FprEN ISO 25178-2

Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms, definitions and surface texture parameters (ISO/FDIS 25178-2:2021)

Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Flächenhaft - Teil 2: Begriffe, Definitionen und Oberflächen-Kenngrößen (ISO/FDIS 25178-2:2021)

Dieses Dokument legt Parameter für die Ermittlung der Oberflächenbeschaffenheit durch flächenhafte Verfahren fest.

Spécification géométrique des produits (GPS) - État de surface: Surfacique - Partie 2: Termes, définitions et paramètres d'états de surface (ISO/FDIS 25178-2:2021)

Specifikacija geometrijskih veličin izdelka (GPS) - Tekstura površine: ploskovna - 2. del: Izrazi, definicije in parametri teksture površine (ISO/DIS 25178-2:2019)

General Information

• Status: Not Published
• ICS: 17.040.20 - Properties of surfaces
• Technical Committee: CEN/TC 290 - Dimensional and geometrical product specification and verification
• Drafting Committee: CEN/TC 290 - Dimensional and geometrical product specification and verification
• Current Stage: 5060 - Closure of Vote - Formal Approval
• Due Date: 26-Oct-2021
• Completion Date: 26-Oct-2021
• Ref Project: oSIST prEN ISO 25178-2:2020 - Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms, definitions and surface texture parameters (ISO/DIS 25178-2:2019)

RELATIONS

• Revised: EN ISO 25178-2:2012 - Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms, definitions and surface texture parameters (ISO 25178-2:2012)
• Effective Date: 04-Oct-2017

Standards Content (sample)

SLOVENSKI STANDARD
oSIST prEN ISO 25178-2:2020
01-februar-2020

Specifikacija geometrijskih veličin izdelka (GPS) - Tekstura površine: ploskovna -

2. del: Izrazi, definicije in parametri teksture površine (ISO/DIS 25178-2:2019)

Geometrical product specifications (GPS) - Surface texture: Areal - Part 2: Terms,

definitions and surface texture parameters (ISO/DIS 25178-2:2019)

Geometrische Produktspezifikation (GPS) - Oberflächenbeschaffenheit: Flächenhaft -

Teil 2: Begriffe, Definitionen und Oberflächen-Kenngrößen (ISO/DIS 25178-2:2019)

Spécification géométrique des produits (GPS) - État de surface: Surfacique - Partie 2:

Termes, définitions et paramètres d'états de surface (ISO/DIS 25178-2:2019)
Ta slovenski standard je istoveten z: prEN ISO 25178-2
ICS:
17.040.20 Lastnosti površin Properties of surfaces
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
oSIST prEN ISO 25178-2:2020 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN ISO 25178-2:2020
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oSIST prEN ISO 25178-2:2020
DRAFT INTERNATIONAL STANDARD
ISO/DIS 25178-2
ISO/TC 213 Secretariat: BSI
Voting begins on: Voting terminates on:
2019-12-20 2020-03-13
Geometrical product specifications (GPS) — Surface
texture: Areal —
Part 2:
Terms, definitions and surface texture parameters
Spécification géométrique des produits (GPS) — État de surface: Surfacique —
Partie 2: Termes, définitions et paramètres d'états de surface
ICS: 17.040.20
THIS DOCUMENT IS A DRAFT CIRCULATED
This document is circulated as received from the committee secretariat.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
ISO/CEN PARALLEL PROCESSING
BEING ACCEPTABLE FOR INDUSTRIAL,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 25178-2:2019(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
PROVIDE SUPPORTING DOCUMENTATION. ISO 2019
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oSIST prEN ISO 25178-2:2020
ISO/DIS 25178-2:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2019

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
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Phone: [phone]
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Website: www.iso.org
Published in Switzerland
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Contents

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

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

3.1  General terms ................................................................................................................................................... 1

3.2  Geometrical parameter terms .................................................................................................................... 5

3.3  Geometrical feature terms ........................................................................................................................ 10

4.1  General ............................................................................................................................................................. 13

4.2  Height parameters ....................................................................................................................................... 13

4.3  Spatial parameters ....................................................................................................................................... 14

4.4  Hybrid parameters ...................................................................................................................................... 16

4.5  Functions and related parameters ......................................................................................................... 16

5.1  General ............................................................................................................................................................. 27

5.2  Type of texture feature ............................................................................................................................... 29

5.3  Segmentation ................................................................................................................................................. 29

5.4  Determining significant features ............................................................................................................ 29

5.5  Section of feature attributes ..................................................................................................................... 31

5.6  Attribute statistics ....................................................................................................................................... 32

5.7  Feature characterization convention .................................................................................................... 33

5.8  Named feature parameters ....................................................................................................................... 33

............................................................................................................................... 34

5.9  Additional parameters

Annex A (informative) Multiscale geometric (fractal) methods .............................................................. 36

Annex B (normative) Determination of areal parameters for stratified functional surfaces ....... 42

Annex C (informative) Basis for areal surface texture standards ........................................................... 44

Annex D (informative) Implementation details .............................................................................................. 45

Annex E (informative) Changes made in this second edition compared to the 2012 edition ........ 49

Annex F (informative) Relation with the GPS matrix ................................................................................... 51

Bibliography ................................................................................................................................................................. 52

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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 on 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 the following URL:
www.iso.org/iso/foreword.html.

The committee responsible for this document is Technical Committee ISO/TC 213, Dimensional and

geometrical product specifications and verification.

This second edition cancels and replaces the first edition (ISO 25178-2:2012), which has been technically

revised.
The main changes compared to the previous edition are described in Annex F.
A list of all parts in the ISO 25178 series can be found on the ISO website.
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Introduction

This part of ISO 25178 is a geometrical product specification (GPS) standard and is to be regarded as a

general GPS standard (see ISO 14638). It influences the chain link B of the chains of standards on profile

and areal surface texture.

The ISO/GPS matrix model given in ISO 14638 gives an overview of the ISO/GPS system of which this

part of ISO 25178 is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this part of

ISO 25178 and the default decision rules given in ISO 14253-1 apply to the specifications made in

accordance with this part of ISO 25178, unless otherwise indicated.

For more detailed information of the relation of this part of ISO 25178 to other standards and the GPS

matrix model, see Annex F.

This part of ISO 25178 develops the terminology, concepts and parameters for areal surface texture.

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DRAFT INTERNATIONAL STANDARD ISO/DIS 25178-2:2019(E)
Geometrical product specifications (GPS) — Surface
texture: Areal —
Part 2:
Terms, definitions and surface texture parameters
1 Scope

This part of ISO 25178 defines terms, definitions and parameters for the determination of surface texture

by areal methods.
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 16610-1:2015, Geometrical product specifications (GPS) — Filtration — Part 1: Overview and basic

concepts

ISO 17450-1:2011, Geometrical product specifications (GPS) — General concepts — Part 1: Model for

geometrical specification and verification
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 17450-1:2011 and ISO 16610-

1:2015, and the following apply.

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

— ISO Online browsing platform: available at http://www.iso.org/obp
— IEC Electropedia: available at http://www.electropedia.org/
3.1 General terms
3.1.1
non‐ideal surface model
skin model

model of the physical interface of the workpiece with its environment

[SOURCE: ISO 17450-1:2011, 3.2.2]
3.1.2
surface texture
geometrical irregularities contained in a scale-limited surface

Note 1 to entry: Surface texture does not include those geometrical irregularities contributing to the form or

shape of the surface.
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3.1.3
mechanical surface

boundary of the erosion, by a sphere of radius r, of the locus of the centre of an ideal tactile sphere, also

with radius r, rolled over the skin model of a workpiece
[SOURCE: ISO 14406:2010, 3.1.1]
3.1.3.1
electromagnetic surface

surface obtained by the electromagnetic interaction with the skin model of a workpiece

[SOURCE: ISO 14406:2010, 3.1.2]
3.1.3.2
auxiliary surface
surface obtained by an arbitrary external source

Note 1 to entry: A software measurement standard is an example for an auxiliary surface. Other physical

measurement principles which differ from a mechanical or electromagnetic surface, such as tunnelling microscopy

or atomic force microscopy, can also serve as an auxiliary surface. See Figure 1.

3.1.4
specification coordinate system
system of coordinates in which surface texture parameters are specified

Note 1 to entry: If the nominal form of the surface is a plane (or portion of a plane), it is common (practice) to

use a rectangular coordinate system in which the axes form a right-handed Cartesian set, the X-axis and the Y-axis

also lying on the nominal surface, and the Z-axis being in an outward direction (from the material to the surrounding

medium). This convention is adopted throughout the rest of this part of ISO 25178.

3.1.5
primary surface

surface portion obtained when a surface portion is represented as a specified primary mathematical

model with specified nesting index
[SOURCE: ISO 16610-1:2015, 3.3]

Note 1 to entry: In this part of ISO 25178, an S-filter is used to derive the primary surface. See Figure 1.

3.1.5.1
primary extracted surface
finite set of data points sampled from the primary surface
[SOURCE: ISO 14406:2010, 3.7]
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Figure 1 – Definition of primary surface
3.1.6
surface filter
filtration operator applied to a surface
3.1.6.1
S‐filter

surface filter which removes small scale lateral components from the surface, resulting in the primary

surface
3.1.6.2
L‐filter

surface filter which removes large scale lateral components from the primary surface or S-F surface

Note 1 to entry: When the L-Filter is not tolerant to form, it must be applied on an S-F surface; when it is tolerant to

form, it can be applied either on the primary surface or on an S-F surface.
3.1.6.3
F‐operation
operation which removes form from the primary surface

Note 1 to entry: Some F-operations (such as association operations) have a very different action to that of

filtration. Though their action can limit the larger lateral scales of a surface this action is very fuzzy. It is represented

in Figure 2 using the same convention as for a filter.

Note 2 to entry: Some L-filters are not tolerant to form and require an F-operation first as a prefilter before being

applied.
3.1.6.4
nesting index
Nis, Nic, Nif

number or set of numbers indicating the relative level of nesting for a particular primary mathematical

model
[SOURCE: ISO 16610-1:2015, 3.2.1]
3.1.7
S‐F surface

surface derived from the primary surface by removing the form using an F-operation

Note 1 to entry: Figure 2 illustrates the relationship between the S-F surface and the S-filter and F-operation.

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Note 2 to entry: If filtered with Nis nesting index to remove the shortest wavelengths from the surface, the surface

is equivalent to a “Primary S-F surface”. In that case, Nis is the areal equivalent of the s cut-off (see f in Figure 2).

Note 3 to entry: If filtered with Nic nesting index to separate longer from shorter wavelengths, the surface is

equivalent to a “Waviness S-F surface”. In that case, Nic is the areal equivalent of the c cut-off (see g in Figure 2).

Note 4 to entry: The concepts of “roughness” or “waviness” are less important in areal surface texture than in

profile surface texture. Some surfaces could exhibit roughness in one direction and waviness in the perpendicular

direction. That is why the concepts of S-L surface and S-F surface are preferred in this document.

3.1.8
S‐L surface

surface derived from the S-F surface by removing the large-scale components using an L-filter

Note 1 to entry: Figure 2 illustrates the relationship between the S-L surface and the S-filter and L-filter.

Note 2 to entry: If the S-Filter nesting index Nis is chosen to remove the shortest wavelengths from the surface

and the L-Filter nesting index Nic is chosen in order to separate longer from shorter wavelengths, the surface is

equivalent to a “Roughness S-L surface”. See h in Figure 2.

Note 3 to entry: A series of S-L surfaces can be generated with narrow bandwidth using a S-Filter and a L-Filter

of close nesting indices (or equal), in order to achieve a multi-scale exploration of the surface. See Figure 3.

Small scale
Large scale
S-Filter
L-Filter
F-Operation
S-F surface
S-F surface (see note 3 of
3.1.7)
S-L surface (see note 2 of
3.1.8)

Figure 2 — Relationships between the S‐filter, L‐filter, F‐operation and S‐F and S‐L surfaces

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Figure 3 — Example of bandpass filters used to generate a bank of S‐L surfaces
3.1.9
scale‐limited surface
S-F surface or S-L surface
3.1.10
reference surface
surface associated to the scale-limited surface according to a criterion
Note 1 to entry: This reference surface is used for surface texture parameters.

Note 2 to entry: Examples of reference surfaces include plane, cylinder and sphere.

3.1.11
evaluation area
portion of the scale-limited surface for specifying the area under evaluation
Note 1 to entry: See ISO 25178-3 for more information.
3.1.12
definition area

portion of the evaluation area for defining the parameters characterizing the scale-limited surface

Note1 to entry: Throughout this document, the symbol A is used for the numerical value of the definition area

and the symbol 𝐴 for the domain of integration.
3.2 Geometrical parameter terms
3.2.1
field parameter
parameter defined from all the points on a scale-limited surface
Note 1 to entry: Field parameters are defined in Clause 4.
3.2.2
feature parameter

parameter defined from a subset of predefined topographic features from the scale-limited surface

Note 1 to entry: Feature parameters are defined in Clause 5.

Note 2 to entry: The parameters Sp, Sv and Sz correspond to the definition of feature parameters but for

historical reasons they are considered as field parameters.
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3.2.3
V‐parameter
material volume or void volume field parameter
3.2.4
S‐parameter
field or feature parameter that is not a V-parameter
3.2.5
height
ordinate value
z(x,y)
signed normal distance from the reference surface to the scale-limited surface

Note1 to entry: Throughout this document, the term “height” is either used for a distance or for an absolute

coordinate. Example: Sz, maximum height, is a distance, and Sp, maximum peak height, is an absolute height.

3.2.5.1
depth
opposite value of height.
3.2.6
local gradient vector
𝝏𝒛�𝒙, 𝒚�𝝏𝒛�𝒙, 𝒚�
� , �
𝝏𝒙 𝝏𝒚

first derivative along x and along y of the scale-limited surface at position x,y

Note 1 to entry: See Annex E for implementation details.
3.2.7
local mean curvature
arithmetic mean of the principal curvatures at position x,y

Note 1 to entry: Principal curvatures are two numbers, k1 and k2 representing the maximum and minimum

� ��
� �
curvatures at a point. The local mean curvature is therefore: .
Note 2 to entry: See Annex E for implementation details.
3.2.8
material ratio

ratio of the area of the surface portion intersected by a plane at height c, to the evaluation area

𝐴 �𝑐�
𝑀 �𝑐��

Note 1 to entry: The curve representing material ratio as a function of height is also called Abbott Firestone curve.

Note 2 to entry: The material ratio may be given in percentage or value between 0 and 1

Note 3 to entry: See Figure 4.
Note 4 to entry: See Annex E for the determination of the material ratio curve.
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Key
c intersecting height c
A areal portions
intersected by plane at
level c
Figure 4 — Area of the surface portion intersected by plane at level c
3.2.9
material ratio curve
material ratio function

function representing the areal material ratio of the scale-limited surface as a function of height

Note 1 to entry: This function can be interpreted as the sample cumulative probability function of the ordinates

z(x,y) within the evaluation area. See Annex E.
Note 2 to entry: See Figure 5.
Key
a height
b material ratio in percent
c intersection level of height c
d material ratio at height c
Figure 5 — Material ratio curve
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3.2.10
inverse material ratio
C(m )
height at which a given material ratio m in percent is satisfied
𝐶�𝑚 ��𝑀 �𝑚�
� � �
3.2.11
height density curve
height density function
hc

curve representing the density of the height of the scale-limited profile z in percent

𝑑𝑀 �𝑐�
ℎ 𝑐 �
𝑑𝑐
Note 1to entry: See Figure 6.
Key
a height
b density in percent
Figure 6 — Height density curve
3.2.12
autocorrelation function
f (t , t )
ACF x y

function which describes the correlation between a surface and the same surface translated by (t , t )

x y
� �
∬ 𝑧 𝑥, 𝑦 𝑧�𝑥 � 𝑡,𝑦 � 𝑡 �𝑑𝑥𝑑𝑦
� �
𝑓 �𝑡,𝑡 ��
��� � �
𝑧 �𝑥, 𝑦�𝑑𝑥𝑑𝑦
B being the intersecting area of the two surfaces at shifts t and t
x y
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3.2.13
Fourier transformation
F(p, q)

operator which transforms the height ordinate values of the scale-limited surface into Fourier space

����������
� �
𝐹 𝑝, 𝑞 ��𝑧�𝑥,𝑦�𝑒 𝑑𝑥𝑑𝑦

Note 1 to entry: The Fourier transformation defined here is using a limited support A, therefore it is an

approximation of the mathematical function called Fourier transformation which has an infinite support.

3.2.13.1
angular spectrum
F(r, s)

Fourier transformation expressed in polar coordinates, with respect to a reference direction   in the

ref
plane of the definition area
� �
𝐹 𝑟, 𝑠 � 𝐹�𝑟 cos�𝑠 � 𝜃�,𝑟 sin�𝑠 � 𝜃��
��� ���

where r is a spatial frequency, s the specified direction and F is the Fourier transformation function

Note 1 to entry: The positive x-axis is defined as the zero angle.

Note 2 to entry: The angle is positive in an anticlockwise direction from the x-axis.

3.2.13.2
angular amplitude density
angular amplitude distribution
f (s)
AAD
integrated amplitude of the angular spectrum for a given direction s
�� | � �|
𝑓 𝑠 �� 𝐹 𝑟, 𝑠 𝑟 𝑑𝑟
���

where r is a spatial frequency, R to R (R < R ) is the range of integration of the frequencies in the radial

1 2 1 2

direction and s the specified direction and F is the Fourier transformation function

Note 1 to entry: the term “density” refers to the value at a given angle, and the term “distribution” refers to the graph

representing the values for all angles.
3.2.13.3
angular power density
angular power distribution
f (s)
APD
integrated squared amplitude of the angular spectrum for a given direction s
�� | � �|
𝑓 𝑠 �� 𝐹 𝑟, 𝑠 𝑟 𝑑𝑟
���

where r is a spatial frequency, R to R (R < R ) is the range of integration of the frequencies in the radial

1 2 1 2

direction and s the specified direction and F is the Fourier transformation function

Note 1 to entry: the term “density” refers to the value at a given angle, and the term “distribution” refers to the graph

representing the values for all angles.
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3.2.14
power spectral density
PSD

squared magnitude of the Fourier transform of the residual surface height function along one dimension

using an appropriate weighting function

Note 1 to entry: The PSD describes surface texture in a spatial frequency context allowing the waviness or ripples

in the surface to be described and controlled.

Note 2 to entry: An alternative and analogous function for describing and controlling surface texture in a spatial

frequency context is the Auto-Covariance or ACV, which is given by the overlap integral of shifted and unshifted 1D

profiles over the evaluation length.
3.3 Geometrical feature terms
3.3.1
peak

point on the surface which is higher than all other points within a neighbourhood of that point

Note 1 to entry: There is a theoretical possibility of a plateau. In practice, this can be avoided by the use of an

infinitesimal tilt.
Note 2 to entry: See Figure 7.
3.3.1.1
hill

region around a peak such that all maximal upward paths end at the peak
Note 1 to entry: This definition is used for feature parameters.
Note 2 to entry: See Figure 7.
3.3.1.2
hill

outwardly directed (from material to surrounding medium) contiguous portion of the scale-limited

surface above the mean plane
Note 1 to entry: This definition is used for field parameters.
3.3.1.3
course line
curve separating adjacent hills
Note to entry: See Figure 7.
3.3.2
pit

point on the surface which is lower than all other points within a neighbourhood of that point

Note 1 to entry: There is a theoretical possibility of a plateau. In practice, this can be avoided by the use of an

infinitesimal tilt.
Note 2 to entry: See Figure 8.
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3.3.2.1
dale

region around a pit such that all maximal downward paths end at the pit
Note 1 to entry: This definition is used for feature parameters.
Note 2 to entry: See Figure 8.
3.3.2.2
dale

an inwardly directed (from surrounding medium to material) contiguous portion of the scale-limited

surface below the mean plane
Note 1 to entry: this definition is used for field parameters.
3.3.2.3
ridge line
curve separating adjacent dales
Note 1 to entry: See Figure 8.
3.3.3
saddle

point or set of points on the scale-limited surface where ridge lines and course lines cross

3.3.3.1
saddle point
saddle consisting of one point

Figure 7 — Representation of a hill (B) in the Figure 8 — Representation of a dale (B) in

context of watershed segmentation with the the context of watershed segmentation with

peak (A) and the course line (C) the pit (A) and the ridge line (C)
3.3.4
motif
hill or dale defined with watershed segmentation

Note 1 to entry: The term motif is used to designate an areal feature obtained by segmentation.

Note 2 to entry: The term motif as defined on a profile in ISO 12085 is a cross section of a dale.

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3.3.5
topographic feature
areal, line or point feature on a scale-limited surface
3.3.5.1
areal feature
hill or dale
3.3.5.2
line feature
course line or ridge line
3.3.5.3
point feature
peak, pit or saddle point
3.3.6
contour line
line on the surface consisting of adjacent points of equal height
3.3.7
segmentation
method which partitions a scale-limited surface into distinct features
3.3.7.1
segmentation function

function which splits a set of “events” into two distinct sets called the significant events and the

insignificant events and which satisfies the three segmentation properties
Note 1 to entry: Examples of events are: ordinate values, point features, etc.

Note 2 to entry: A full mathematical description of the segmentation function and the three segmentation

properties can be found in Scott (2004) (see Reference [22]) and in ISO 16610-85.

3.3.8
change tree

graph where each contour line is plotted as a point against height in such a way that adjacent contour

lines are adjacent points on the graph

Note 1 to entry: Peaks and pits are represented on a change tree by the end of lines. Saddle points are represented

on a change tree by joining lines. See Annex A of ISO 16610-85 for more details concerning change trees.

3.3.8.1
pruning
method to simplify a ch
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