC

profile

The following procedure should be used to compute the faces and vertices of a gamut boundary

description from an ICC profile for the reproduction system. The procedure is applicable to RGB and

CMYK devices.

Where used, the ICC profile shall be created according to ISO 15076-1, from characterization data

representing the printing process whose gamut is to be described. This method estimates the gamut of

the device represented by the profile, and depending on the accuracy of the AToB1 tag and the BToA1

tag of the profile this estimate might or might not itself be accurate. The accuracy of AToB1 and BToA1

tags shall be reported.

To maintain accuracy, the precision of data used for both device coordinates and CIELAB coordinates

shall be 16 bits or greater.

1) Generate an image whose pixels represent a set of device coordinates on the gamut boundary of the

encoding. The image should be arranged so that the ratio of the relative colorant amounts varies in

the horizontal direction, and the total colorant amount varies in the vertical direction. The white

point and black point are repeated across the first and last rows in the coordinate array. Annex A

gives details of images for this purpose for RGB and CMYK reproduction systems.

2) Convert the image in step 1) to CIELAB using an ICC profile for the reproduction medium, selecting

the ICC-Absolute Colorimetric rendering intent.

The values calculated following step 2) are the gamut vertices of the device gamut for RGB and

CMYK systems. These are also the usable gamut of an RGB reproduction system.

3) To obtain the usable gamut of a reproduction system, convert the CIELAB coordinates back to

device coordinates and then back to PCS CIELAB coordinates, in both cases using the ICC-Absolute

Colorimetric rendering intent. This step is necessary to ensure that only colorant values that are

permitted by the colour separation model are represented in the gamut description.

4) The CIELAB coordinates for each patch from step 3) are read row-wise and arranged as an m × n × 3

array to form the vertex array where m is the number of columns in the test image and n is the

number of rows.

5) To construct the face array for this data, start with the upper left device coordinate and move

clockwise to the two coordinates in the next row, as shown in Figure 1. The first row of the faces

list is therefore [1, m+2, m+1]. The next row in the faces list is [1, 2, m+2]. Continue to move through

the device coordinates until the face list is fully populated with one row per face.

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ISO/TS 18621-11:2022(E)
Key
a m pixels
b n pixels
Figure 1 — Triangulation of gamut target image

4.4.3 Procedure for describing the device gamut of a reproduction system based on its

characterization model

The following procedure can be used to compute the faces and vertices of a gamut boundary description

of a reproduction system using its characterization model.

1) From the device data in the test chart described in step 1) of 4.4.2, compute CIELAB values for each

colour patch using the characterization model.
2) Follow steps 4) to 5) from 4.4.2 to obtain the face and vertex list.

4.4.4 Procedure for describing the device gamut of a reproduction system based on

measurement of a printed gamut target

The following procedure can be used to derive the faces and vertices of a gamut boundary description

of a reproduction system using computations based on direct measurement of printed specimens.

1) Print the test chart described in step 1) of 4.4.2 on the printer without colour management and

measure the printed patches.

NOTE In order to determine the printer gamut independently on any ICC profile, colour management is

not applied.
2) Follow steps 4) to 5) from 4.4.2 to obtain the face and vertex list.

4.4.5 Procedure for describing the device gamut of a reproduction system based on

characterization data

The following procedure can be used to compute the faces and vertices of a gamut boundary description

of a reproduction system from characterization data.

1) Select the characterization data set which represents the device, using a test chart such as that

[1]
described in ISO 12642-1 .
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[3], [4], [5]

2) Use the alpha shapes method to determine the set of connected faces which enclose the

coordinates in step 1).

An alpha shapes radius of 40 is recommended. Since the radius depends on sampling size and

distribution, other values may be optimal for a given data set. Alpha shapes may generate an error

depending on the chosen radius.

NOTE The face list returned by the alpha shapes method will be different from that obtained by the

procedure in 4.4.3 and 4.4.4, but the volume calculated from these data according to Clause 5 has been found to

be in good agreement. See Reference [2] for more details.
5 Computing the volume of a colour reproduction gamut
5.1 General
The volume of colour reproduction gamuts shall be defined as follows.
5.2 Volume of a single gamut
5.2.1 Volume calculation
The gamut volume shall be calculated as shown below.

1) Define a point at the approximate centre of the gamut volume, whose CIELAB coordinates are the

average of the coordinates of the white and black point of the gamut.

2) Add this point to the set of points defining each gamut face to form a set of tetrahedra spanning the

gamut volume.

3) For each tetrahedron in turn, let the four vertices be p , p , and p (corresponding to the planar face

1 2 3

on the gamut boundary) and p (the approximate gamut centroid), as shown in Figure 2. If each

vertex p , etc is represented by its CIELAB L*, a* and b* coordinates, the (signed) volume of each

tetrahedron should then be computed using the scalar triple product shown in Formula (1):

 
ab⋅×c
V =− (1)
where
ap=−p
bp=−p
cp=−p
The ‘·’ and ‘ × ’ symbols denote dot product and cross product, respectively.
4) Sum the volumes of all the tetrahedra to obtain the total gamut volume.
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Key
1 gamut face p , p , p viewed from outside
1 2 3
2 fixed point p at approximate gamut centre

Figure 2 — Tetrahedron formed from single gamut face defined by vertices p and fixed point

1-3

NOTE 1 The sign of the scalar triple product in Formula (1) depends on the winding order of the planar face,

and in the clock-wise order defined, as shown in Figure 2, it is negative.

NOTE 2 If the scalar triple product is positive for a given tetrahedron, this might indicate a "fold" in the colour

gamut. See Annex C for more details.

The volume shall be reported as the number of "cubic CIELAB units", i.e. the number of hexahedra with

sides of 1,0 in the dimensions of CIELAB L*, a* and b*.
5.2.2 Verifying the volume calculation

If the conditions in 4.2 are met, the procedure in 5.2.1 will result in an accurate estimate of the gamut

volume. An additional check can be performed by computing the solid angle of each tetrahedron and

summing them. If the faces of the gamut surface correctly enclose the volume, the resulting value will

be equal to the solid angle of a sphere, i.e. 4π steradians.

NOTE A method of calculating the solid angle of a tetrahedron is given in Reference [6].

For guidance, the gamut volumes calculated from a set of reference profiles is provided in Annex B. This

can be used to verify the correctness of the procedure used.

In practice it can be difficult to satisfy the conditions in 4.2 for every face in a gamut. It is recommended

that the total solid angle is reported with the estimated volume. The volume associated with the number

of incorrect
...

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