Graphic technology and photography -- Colour characterization of digital still cameras (DSCs)

This document describes sample methods to generate spectra for colour targets comprised of highly saturated colours for colour characteristic evaluation of colorimetric image capture capability of digital still cameras (DSCs).

Technologie graphique et photographie -- Caractérisation de la couleur des appareils photonumériques

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TECHNICAL ISO/TR
REPORT 17321-5
First edition
2021-01
Graphic technology and
photography — Colour
characterization of digital still
cameras (DSCs) —
Part 5:
Colour targets including saturated
colours for colour characteristic
evaluation test for colorimetric
image capture
Technologie graphique et photographie — Caractérisation de la
couleur des appareils photonumériques —
Partie 5: Cibles de couleurs incluant des couleurs saturées pour l’essai
d’évaluation des caractéristiques chromatiques pour la capture
d’images en mode colorimétrique
Reference number
ISO/TR 17321-5:2021(E)
ISO 2021
---------------------- Page: 1 ----------------------
ISO/TR 17321-5:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021

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
ii © ISO 2021 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TR 17321-5:2021(E)
Contents Page

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

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

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

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

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

4 Highly-saturated colour targets ............................................................................................................................................................ 2

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

4.2 Extension of real existing spectra using eigenvector method ........................................................................ 2

4.2.1 General...................................................................................................................................................................................... 2

4.2.2 Selection of spectra database ................................................................................................................................ 2

4.2.3 Spectral reconstruction from the eigenvectors ..................................................................................... 3

4.3 Artificial (LED-based) spectra whose wavelength peak is on colour-difference-

sensitive wavelength (CDSW) .................................................................................................................................................... 4

4.3.1 General...................................................................................................................................................................................... 4

4.3.2 The method to define the colour-difference-sensitive wavelength (CDSW) ................ 4

4.3.3 Selection of LED for CDSW targets ................................................................................................................... 6

5 FOM metric for evaluation of overall sensor spectral sensitivities, used in the digital

cameras .......................................................................................................................................................................................................................... 8

5.1 General ........................................................................................................................................................................................................... 8

5.2 Evaluation metrics for OSSS ........................................................................................................................................................ 8

5.3 Advantages and disadvantages of ΔE (deltaE) evaluation ................................................................................. 9

5.4 How 17321-5 datasets can be used for FOMs..............................................................................................................9

5.5 Worked examples ..............................................................................................................................................................................11

Annex A (informative) Selection and eigenvectors of spectral distribution set ...................................................13

Annex B (informative) Colour gamut of boundary colour ...........................................................................................................15

Annex C (informative) Worked example for spectral distribution generation of Pointer’s

surface colours ....................................................................................................................................................................................................16

Annex D (informative) Background information for defining CDSW ..............................................................................26

Annex E (informative) Additional 410nm to colour-difference-sensitive wavelengths (CDSW) ........29

Annex F (informative) Colour differences of patches of CDSW target.............................................................................30

Annex G (informative) Spectral distribution of CDSW target for ITU-R BT.2020 ................................................31

Annex H (informative) Spectral distribution dataset for users to download ..........................................................34

Bibliography .............................................................................................................................................................................................................................35

© ISO 2021 – All rights reserved iii
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ISO/TR 17321-5:2021(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 42, Photography.
A list of all parts in the ISO 17321 series can be found on the ISO website.
iv © ISO 2021 – All rights reserved
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ISO/TR 17321-5:2021(E)
Introduction

There are many application areas such as medical imaging, cosmetics, e-commerce, sales catalogue,

fine art reproduction, art archive etc. where colorimetric image capture and colorimetric image

reproduction are desired. When precise colorimetric reproduction is required for the subjects that

include highly-saturated colours, it is desirable that overall sensor spectral sensitivities are close to

linear combinations of CIE 1931 colour matching functions.

On the other hand, real DSCs have overall sensor spectral sensitivities that deviates from linear

combination of CIE 1931 colour matching functions, and yet reproduces reasonable colours for general

low-saturated colour objects. This is because most of spectral distribution of real-existing objects are

well self-correlated in the wavelength direction. This is also true for the frequently-used colour target

such as X-rite colour checker classic.

Therefore, when the precise colour reproduction is required for highly-saturated colour objects, it is

important to use spectral distribution that are less self-correlated in the wavelength direction, for the

evaluation of overall sensor spectral sensitivities.

For this purpose, Clause 3 proposes two methods for generating highly-saturated colour targets. The

first method is statistical extension of existing objects spectra, and the second one is selection from

artificial (LED-based) spectra.

Clause 4 then describes how these highly-saturated colour targets can be used for goodness evaluation

of overall sensor spectral sensitivities. Applicability of several existing evaluation metrics (such as

Voraʼs μ-factor and Sharmaʼs FOM) are compared, using highly-saturated targets generated by the

methods proposed in Clause 4.

Annex B gives details on colour gamut of boundary colour and Annex F gives more information on

colour differences of patches of CDSW target.
© ISO 2021 – All rights reserved v
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TECHNICAL REPORT ISO/TR 17321-5:2021(E)
Graphic technology and photography — Colour
characterization of digital still cameras (DSCs) —
Part 5:
Colour targets including saturated colours for colour
characteristic evaluation test for colorimetric image capture
1 Scope

This document describes sample methods to generate spectra for colour targets comprised of highly

saturated colours for colour characteristic evaluation of colorimetric image capture capability of digital

still cameras (DSCs).
2 Normative references
There are no normative references in this document.
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 http:// www .electropedia .org/
3.1
colour-difference-sensitive wavelength
CDSW
wavelength sensitive to colour difference
3.2
colour matching functions
tristimulus values of monochromatic stimuli of equal radiant power
[SOURCE: CIE Publication 17.4, 845-03-23]
3.3
digital still camera
DSC

device which incorporates an image sensor and produces a digital signal representing a still picture

[SOURCE: ISO 12232:2012, 3.40, modified — Notes 1 and 2 to entry have been deleted.]

3.4
light-emitting diode
LED

semiconductor diode that emits non coherent optical radiation through stimulated emission resulting

from the recombination of electrons and photons, when excited by an electric current

[SOURCE: IEC 60050-521, 521-04-39]
© ISO 2021 – All rights reserved 1
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ISO/TR 17321-5:2021(E)
3.5
overall sensor spectral sensitivities
OSSS

spectral sensitivities of overall sensor components, which could be derived as spectral sensitivities’

product of optical elements (including IR/UV-cut filter), colour filter sets, and image sensor

3.6
tristimulus values

amounts of the three reference colour stimuli, in a given trichromatic system, required to match the

colour of the stimulus considered. (see colour matching functions)
[SOURCE: CIE Publication 17.4, 845-03-22]
4 Highly-saturated colour targets
4.1 General

This document proposes two different methods for generating highly-saturated colour targets.

First one is “Extension of real existing spectra using an eigenvector method”. Naturally existing

saturated colour spectra are usually very difficult to obtain by measurement. Therefore, computed

spectra are extended from the eigenvectors generated from spectral databases.

Second one is “Artificial (LED-based) spectra whose wavelength peak is on colour-difference-sensitive

wavelength (CDSW)”. Mathematical analysis was performed to select the wavelengths which were

colour-difference-sensitive. Artificial (LED-based) spectra were then generated whose peak matches

colour-difference-sensitive wavelength (CDSW).
4.2 Extension of real existing spectra using eigenvector method
4.2.1 General

The eigenvector-based procedure for generating highly-saturated colour targets is as follows:

— selection of spectral database (see 4.2.2);
— spectral reconstruction from the eigenvectors (see 4.2.3);
— calculation of boundary colours (see 4.2.3.2);

— calculation of saturated-colours using reference spectral distribution (see 4.2.3.3).

4.2.2 Selection of spectra database
[7]

The wavelength range and wavelength increment are user-definable. ISO 17321-1 described that

the wavelength range is 380 nm to 730 nm with a sampling interval of 10 nm or less. The spectral

distribution set selected depends on user’s application.

The brightness level of the spectral distribution selected can be ignored because the brightness level

is tuneable by scaling the eigenvectors used for spectral distribution reconstruction. Hue angle of the

selected spectral distribution is very important and the use of evenly-spaced hue angle is recommended.

An example of the eigenvector sets (E ) is calculated on the selected spectral distribution set (described

in Annex A).
2 © ISO 2021 – All rights reserved
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ISO/TR 17321-5:2021(E)
4.2.3 Spectral reconstruction from the eigenvectors
4.2.3.1 General

Spectra from the original dataset using Formula 1 can be computed as linear combination of

eigenvectors.
The following notation is used for this example:
M : number of wavelengths to be used,
N : number of eigenvectors to be used,
Ε : i-th wavelength component of the j-th eigenvector (i = 1, M; j = 1, N),
w : weight of j-th eigenvector ( j = 1, N),
r : i-th wavelength component of a spectrum (i = 1, M).
rw= ⋅E (1)
i jij
j =1

Conversely, the weights required to reconstruct a reflectance spectrum from the dataset are a linear

combination of the reflectance spectrum and the eigenvectors:
wr= ⋅E (2)
j iij
i = 1
Two cases are considered here:

a) The boundary colour case determines the set of spectra that represent the chromatic limit as a

function of hue maximally achievable based on the fundamental characteristics of an underlying

spectral dataset where the resulting spectra are linear combinations of a subset of selected dataset

eigenvectors.

b) The saturated colour case produces arbitrary highly saturated spectra from a linear combination of

a subset of selected eigenvectors of a spectral dataset even though the target spectra are not from

the dataset from which the eigenvectors are computed and therefore will only be an approximate

match to the target spectra.

Both use Formula (1) but have different constraint conditions for the optimization process.

4.2.3.2 Boundary colour generation

Boundary colours are those colours whose spectral distributions have maximum chroma for a given

hue angle.

There are numerous ways to identify which spectral reflectance vectors r have to be selected. The

simplest method is to index through all weights w at a reasonable increment to produce a large set of

r , compute the resulting hue and chroma values for the set of r , then select the subset of r that yields

i i i
maximum chroma for each hue angle of interest.

However, it is preferred to recast Formula (1) so that it can be constrained for maximum chroma, hue

angle, smoothness, or other conditions that are suitable for the intended application and to use general-

purpose numerical optimization methods to solve for the optimal weights w directly. The resulting

spectral reflectance vector r is constrained to the range [0,0,1.0]. Annex H describes those spectral

distributions.
© ISO 2021 – All rights reserved 3
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ISO/TR 17321-5:2021(E)
4.2.3.3 Saturated-colour generation using the reference spectra distribution set

It is possible to approximate an arbitrary target spectrum r using the eigenvectors of a spectral dataset,

even if the target spectrum does not share the same fundamentals as the reference spectral dataset

from which the eigenvectors were derived. This approximation r’ is the least-squares match to the

target spectrum r, typically subject to constraints.

For instance, it is possible to calculate highly saturated colour target spectra r’ having a C* value larger

than a reference spectrum while maintaining L* and hue angle. This C* for each reference colour target

is determined prior to nonlinear optimization described in Annex C. Objective parameter for nonlinear

optimization is to keep predetermined C*. Annex C shows an example in the case of Pointer’s surface

colours. There are many metamers of the candidate spectrum and users need to select the appropriate

spectrum from many metamers. This step is applicable to other cases where any reference distribution

and its objective chromaticity are given.

Annex C shows a generation method which calculates spectral distribution corresponding to CIELAB

[6]

values of Pointer’s surface colour . Annex H describes those spectral distributions.

Given an arbitrary highly saturated target spectrum r, the goal is to produce an approximate match r’

from a selected subset of the eigenvectors of the reference spectral dataset. However, there are many

possible candidate matches r’ depending on the initial w selected for the optimization process. One

approach is to compute the starting weights for nonlinear numerical optimization with Formula 2. The

weights w are substituted into Formula 1 producing an approximate match r’ and w is iterated until the

error between r’ and r is minimized. Using generalized numerical optimization, this method calculates

w to minimize the sum of the squares of the differences between the closest matching spectrum

achievable r’ by the selected eigenvector subset.

4.3 Artificial (LED-based) spectra whose wavelength peak is on colour-difference-

sensitive wavelength (CDSW)
4.3.1 General

The wavelength range for colour target spectra for camera uses is from 380 nm to 730 nm according to

ISO 17321-1.

The CDSW-based procedure for generating highly-saturated colour targets is as follows:

— The method to define CDSW (See 4.3.2)
— Selection of CDSW (See 4.3.3)
4.3.2 The method to define the colour-difference-sensitive wavelength (CDSW)

Factors of colour difference, Fac_a* and Fac_b* are defined based on the colour matching functions as

shown in Formulae (3) and (4). Fac_a* and Fac_b* are function of X and Z, respectively. The reasons and

the processes of deriving Fac_a* and Fac_b* are described in Annex D.
  x λ  
() 16
 
Faca_ λ =×500 f − (3)
 
()  
 
Xn 116
 
   
  z λ  
 
Facb_ λ =×200 f − (4)
()  
 
 
Zn 116
 
   
where
4 © ISO 2021 – All rights reserved
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ISO/TR 17321-5:2021(E)
 
t> 0,008856
 
t ,
f (t)=
 
t≤ 0,008856
 
7,,787×+t 0 138.
 
Xn=0,9504, Zn=1,0889
Faca__λΔ+ −Faca λ
() ()
Diff Fac_a λ = (5)
Facb__λΔ+ −Facb λ
() ()
Diff Fac_b λ = (6)

Calculated values of the factors are drawn against wavelength in Figure 1. It can be said that the

wavelength where the colour difference between the colour matching functions and the camera is most

likely to be the maximum and peak wavelength of the slope of the waveform in Figure 1. Wavelength

ranges where the Δa* and Δb* have peak values are very similar to those of the maximum, minimum

and inflection points of the curves of the factors.

In order to find those points, the derivatives of Fac_a* and Fac_b* with wavelength as shown in

Formulae (5) and (6) are calculated (Figure 2). Wavelengths at which large colour differences most

likely appear are determined by the points where the derivative is maximum, minimum and crosses

zero from plus to minus and vice versa. Wavelengths corresponding to those points are 420 nm, 440 nm,

480 nm, 500 nm, 505 nm, 510 nm, 600 nm and 650 nm. These wavelengths are listed Table 1 and also

indicated in Figure 2.

NOTE The reasons why we use the wavelength where the derivative is maximum, minimum and zero are

as follows. The optimization process to obtain conversion matrix from camera sensitivity to colour matching

function was carried out using the least square method to minimize ∆S. In the process, each one of transformed

XYZ functions is adjusted to one of the matching functions by increasing (decreasing) intensity at peak wavelength

where the derivative is zero, and simultaneously decreasing (increasing) it at steep slope’s wavelength where the

derivative is maximum or minimum. Therefore, at wavelengths where derivative is maximum, minimum and

zero, colour differences can often appear.
Key
X wavelength, λ, in nm
Figure 1 — Fac_a* and Fac_b*plot against wavelength
© ISO 2021 – All rights reserved 5
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ISO/TR 17321-5:2021(E)
Key
X wavelength, λ, in nm
Figure 2 — Differentiated values of Fac_a* and Fac_b*

Wavelengths of 500 nm, 505 nm and 510 nm are very close to each other and their effect on colour

difference is similar and so the wavelength of 505 nm is chosen to represent these three wavelengths.

Table 1 — Candidate of CDSW corresponding to maximum, minimum and zero of derivative

↗,↘ and →signs in Table 1 mean “increase”, “decrease” and “no change” respectively.

Based on this analysis, wavelengths of 420 nm, 440 nm, 480 nm, 505 nm, 600 nm and 650 nm are

selected as the colour-difference-sensitive wavelengths (CDSW).
4.3.3 Selection of LED for CDSW targets

In the next step, the spectral distribution of highly saturated colour target will be specified based

on CDSWs.

It is ideal for CDSW target to use laser devices. However considering availability at this time, LEDs are

recommended and may be more practical. Appropriate devices in accordance with technology progress

in future will be adopted.
It is recommended that LEDs used for CDSW targets have the following conditions.

— Use existing LEDs which has the peak wavelength of LEDs is within +- 3 nm of CDSWs,

— Or Find similar LEDs with the peak wavelength defined by CDSW (peak does not have to be exact).

— Find LED-like width and generate the spectra artificially.
6 © ISO 2021 – All rights reserved
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ISO/TR 17321-5:2021(E)

NOTE LED-like width is easily found because it is naturally determined according to LED’s materials and

structures at around the CDSWs.
— The shape of the spectrum is that of Gaussian distribution.
— The LEDs don’t have any phosphors,
— The LEDs have no side peaks.

Figure 3 shows spectral distribution of the LEDs which are selected under above conditions.

In Figure 3, a set of realisable spectral distributions are shown corresponding to the six CDSWs.

The six-colour patches are named ‘CDSW target’. Spectral values for the colours of these patches are

listed in Table H.1.

For reader relevance, calculated chromaticities of the six highly saturated colours and their

chromaticities as captured (and estimated) by camera A and camera B are also plotted in Figure F.1.

In addition to these CDSW targets, the colour differences are equally large for wavelengths around

410 nm on several cameras when colour difference analysis is carried out as described in Annex E.

Therefore, 410 nm wavelength can be added to CDSW targets in place of 420nm wave length depending

on user’s application.
Key
X wavelength, λ, in nm
Y relative intensity
Figure 3 — Spectral distribution of each patch of CDSW target

In 2018, very wide gamut broadcast service, ITU-R BT.2020, were launched. It is very useful to show

how to use CDSW targets in practice by applying to the specific system.

Annex G describes a method to define a highly saturated colour target for cameras designed to capture

specific RGB colour spaces. When the destination RGB of a camera is fixed, the method for creating

[5]

highly saturated colour target is explained using the ITU-R BT.2020 standard as an example.

© ISO 2021 – All rights reserved 7
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ISO/TR 17321-5:2021(E)

5 FOM metric for evaluation of overall sensor spectral sensitivities, used in the

digital cameras
5.1 General

This clause provides how the highly-saturated colour targets can be used for evaluation for overall

sensor spectral sensitivities (hereafter abbreviated as OSSS), which are described in 4.2 (Extension

of real existing spectra using the eigenvectors method) and 4.3 [Artificial (LED-based) spectra whose

wavelength peak is on Colour-difference-sensitive wavelength (CDSW)].
5.2 Evaluation metrics for OSSS

There has been many evaluation metrics for evaluating the goodness of OSSS, such as Neugebauer's

[2] [1] [4]

Q-factor , Vora’s μ-factor and Sharma’s FOM. . If the colour filter set is perfect linear combination

of CMF (colour matching function), the value of these metrics becomes 1.00, and the value decreases as

the linear combination of the OSSS deviates from CMF.

NOTE Q-factor metric evaluates sensor colour filter one by one, not as a filter set.

However, OSSS with low (i.e. bad) μ-factor could sometimes have good colour reproduction. This is

because μ-factor does not consider the reflectance spectra of the target subjects at all. The distinguished

difference of FOM metric to other two metrics is the consideration of reflectance spectra. Following

formula indicates simplified version of FOM, and it is called FOM in this document. The K correlation

S r

matrix is used in the metric, which describes the characteristics of the reflectance spectra r.

 
TT T
tr AK⋅⋅GG⋅⋅KG⋅⋅GK⋅⋅A
 
rr r
 
FOM AG,,K = (7)
S r
tr AK⋅⋅A
(()
   
rr rr
1,,400 n 400 1,,400 1 700
   
 
where Kr=EE⋅r =    ⋅   
{}  
   
 
rr rr
   
 
1,,700 n 700 nn,,400 700
   
— A is the N x 3 matrix of CIE colour matching functions (CMF).
— G is the N x 3 matrix of OSSS.
— K is the N x N correlation matrix defined by above formula.

— r is the reflectance spectra (400 nm to 700 nm, 10 nm interval, was used in this case).

[4]

While the original FOM paper by Sharma describes many variations for the FOM metric, “Type A:

XYZ mean-square-error-based FOM” was chosen for its calculation simplicity in this case. Several

additional simplifications were applied to the original FOM definition. First, K term which describes

measurement noise, was ignored. Since the noise is produced by the image sensor and electronic

circuits, this can be considered irrelevant to the evaluation of OSSS characteristics. Second, illuminant

consideration was ignored. In the Sharma’s paper, since its target was colour scanners, the product of

illuminant spectra and colour filter spectra was used as A . For the digital cameras, since the illuminant

cannot be predefined, the product with illuminant was not used.
8 © ISO 2021 – All rights reserved
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ISO/TR 17321-5:2021(E)

When K becomes unity matrix E, which means that there is no correlation for reflectance spectra (in

the wavelength direction), FOM is reduced very close to the μ-factor as below, except that μ-factor uses

orthonormal space for CMF (colour matching functions).
 
TT T
trA ⋅⋅GG ⋅⋅GG ⋅A
 
 
FOMEAG,,K = = (8)
S r
trA ⋅A

Since FOM includes K term, the metric correlates well with average ΔE (deltaE) of the colour target

S r

set. This is large advantage for FOM over μ-factor, since the metric correlates very well with the colour

reprodu
...

TECHNICAL ISO/TR
REPORT 17321-5
First edition
Graphic technology and
photography — Colour
characterization of digital still
cameras (DSCs) —
Part 5:
Colour targets including saturated
colours for colour characteristic
evaluation test for colorimetric
image capture
Technologie graphique et photographie — Caractérisation de la
couleur des appareils photonumériques —
Partie 5: Cibles de couleurs incluant des couleurs saturées pour l’essai
d’évaluation des caractéristiques chromatiques pour la capture
d’images en mode colorimétrique
PROOF/ÉPREUVE
Reference number
ISO/TR 17321-5:2020(E)
ISO 2020
---------------------- Page: 1 ----------------------
ISO/TR 17321-5:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2020

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
ii PROOF/ÉPREUVE © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TR 17321-5:2020(E)
Contents Page

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

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

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

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

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

4 Highly-saturated colour targets ............................................................................................................................................................ 2

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

4.2 Extension of real existing spectra using eigenvector method ........................................................................ 2

4.2.1 General...................................................................................................................................................................................... 2

4.2.2 Selection of spectra database ................................................................................................................................ 2

4.2.3 Spectral reconstruction from the eigenvectors ..................................................................................... 3

4.3 Artificial (LED-based) spectra whose wavelength peak is on colour-difference-

sensitive wavelength (CDSW) .................................................................................................................................................... 4

4.3.1 General...................................................................................................................................................................................... 4

4.3.2 The method to define the colour-difference-sensitive wavelength (CDSW) ................ 4

4.3.3 Selection of LED for CDSW targets ................................................................................................................... 6

5 FOM metric for evaluation of overall sensor spectral sensitivities, used in the digital

cameras .......................................................................................................................................................................................................................... 7

5.1 General ........................................................................................................................................................................................................... 7

5.2 Evaluation metrics for OSSS ........................................................................................................................................................ 8

5.3 Advantages and disadvantages of ΔE (deltaE) evaluation ................................................................................. 8

5.4 How 17321-5 datasets can be used for FOMs..............................................................................................................9

5.5 Worked examples ..............................................................................................................................................................................11

Annex A (informative) Selection and eigenvectors of spectral distribution set ...................................................13

Annex B (informative) Colour gamut of boundary colour ...........................................................................................................15

Annex C (informative) Worked example for spectral distribution generation of Pointer’s

surface colours ....................................................................................................................................................................................................16

Annex D (informative) Background information for defining CDSW ..............................................................................26

Annex E (informative) Additional 410nm to colour-difference-sensitive wavelengths (CDSW) ........29

Annex F (informative) Colour differences of patches of CDSW target.............................................................................30

Annex G (informative) Spectral distribution of CDSW target for ITU-R BT.2020 ................................................31

Annex H (informative) Spectral distribution dataset for users to download ..........................................................34

Bibliography .............................................................................................................................................................................................................................35

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ISO/TR 17321-5:2020(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 42, Photography.
A list of all parts in the ISO 17321 series can be found on the ISO website.
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ISO/TR 17321-5:2020(E)
Introduction

There are many application areas such as medical imaging, cosmetics, e-commerce, sales catalogue,

fine art reproduction, art archive etc. where colorimetric image capture and colorimetric image

reproduction are desired. When precise colorimetric reproduction is required for the subjects that

include highly-saturated colours, it is desirable that overall sensor spectral sensitivities are close to

linear combinations of CIE 1931 colour matching functions.

On the other hand, real DSCs have overall sensor spectral sensitivities that deviates from linear

combination of CIE 1931 colour matching functions, and yet reproduces reasonable colours for general

low-saturated colour objects. This is because most of spectral distribution of real-existing objects are

well self-correlated in the wavelength direction. This is also true for the frequently-used colour target

such as X-rite colour checker classic.

Therefore, when the precise colour reproduction is required for highly-saturated colour objects, it is

important to use spectral distribution that are less self-correlated in the wavelength direction, for the

evaluation of overall sensor spectral sensitivities.

For this purpose, Clause 3 proposes two methods for generating highly-saturated colour targets. The

first method is statistical extension of existing objects spectra, and the second one is selection from

artificial (LED-based) spectra.

Clause 4 then describes how these highly-saturated colour targets can be used for goodness evaluation

of overall sensor spectral sensitivities. Applicability of several existing evaluation metrics (such as

Voraʼs μ-factor and Sharmaʼs FOM) are compared, using highly-saturated targets generated by the

methods proposed in Clause 4.

Annex B gives details on colour gamut of boundary colour and Annex F gives more information on

colour differences of patches of CDSW target.
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TECHNICAL REPORT ISO/TR 17321-5:2020(E)
Graphic technology and photography — Colour
characterization of digital still cameras (DSCs) —
Part 5:
Colour targets including saturated colours for colour
characteristic evaluation test for colorimetric image capture
1 Scope

This document describes sample methods to generate spectra for colour targets comprised of highly

saturated colours for colour characteristic evaluation of colorimetric image capture capability of digital

still cameras (DSCs).
2 Normative references
There are no normative references in this document.
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 http:// www .electropedia .org/
3.1
colour-difference-sensitive wavelength
CDSW
wavelength sensitive to colour difference
3.2
colour matching functions
tristimulus values of monochromatic stimuli of equal radiant power
[SOURCE: CIE Publication 17.4, 845-03-23]
3.3
digital still camera
DSC

device which incorporates an image sensor and produces a digital signal representing a still picture

[SOURCE: ISO 12232:2012, 3.40, modified — Notes 1 and 2 to entry have been deleted.]

3.4
light-emitting diode
LED

semiconductor diode that emits non coherent optical radiation through stimulated emission resulting

from the recombination of electrons and photons, when excited by an electric current

[SOURCE: IEC 60050-521, 521-04-39]
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ISO/TR 17321-5:2020(E)
3.5
overall sensor spectral sensitivities
OSSS

spectral sensitivities of overall sensor components, which could be derived as spectral sensitivities’

product of optical elements (including IR/UV-cut filter), colour filter sets, and image sensor

3.6
tristimulus values

amounts of the three reference colour stimuli, in a given trichromatic system, required to match the

colour of the stimulus considered. (see colour matching functions)
[SOURCE: CIE Publication 17.4, 845-03-22]
4 Highly-saturated colour targets
4.1 General

This document proposes two different methods for generating highly-saturated colour targets.

First one is “Extension of real existing spectra using an eigenvector method”. Naturally existing

saturated colour spectra are usually very difficult to obtain by measurement. Therefore, computed

spectra are extended from the eigenvectors generated from spectral databases.

Second one is “Artificial (LED-based) spectra whose wavelength peak is on colour-difference-sensitive

wavelength (CDSW)”. Mathematical analysis was performed to select the wavelengths which were

colour-difference-sensitive. Artificial (LED-based) spectra were then generated whose peak matches

colour-difference-sensitive wavelength (CDSW).
4.2 Extension of real existing spectra using eigenvector method
4.2.1 General

The eigenvector-based procedure for generating highly-saturated colour targets is as follows:

— selection of spectral database (see 4.2.2);
— spectral reconstruction from the eigenvectors (see 4.2.3);
— calculation of boundary colours (see 4.2.3.2);

— calculation of saturated-colours using reference spectral distribution (see 4.2.3.3).

4.2.2 Selection of spectra database
[7]

The wavelength range and wavelength increment are user-definable. ISO 17321-1 described that

the wavelength range is 380 nm to 730 nm with a sampling interval of 10 nm or less. The spectral

distribution set selected depends on user’s application.

The brightness level of the spectral distribution selected can be ignored because the brightness level

is tuneable by scaling the eigenvectors used for spectral distribution reconstruction. Hue angle of the

selected spectral distribution is very important and the use of evenly-spaced hue angle is recommended.

An example of the eigenvector sets (E ) is calculated on the selected spectral distribution set (described

in Annex A).
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4.2.3 Spectral reconstruction from the eigenvectors
4.2.3.1 General

Spectra from the original dataset using Formula 1 can be computed as linear combination of

eigenvectors.
The following notation is used for this example:
M : number of wavelengths to be used,
N : number of eigenvectors to be used,
Ε : i-th wavelength component of the j-th eigenvector (i = 1, M; j = 1, N),
w : weight of j-th eigenvector ( j = 1, N),
r : i-th wavelength component of a spectrum (i = 1, M).
rw= ⋅E (1)
i jij
j =1

Conversely, the weights required to reconstruct a reflectance spectrum from the dataset are a linear

combination of the reflectance spectrum and the eigenvectors:
wr= ⋅E (2)
j iij
i = 1
Two cases are considered here:

a) The boundary colour case determines the set of spectra that represent the chromatic limit as a

function of hue maximally achievable based on the fundamental characteristics of an underlying

spectral dataset where the resulting spectra are linear combinations of a subset of selected dataset

eigenvectors.

b) The saturated colour case produces arbitrary highly saturated spectra from a linear combination of

a subset of selected eigenvectors of a spectral dataset even though the target spectra are not from

the dataset from which the eigenvectors are computed and therefore will only be an approximate

match to the target spectra.

Both use Formula (1) but have different constraint conditions for the optimization process.

4.2.3.2 Boundary colour generation

Boundary colours are those colours whose spectral distributions have maximum chroma for a given

hue angle.

There are numerous ways to identify which spectral reflectance vectors r have to be selected. The

simplest method is to index through all weights w at a reasonable increment to produce a large set of

r , compute the resulting hue and chroma values for the set of r , then select the subset of r that yields

i i i
maximum chroma for each hue angle of interest.

However, it is preferred to recast Formula (1) so that it can be constrained for maximum chroma, hue

angle, smoothness, or other conditions that are suitable for the intended application and to use general-

purpose numerical optimization methods to solve for the optimal weights w directly. The resulting

spectral reflectance vector r is constrained to the range [0,0,1.0]. Annex H describes those spectral

distributions.
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4.2.3.3 Saturated-colour generation using the reference spectra distribution set

It is possible to approximate an arbitrary target spectrum r using the eigenvectors of a spectral dataset,

even if the target spectrum does not share the same fundamentals as the reference spectral dataset

from which the eigenvectors were derived. This approximation r’ is the least-squares match to the

target spectrum r, typically subject to constraints.

For instance, it is possible to calculate highly saturated colour target spectra r’ having a C* value larger

than a reference spectrum while maintaining L* and hue angle. This C* for each reference colour target

is determined prior to nonlinear optimization described in Annex C. Objective parameter for nonlinear

optimization is to keep predetermined C*. Annex C shows an example in the case of Pointer’s surface

colours. There are many metamers of the candidate spectrum and users need to select the appropriate

spectrum from many metamers. This step is applicable to other cases where any reference distribution

and its objective chromaticity are given.

Annex C shows a generation method which calculates spectral distribution corresponding to CIELAB

[6]

values of Pointer’s surface colour . Annex H describes those spectral distributions.

Given an arbitrary highly saturated target spectrum r, the goal is to produce an approximate match r’

from a selected subset of the eigenvectors of the reference spectral dataset. However, there are many

possible candidate matches r’ depending on the initial w selected for the optimization process. One

approach is to compute the starting weights for nonlinear numerical optimization with Formula 2. The

weights w are substituted into Formula 1 producing an approximate match r’ and w is iterated until the

error between r’ and r is minimized. Using generalized numerical optimization, this method calculates

w to minimize the sum of the squares of the differences between the closest matching spectrum

achievable r’ by the selected eigenvector subset.

4.3 Artificial (LED-based) spectra whose wavelength peak is on colour-difference-

sensitive wavelength (CDSW)
4.3.1 General

The wavelength range for colour target spectra for camera uses is from 380 nm to 730 nm according to

ISO 17321-1.

The CDSW-based procedure for generating highly-saturated colour targets is as follows:

— The method to define CDSW (See 4.3.2)
— Selection of CDSW (See 4.3.3)
4.3.2 The method to define the colour-difference-sensitive wavelength (CDSW)

Factors of colour difference, Fac_a* and Fac_b* are defined based on the colour matching functions as

shown in Formulae (3) and (4). Fac_a* and Fac_b* are function of X and Z, respectively. The reasons and

the processes of deriving Fac_a* and Fac_b* are described in Annex D.
  x λ  
() 16
 
Faca_ λ =×500 f − (3)
 
()  
 
Xn 116
 
   
  ~ λ  
 
Facb_ λ =×200 f − (4)
()  
 
 
Zn 116
 
   
where
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ISO/TR 17321-5:2020(E)
 
t> 0,008856
 
t ,
f (t)=
 
t< 0,008856
 
7,,787×+t 0 138.
 
Xn=0,9504, Zn=1,0889
Faca__λΔ+ −Faca λ
() ()
Diff Fac_a λ = (5)
Facb__λΔ+ −Facb λ
() ()
Diff Fac_b λ = (6)

Calculated values of the factors are drawn against wavelength in Figure 1. It can be said that the

wavelength where the colour difference between the colour matching functions and the camera is most

likely to be the maximum and peak wavelength of the slope of the waveform in Figure 1. Wavelength

ranges where the Δa* and Δb* have peak values are very similar to those of the maximum, minimum

and inflection points of the curves of the factors.

In order to find those points, the derivatives of Fac_a* and Fac_b* with wavelength as shown in

Formulae (5) and (6) are calculated (Figure 2). Wavelengths at which large colour differences most

likely appear are determined by the points where the derivative is maximum, minimum and crosses

zero from plus to minus and vice versa. Wavelengths corresponding to those points are 420 nm, 440 nm,

480 nm, 500 nm, 505 nm, 510 nm, 600 nm and 650 nm. These wavelengths are listed Table 1 and also

indicated in Figure 2.

NOTE The reasons why we use the wavelength where the derivative is maximum, minimum and zero are

as follows. The optimization process to obtain conversion matrix from camera sensitivity to colour matching

function was carried out using the least square method to minimize ∆S. In the process, each one of transformed

XYZ functions is adjusted to one of the matching functions by increasing (decreasing) intensity at peak wavelength

where the derivative is zero, and simultaneously decreasing (increasing) it at steep slope’s wavelength where the

derivative is maximum or minimum. Therefore, at wavelengths where derivative is maximum, minimum and

zero, colour differences can often appear.
Figure 1 — Fac_a* and Fac_b*plot against wavelength
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ISO/TR 17321-5:2020(E)
Figure 2 — Differentiated values of Fac_a* and Fac_b*

Wavelengths of 500 nm, 505 nm and 510 nm are very close to each other and their effect on colour

difference is similar and so the wavelength of 505 nm is chosen to represent these three wavelengths.

Table 1 — Candidate of CDSW corresponding to maximum, minimum and zero of derivative

↗,↘ and →signs in Table 1 mean “increase”, “decrease” and “no change” respectively.

Based on this analysis, wavelengths of 420 nm, 440 nm, 480 nm, 505 nm, 600 nm and 650 nm are

selected as the colour-difference-sensitive wavelengths (CDSW).
4.3.3 Selection of LED for CDSW targets

In the next step, the spectral distribution of highly saturated colour target will be specified based

on CDSWs.

It is ideal for CDSW target to use laser devices. However considering availability at this time, LEDs are

recommended and may be more practical. Appropriate devices in accordance with technology progress

in future will be adopted.
It is recommended that LEDs used for CDSW targets have the following conditions.

— Use existing LEDs which has the peak wavelength of LEDs is within +- 3 nm of CDSWs,

— Or Find similar LEDs with the peak wavelength defined by CDSW (peak does not have to be exact).

— Find LED-like width and generate the spectra artificially.

NOTE LED-like width is easily found because it is naturally determined according to LED’s materials and

structures at around the CDSWs.
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ISO/TR 17321-5:2020(E)
— The shape of the spectrum is that of Gaussian distribution.
— The LEDs don’t have any phosphors,
— The LEDs have no side peaks.

Figure 3 shows spectral distribution of the LEDs which are selected under above conditions.

In Figure 3, a set of realisable spectral distributions are shown corresponding to the six CDSWs.

The six-colour patches are named ‘CDSW target’. Spectral values for the colours of these patches are

listed in Table H.1.

For reader relevance, calculated chromaticities of the six highly saturated colours and their

chromaticities as captured (and estimated) by camera A and camera B are also plotted in Figure F.1.

In addition to these CDSW targets, the colour differences are equally large for wavelengths around

410 nm on several cameras when colour difference analysis is carried out as described in Annex E.

Therefore, 410 nm wavelength can be added to CDSW targets in place of 420nm wave length depending

on user’s application.
Figure 3 — Spectral distribution of each patch of CDSW target

In 2018, very wide gamut broadcast service, ITU-R BT.2020, were launched. It is very useful to show

how to use CDSW targets in practice by applying to the specific system.

Annex G describes a method to define a highly saturated colour target for cameras designed to capture

specific RGB colour spaces. When the destination RGB of a camera is fixed, the method for creating

[5]

highly saturated colour target is explained using the ITU-R BT.2020 standard as an example.

5 FOM metric for evaluation of overall sensor spectral sensitivities, used in the

digital cameras
5.1 General

This clause provides how the highly-saturated colour targets can be used for evaluation for overall

sensor spectral sensitivities (hereafter abbreviated as OSSS), which are described in 4.2 (Extension

of real existing spectra using the eigenvectors method) and 4.3 [Artificial (LED-based) spectra whose

wavelength peak is on Colour-difference-sensitive wavelength (CDSW)].
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5.2 Evaluation metrics for OSSS

There has been many evaluation metrics for evaluating the goodness of OSSS, such as Neugebauers

[2] [1] [4]

Q-factor , Vora’s μ-factor and Sharma’s FOM. . If the colour filter set is perfect linear combination

of CMF (colour matching function), the value of these metrics becomes 1.00, and the value decreases as

the linear combination of the OSSS deviates from CMF.

NOTE Q-factor metric evaluates sensor colour filter one by one, not as a filter set.

However, OSSS with low (i.e. bad) μ-factor could sometimes have good colour reproduction. This is

because μ-factor does not consider the reflectance spectra of the target subjects at all. The distinguished

difference of FOM metric to other two metrics is the consideration of reflectance spectra. Following

formula indicates simplified version of FOM, and it is called FOM in this document. The K correlation

S r

matrix is used in the metric, which describes the characteristics of the reflectance spectra r.

 
T T T
tr AK⋅⋅GG⋅⋅KG⋅⋅GK⋅⋅A
 
r r r
 
FOMA,,GK = (7)
tr AK⋅⋅A
(()
   
rr rr
1,,400 n 400 1,,400 1 700
   
 
whereK =Er⋅rE=    ⋅   
{}  
   
 
rr rr
   
 
 1,,700 n 700  nn,,400 700
— A is the N x 3 matrix of CIE colour matching functions (CMF).
— G is the N x 3 matrix of OSSS.
— K is the N x N correlation matrix defined by above formula.

— r is the reflectance spectra (400 nm to 700 nm, 10 nm interval, was used in this case).

[4]

While the original FOM paper by Sharma describes many variations for the FOM metric, “Type A:

XYZ mean-square-error-based FOM” was chosen for its calculation simplicity in this case. Several

additional simplifications were applied to the original FOM definition. First, K term which describes

measurement noise, was ignored. Since the noise is produced by the image sensor and electronic

circuits, this can be considered irrelevant to the evaluation of OSSS characteristics. Second, illuminant

consideration was ignored. In the Sharma’s paper, since its target was colour scanners, the product of

illuminant spectra and colour filter spectra was used as A . For the digital cameras, since the illuminant

cannot be predefined, the product with illuminant was not used.

When K becomes unity matrix E, which means that there is no correlation for reflectance spectra (in

the wavelength direction), FOM is reduced very close to the μ-factor as below, except that μ-factor uses

orthonormal space for CMF (colour matching functions).
 
TT T
tr AG⋅⋅ GG⋅⋅GA⋅
 
 
FOMA,,GK =E = (8)
tr AA⋅

Since FOM includes K term, the metric correlates well with average ΔE (deltaE) of the colour target

S r

set. This is large advantage for FOM over μ-factor, since the metric correlates very well with the colour

reproduction, as written in the FOM paper.
5.3 Advantages and disadvantages of ΔE (delta
...

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