Representation of results of particle size analysis

ISO 9276-6:2008 specifies rules and nomenclature for the description and quantitative representation of particle shape and morphology. To achieve a more comprehensive description of a particle or particle system, particle size information can be used together with other information but, in most cases, the particle size information cannot be replaced. The averaging of shape over all particles in a sample has been shown to be an ineffective approach. Distributions of other particle characteristics are required in addition to particle size distributions (see ISO 9276‑1). The relevance, to technological applications, of any method of representing particle shape is the deciding factor in its use. Therefore this part of ISO 9276 is restricted to methods which can be correlated with physical properties in industrial applications. The aim of particle analysis is to determine the most appropriate characterization method for a particular application. This implies a profound understanding of the relationship between particle characteristics and macroscopic product and process properties (or at least a database of broad empirical data). Problems of shape and morphology would normally be three-dimensional problems, but most definitions in this part of ISO 9276 are in fact given for two dimensions because of the widespread use of image analysis methods.

Représentation de données obtenues par analyse granulométrique

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Published
Publication Date
08-Sep-2008
Current Stage
6060 - International Standard published
Start Date
15-Aug-2008
Completion Date
09-Sep-2008
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INTERNATIONAL ISO
STANDARD 9276-6
First edition
2008-09-15
Representation of results of particle size
analysis —
Part 6:
Descriptive and quantitative
representation of particle shape and
morphology
Représentation de données obtenues par analyse granulométrique —
Partie 6: Description et représentation quantitative de la forme et de la
morphologie des particules
Reference number
ISO 9276-6:2008(E)
ISO 2008
---------------------- Page: 1 ----------------------
ISO 9276-6:2008(E)
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...

INTERNATIONAL ISO
STANDARD 9276-6
First edition
2008-09-15
Representation of results of particle size
analysis —
Part 6:
Descriptive and quantitative
representation of particle shape and
morphology
Représentation de données obtenues par analyse granulométrique
Partie 6: Description et représentation quantitative de la forme et de la
morphologie des particules
Reference number
ISO 9276-6:2008(E)
ISO 2008
---------------------- Page: 1 ----------------------
ISO 9276-6:2008(E)
PDF disclaimer

This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but

shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In

downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat

accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.

Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation

parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In

the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.

COPYRIGHT PROTECTED DOCUMENT
© ISO 2008

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,

electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or

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Published in Switzerland
ii © ISO 2008 – All rights reserved
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ISO 9276-6:2008(E)
Contents Page

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

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

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

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

3 Symbols and abbreviated terms ..........................................................................................................2

4 Criteria for the evaluation of shape description methods ................................................................3

5 Classification of methods and descriptors.........................................................................................4

5.1 General classification ...........................................................................................................................4

5.2 Levels of shape......................................................................................................................................4

5.3 Principles for deriving shape descriptors ..........................................................................................6

6 Errors which can occur in the analysis of a single image ................................................................7

6.1 Generation of shape descriptors .........................................................................................................7

6.2 Image resolution....................................................................................................................................7

6.3 Binarization ............................................................................................................................................8

6.4 Algorithms for calculating shape descriptors....................................................................................8

7 Size parameters for normalization of shape descriptors ..................................................................9

8 Shape descriptors ...............................................................................................................................10

8.1 Macroshape descriptors .....................................................................................................................10

8.2 Mesoshape descriptors ......................................................................................................................12

8.3 Combination of shape descriptors ....................................................................................................13

8.4 Roughness descriptor ........................................................................................................................14

Annex A (normative) Some computation equations .....................................................................................15

Annex B (informative) Examples of methods of presentation of shape and size distribution data.........16

Bibliography......................................................................................................................................................22

© ISO 2008 – All rights reserved iii
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ISO 9276-6:2008(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.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

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.

ISO 9276-6 was prepared by Technical Committee ISO/TC 24, Particle characterization including sieving,

Subcommittee SC 4, Sizing by methods other than sieving.

ISO 9276 consists of the following parts, under the general title Representation of results of particle size

analysis:
⎯ Part 1: Graphical representation

⎯ Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions

⎯ Part 3: Adjustment of an experimental curve to a reference model
⎯ Part 4: Characterization of a classification process

⎯ Part 5: Methods of calculation relating to particle size analyses using logarithmic normal probability

distribution

⎯ Part 6: Descriptive and quantitative representation of particle shape and morphology

iv © ISO 2008 – All rights reserved
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ISO 9276-6:2008(E)
Introduction

A variety of different methods for the descriptive and quantitative representation of particle shape and

morphology are known. Even for the term particle size, there is no single definition. Different methods of size

analysis are based on the measurement of different physical properties. In ISO 9276-1, the particle size is

defined as the diameter of a sphere having the same physical property. This is known as the equivalent

spherical diameter. So-called property functions help to correlate it with the property of primary interest, which

may, for instance, be flowability, taste or dissolution time.

Broad application of sizing methods in particle characterization shows that particle size is often an important

factor. But particle size alone is not sufficient to allow particle phenomena such as powder flow, mixing,

abrasion or biological response to be understood. Particle shape and morphology play an important role in

particle systems and therefore it is also necessary to characterize and describe these characteristics

quantitatively.

Including additional shape parameters in property functions is supposed to give a better correlation with the

particular property of the particle system. For instance, knowledge of the size of grinding particles and of the

sharpness of their edges will make it possible not only to distinguish between fresh and used grinding particles

but also to predict their abrasive effect quantitatively by means of a property function.

ISO 13322-1 and ISO 13322-2 give guidance on the measurement, description and validation methodologies

used when determining particle sizes by static and dynamic image analysis, respectively. Broad industrial use

of image analysis techniques requires standardized methods of measurement for the characterization of the

size, geometrical shape and morphology of particles.

A particle's shape is the envelope formed by all the points on the surface of the particle. Particle morphology

represents the extension of a simple shape description of this kind to more complex descriptions including

characteristics such as porosity, roughness and texture.

Various glossaries of terms giving descriptions, in words, of particle shape and morphology already exist (see

Clause 5). These descriptions may be useful for the classification or identification of particles but, at the

moment, there is insufficient consensus on the definition of particle shape and morphology in the quantitative

terms necessary for them to be implemented in software routines. A future revision of this part of ISO 9276

may cover this.
© ISO 2008 – All rights reserved v
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INTERNATIONAL STANDARD ISO 9276-6:2008(E)
Representation of results of particle size analysis —
Part 6:
Descriptive and quantitative representation of particle shape
and morphology

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 part of ISO 9276 specifies rules and nomenclature for the description and quantitative representation of

particle shape and morphology. To achieve a more comprehensive description of a particle or particle system,

particle size information can be used together with other information but, in most cases, the particle size

information cannot be replaced.

The averaging of shape over all particles in a sample has been shown to be an ineffective approach.

Distributions of other particle characteristics are required in addition to particle size distributions (see

ISO 9276-1).

The relevance, to technological applications, of any method of representing particle shape is the deciding

factor in its use. Therefore this part of ISO 9276 is restricted to methods which can be correlated with physical

properties in industrial applications.

The aim of particle analysis is to determine the most appropriate characterization method for a particular

application. This implies a profound understanding of the relationship between particle characteristics and

macroscopic product and process properties (or at least a database of broad empirical data).

Problems of shape and morphology would normally be three-dimensional problems, but most definitions in

this part of ISO 9276 are in fact given for two dimensions because of the widespread use of image analysis

methods.

With the help of the evaluation criteria given in Clause 4, a minimum set of shape descriptors is derived in

Clause 8 from the various descriptors and methods in Clause 5, enabling a direct comparison of different

shape analysis equipment or methods to be made within the limits discussed in Clause 6.

2 Normative references

The following referenced documents are indispensable for the application 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 9276-1:1998, Representation of results of particle size analysis — Part 1: Graphical representation (and

its Technical Corrigendum ISO 9276-1:1998/Cor.1:2004)

ISO 13322-1:2004, Particle size analysis — Image analysis methods — Part 1: Static image analysis methods

© ISO 2008 – All rights reserved 1
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ISO 9276-6:2008(E)
3 Symbols and abbreviated terms

For the purposes of this document, the symbols given in ISO 13322-1 and ISO 9276-1 and the following apply.

In ISO 9276-1, the symbol x is used to denote the particle size or the diameter of a sphere. However, it is

recognized that the symbol d is also widely used to designate these values. Therefore, in this part of ISO 9276,

the symbol x may be replaced by d wherever it appears.
Symbols for the particle size other than x or d shall not be used.
A projection area
A Feret box area
box
A area of the convex hull (envelope) bounding the particle
b intercept on graph for fractal dimension
C circularity
CI global surface concavity index
D fractal dimension
d diameter of the minimum circumscribed circle
cmin
d diameter of the maximum inscribed circle
imax

d spacing of a series of parallel lines [for use in the Cauchy-Crofton formula (see Clause A.1)]

E thickness
I number of intercepts [for use in the Cauchy-Crofton formula (see Clause A.1)]
L geodesic length
N number
P length of perimeter
P length of the perimeter of the convex hull (envelope) bounding the particle
Rn roundness
S surface area
V volume
x area-equivalent diameter of particle
x thickness of a very long particle
x maximum Feret diameter
Fmax
x minimum Feret diameter
Fmin

x Feret diameter perpendicular to the minimum Feret diameter, normally known as “length”

x geodesic length of a very long particle
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ISO 9276-6:2008(E)
x length of major axis of Lengendre ellipse of inertia
Lmax
length of minor axis of Lengendre ellipse
Lmin
x perimeter-equivalent diameter of particle
x surface-equivalent diameter of particle
x volume-equivalent diameter of particle
α angle or direction
Ω robustness
Ω largest concavity index
Ω concavity/robustness ratio
ω number of erosions
Ψ Wadell’s sphericity
Ψ average concavity
4 Criteria for the evaluation of shape description methods

A common problem in shape description is how to judge the quality of a shape description method. Not all

methods are suitable for every kind of shape and application. Until now, consistent evaluation criteria have not

existed for shape description methods.
Criteria for the evaluation of shape description methods:

⎯ accessibility, which describes how easy it is to compute a shape descriptor in terms of memory

requirements and computation time;

⎯ scope, which refers to the classes of shape that can be described by the method;

⎯ uniqueness, which describes whether a one-to-one mapping relationship exists between shapes and

shape descriptors;

⎯ stability and sensitivity, which describe how sensitive a shape description is to “small” changes in shape.

Each method shall use descriptors with a specific degree of complexity. In general, descriptors can be

described as sets of numbers that are produced to describe a given shape. The shape may not be entirely

reconstructable from these descriptors, but the descriptors for different shapes shall be sufficiently different to

make it possible to discriminate between the shapes.
Criteria for shape descriptors:

⎯ invariance with respect to rotation and reflection — for a given shape, the values of the descriptors shall

be the same irrespective of the orientation of the particle;

⎯ invariance with respect to scale — for a given shape, the values of the descriptors shall be the same

irrespective of the size of the particle;

⎯ independence — if the elements of the descriptors are independent, some can be discarded without the

need to recalculate the others;
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ISO 9276-6:2008(E)

⎯ economy — it is desirable that the descriptors be economical in the number of terms used to describe a

shape.

The above three invariance conditions (concerning rotation, reflection and scale) guarantee that the result of a

shape analysis is not affected by the parameters of the analysis and is independent of the particle size. It

should, however, be stressed that the particle size at which certain shape information is obtained may be of

practical relevance, as in the case of surface roughness, and size shall therefore be included in the shape

analysis.

The robustness of shape descriptors with respect to the density, translation and rotation of the sampling grid

can indicate whether it is acceptable to compare measurement results from different algorithms or different

[1]
image analysers .
5 Classification of methods and descriptors
5.1 General classification

Methods of shape description, as well as the various shape descriptors, can be classified according to

different criteria. An obvious way of classifying shape descriptors is to determine whether they are qualitative

or quantitative in nature:

a) Qualitative description, i.e. in words: expressions such as “needlelike particles” and “oblate shape”.

[2]

Examples of this type of shape characterization are given in the US Pharmacopoeial Convention , in

[3] [4]

ASTM F 1877 and in the glossary made available by the NIST Center for Analytical Chemistry .

b) Quantitative description: in the following text, shape descriptors will be understood as numbers that can

be calculated from particle images or physical particle properties via mathematical or numerical

operations.
5.2 Levels of shape

For a better understanding of shape description, it is important to establish definitions regarding the basic

characteristics of an arbitrary object. The shape of an arbitrary object can be defined in many ways. One such

definition describes shape as a binary image representing the extent of the particle. This can be understood

[5]

as the silhouette of the particle. Barrett recognizes three potentially independent particle shape properties

(see Figure 1):
⎯ form, which reflects the geometrical proportions of a particle;
⎯ roundness, which expresses the radius of curvature at the particle corners;

⎯ surface texture, which is taken as defining local roughness features at corners and at edges between

corners only.

These particle shape properties may not suffice for a complete description of the shape of a particular particle

and may be defined differently by different authors. But they give us a good idea of how shape parameters

can be measured at different levels of size. Three corresponding levels of shape can thus be distinguished:

macroshape, mesoshape and microshape.
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ISO 9276-6:2008(E)
Key
1 form
2 roundness
3 surface texture
[6]
Figure 1 — Illustration of form, roundness and surface texture

Macrodescription is a description of the overall form of a particle defined in terms of the geometrical

proportions of the particle. In general, simple geometrical descriptors calculated from size measurements

made on the particle silhouette are used. Low-order Fourier descriptors can also be regarded as

macrodescriptors.

Mesodescription provides information about details of the particle shape and/or surface structure that are in a

[5]

size range not much smaller than the particle proportions, like Barrett’s roundness and concavity.

The following mesodescriptors can be defined:

a) morphological mathematical descriptors, computing robustness and largest concavity index;

b) a concavity tree, providing general insight into the organization of concavities and their complexity;

c) angularity descriptors, determining those parts of the boundary that are active in the abrasion process:

1) an angularity factor, selecting the apices of corners which are coincident with the convex hull

because it is these points that will make contact with the surface of another particle,

2) a quadratic spike parameter, taking into account those spikes that are outside a circle, of area equal

to that of the particle, centred over the particle centroid,

3) slip chording, generating information on the number of cutting edges and their sharpness in the facet

signature waveform;
© ISO 2008 – All rights reserved 5
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ISO 9276-6:2008(E)

d) fractal dimension, providing data on the overall structural complexity by consideration of a larger

measurement step;

e) Fourier descriptors, of higher order than macrodescriptors, specifying the smaller-scale components of

morphology;
f) bending energy, measuring the overall complexity of contour lines.

Microdescription determines the roughness of shape boundaries using two of the descriptors mentioned

above:

⎯ fractal dimension, measured using a measurement step smaller than that used for structural description;

⎯ higher-order Fourier descriptors/coefficients for surface-textural analysis.
5.3 Principles for deriving shape descriptors

The level of inspection used in a method is a very practical criterion for the classification of the method, since

many methods provide shape information at different size levels. Another convenient way of classifying

methods is to differentiate between those which derive shape descriptors from particle images and those

which derive shape descriptors from physical properties:
a) Calculation of geometrical descriptors/shape factors:

Geometrical shape factors are ratios between two different geometrical properties, such properties

usually being some measure of the proportions of the image of the whole particle or some measure of the

proportions of an ideal geometrical body that envelops, or forms an envelope around, the particle. These

results are macroshape descriptors similar to an aspect ratio.
b) Calculation of dynamic shape factors from physically equivalent diameters:

These shape factors are similar to geometrical shape factors except that at least one physical property is

considered in the comparison. Usually, the results are expressed as a ratio of equivalent diameters, e.g.

Stokes sedimentation velocity to volume-equivalent diameter x /x .
Stokes V
c) Morphological analysis:

Morphological analysis descriptors give mean values of particle shape that are not much smaller than the

proportions of the whole particle. A typical example is concavity analysis.
d) Analysis of the contour line (shape boundary):

Multiple operations on the contour line of a particle can produce a set of shape descriptors. This set of

shape descriptors contains information on the particle shape at different size levels. Methods belonging to

this group include fractal dimension analysis and the use of Fourier analysis.
e) Analysis of grey-level images:

Multiple operations on the grey-level pixel image of a particle can produce a set of shape descriptors

which can be correlated with the topology or surface texture of the particle.
f) Analysis of physical spectra:

Multiple operations on, or the mathematical treatment of, the physical spectra of a single particle can

extract the shape information as a set of descriptors. Such a procedure has been described for shape

analysis by azimuthal light scattering and diffraction spectroscopy.
6 © ISO 2008 – All rights reserved
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ISO 9276-6:2008(E)
Figure 2 — Classification of some methods for particle shape description

The choice of an appropriate shape description method depends on the measurement technique available

and the particle system under examination (in particular its size range). Methods based on mathematical

operations on contour lines (e.g. fractal dimension analysis or Fourier analysis) require a relatively high

resolution of particle images. This may be obtained by using a scanning electron or light microscope. Apart

from such factors, the results of shape analysis may also be significantly affected by sample preparation (e.g.

by the sample size and whether the sample is representative, by particle orientation in 2D-analysis).

This part of ISO 9276 defines the set of parameters necessary for the comparison of shape analysis methods

and shape analysis instruments. Any other shape descriptors used shall be clearly defined.

6 Errors which can occur in the analysis of a single image
6.1 Generation of shape descriptors

Problems associated with image analysis are manifold and errors can be introduced in the generation of

shape descriptors. These errors can exist at many levels, but most of them are fundamentally different from

those observed in the more traditional techniques used for the characterization of dispersed matter. Such

shape descriptor errors are usually introduced by the protocols necessary to perform calculations on any

given image (see ISO 13322-1:2004, Annex D). The common sources of errors which occur when performing

image analysis and in the comparison of image analysis protocols are specified in 6.2 to 6.4.

6.2 Image resolution

The optimum resolution shall not and cannot be stated absolutely, but shall rather be related to the size of the

element features to be determined (e.g. agglomerate branches, roughness scale). Analysis of image

parameters is generally based on a digitized image. The process of digitizing an image can result in

information loss because of the transformation of the continuous features innate to the particle into discrete

elements of finite size — the finite resolution. For pixel errors smaller than 5 % for a circle, the necessary pixel

numbers per particle range from 100 to 200 for robust parameters, like projection area and ellipse ratio, up to

[1], [7], [8]
5 000 for parameters using the perimeter .
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ISO 9276-6:2008(E)

The resolution of a particle in terms of pixels per unit length cannot be greater than the optical resolution of the

same particle. This limitation is due to the sharpness of the particle image generated by the focal depths

achievable with optical microscopy and the numerical aperture of the objective lenses (see ISO 13322-1:2004,

Annex C).
6.3 Binarization

To discriminate between particles of irregular shape against a background, several techniques can be

employed. One example is the application of a threshold limit for the colour or grey levels within the image. All

pixels with colour levels or a specific grey level on one side of a threshold may be considered as part of the

background, whilst all other pixels are deemed to be part of the particle. The threshold value selected requires

a criterion representing an appropriate value. This criterion can be chosen using an image analysis algorithm

or can be selected manually, in which case it will be subject to individual perception.

Systematic errors of both calibration and binarization can be determined experimentally by use of reference

particles with a known size or area.
6.4 Algorithms for calculating shape descriptors

Information gathered from a digitized image by an image analysis software programme to determine features

such as lengths and areas includes only colour and discrete locational information. Therefore, to determine a

feature such as the diameter of a particle, the image analysis system and software has to provide an algorithm

capable of extracting this desired feature.

Consequently, no single particle parameter, be it a length, a fractal dimension or an area, is “natural” to image

analysis. In every image analysis, logic has to be applied to extract the desired feature from the lower-level

information limits of colour and discrete locational information.

The intention of image analysis algorithms is to be as close as possible to the original meaning of a feature, or

to any other (non-image-processing tool) methods, regardless of the small basis of lower-level information

which can occur in the process of analysis. In order to achieve this intention, several algorithms may be

applied for the determination of each feature, each based on a different set of assumptions. These

assumptions should be congruent with each other, but often are not. In some cases, parameters within the

algorithm need to be adjusted.

If basic pixel routines are not sufficiently documented, image analysis software can deliver non-explainable

differences in shape descriptors.
8 © ISO 2008 – All rights reserved
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ISO 9276-6:2008(E)
7 Size parameters for normalization of shape descriptors
Volume V 3D descriptor
Ideal normalization paramet
...

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