SIST EN ISO 16610-45:2025

SLOVENSKI STANDARD
01-maj-2025
Specifikacija geometrijskih veličin izdelka (GPS) - Filtriranje - 45. del: Morfološki
profilni filtri: Segmentacija (ISO 16610-45:2025)
Geometrical product specifications (GPS) - Filtration - Part 45: Morphological profile
filters: Segmentation (ISO 16610-45:2025)
Geometrische Produktspezifikation (GPS) - Filterung - Teil 45: Morphologische
Profilfilter: Segmentierung (ISO 16610-45:2025)
Spécification géométrique des produits (GPS) - Filtrage - Partie 45: Titre manque (ISO
16610-45:2025)
Ta slovenski standard je istoveten z: EN ISO 16610-45:2025
ICS:
17.040.20 Lastnosti površin Properties of surfaces
17.040.40 Specifikacija geometrijskih Geometrical Product
veličin izdelka (GPS) Specification (GPS)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 16610-45
EUROPEAN STANDARD
NORME EUROPÉENNE
March 2025
EUROPÄISCHE NORM
ICS 17.040.20; 17.040.40
English Version
Geometrical product specifications (GPS) - Filtration - Part
45: Morphological profile filters: Segmentation (ISO
16610-45:2025)
Spécification géométrique des produits (GPS) - Filtrage Geometrische Produktspezifikation (GPS) - Filterung -
- Partie 45: Filtres de profil morphologiques : Teil 45: Morphologische Profilfilter: Segmentierung
Segmentation (ISO 16610-45:2025) (ISO 16610-45:2025)
This European Standard was approved by CEN on 1 November 2024.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2025 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 16610-45:2025 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 16610-45:2025) has been prepared by Technical Committee ISO/TC 213
"Dimensional and geometrical product specifications and verification" in collaboration with Technical
Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the
secretariat of which is held by AFNOR.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by September 2025, and conflicting national standards
shall be withdrawn at the latest by September 2025.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 16610-45:2025 has been approved by CEN as EN ISO 16610-45:2025 without any
modification.
International
Standard
ISO 16610-45
First edition
Geometrical product specifications
2025-02
(GPS) — Filtration —
Part 45:
Morphological profile filters:
Segmentation
Spécification géométrique des produits (GPS) — Filtrage —
Partie 45: Filtres de profil morphologiques : Segmentation
Reference number
ISO 16610-45:2025(en) © ISO 2025

ISO 16610-45:2025(en)
© ISO 2025
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
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or ISO’s member body in the country of the requester.
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Email: copyright@iso.org
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Published in Switzerland
ii
ISO 16610-45:2025(en)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 Terms related to geometrical features.1
3.2 Terms related to segmentation .3
3.3 Terms related to pruning .6
3.4 Terms related to the motif method .9
4 Segmentation details . 10
4.1 General .10
4.2 Basic segmentation .10
4.3 Watershed segmentation using Wolf pruning .11
4.3.1 General .11
4.3.2 Calculation method for watershed segmentation using Wolf pruning .11
4.4 Crossing-the-line segmentation . 12
4.4.1 General . 12
4.4.2 Calculation method for crossing-the-line segmentation . 12
5 General information . 14
Annex A (informative) Crossing-the-line segmentation to determine profile elements.15
Annex B (informative) Other segmentation information — Hyperreal numbers .21
Annex C (informative) Relationship to the filtration matrix model .23
Annex D (informative) Concept diagrams .24
Annex E (informative) Relationship to the GPS matrix model .28
Bibliography .29

iii
ISO 16610-45:2025(en)
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 document 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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
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 213, Dimensional and geometrical product
specifications and verification, in collaboration with the European Committee for Standardization (CEN)
Technical Committee CEN/TC 290, Dimensional and geometrical product specification and verification, in
accordance with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
A list of all parts in the ISO 16610 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
ISO 16610-45:2025(en)
Introduction
This document is a geometrical product specification (GPS) standard and is to be regarded as a general GPS
standard (see ISO 14638). It influences chain links C and E in the GPS matrix structure.
The ISO GPS matrix model given in ISO 14638 gives an overview of the ISO GPS system of which this
document is a part. The fundamental rules of ISO GPS given in ISO 8015 apply to this document and the
default decision rules given in ISO 14253-1 apply to specifications made in accordance with this document,
unless otherwise indicated.
For more information on the relationship of this document to filtration matrix model, see Annex C.
For more detailed information on the relationship of this document to other standards and the GPS matrix
model, see Annex E.
This document develops the terminology and concepts for profile segmentation.
This document will replace part of ISO 21920-2 as the source document for profile segmentation. ISO 21920-2
is under revision and its definitions will be aligned with this document.

v
International Standard ISO 16610-45:2025(en)
Geometrical product specifications (GPS) — Filtration —
Part 45:
Morphological profile filters: Segmentation
1 Scope
This document defines the terminology and develops concepts for profile morphological segmentation. In
particular it specifies the watershed segmentation method, the Wolf pruning method and the crossing-the-
line method. This document assumes a continuous surface.
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, Geometrical product specifications (GPS) — Filtration — Part 1: Overview and basic concepts
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16610-1 and the following apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1 Terms related to geometrical features
3.1.1
topographic feature
line or point feature on a profile
3.1.1.1
line feature
hill or dale
3.1.1.2
point feature
peak or pit
3.1.2
peak
point on the profile which is higher than all other points within the
neighbourhood of that point
Note 1 to entry: There is a theoretical possibility of a plateau. In this case, the peak is the middle single point on the
plateau. Alternatively, techniques given in Annex B can be used.

ISO 16610-45:2025(en)
3.1.3
peak
highest point of a hill (3.1.7)
Note 1 to entry: There is a theoretical possibility of a plateau. In this case, the peak is the middle single point on the
plateau. Alternatively, techniques given in Annex B can be used.
3.1.4
pit
point on the profile which is lower than all other points within the neighbourhood
of that point
Note 1 to entry: There is a theoretical possibility of a plateau. In this case, the pit is the middle single point on the
plateau. Alternatively, techniques given in Annex B can be used.
3.1.5
pit
lowest point of a dale (3.1.9)
Note 1 to entry: There is a theoretical possibility of a plateau. In this case, the pit is the middle single point on the
plateau. Alternatively, techniques given in Annex B can be used.
3.1.6
hill
region around a peak such that all maximal upward paths end at the peak
Note 1 to entry: See Figure 1.
Key
X X-axis (reference line)
Y height
A peak
B pit
C hill local height
D dale local depth
Figure 1 — Hill local height and dale local depth (watershed segmentation)
3.1.7
hill
outwardly directed (from material to surrounding medium) contiguous portion of the profile
above the reference line bounded by the two adjacent points where the ordinate values change their sign
Note 1 to entry: See Figure 2.

ISO 16610-45:2025(en)
Key
X X-axis (reference line) D dale
Y height E change of sign of the ordinate values
A peak F peak height
B pit G pit depth
C hill
Figure 2 — Peak height and pit depth (reference line)
3.1.8
dale
region around a pit such that all maximal downward paths end at the pit
Note 1 to entry: See Figure 1.
3.1.9
dale
inwardly directed (from surrounding medium to material) contiguous portion of the profile
below the reference line bounded by the two adjacent points where the ordinate values change their sign
Note 1 to entry: See Figure 2.
3.2 Terms related to segmentation
3.2.1
segmentation
method which partitions a profile into distinct topographic features
Note 1 to entry: In this document, there are two types of segmentation:
a) watershed segmentation (see 4.3);
b) crossing-the-line segmentation (see 4.4).
3.2.1.1
watershed segmentation
filtration operation that spatially decomposes a profile into mutually exclusive portions of that profile
3.2.1.2
crossing-the-line segmentation
operation based on crossings of the reference line by a profile in conjunction with a combination algorithm,
to leave a set of significant segments
Note 1 to entry: The crossing-the-line segmentation requires height discrimination (see 3.3.6.2).

ISO 16610-45:2025(en)
3.2.1.3
event
mutually exclusive profile portions whose union covers the profile
EXAMPLE Ordinate values, motifs.
3.2.2
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: A full mathematical description of the segmentation function and the three segmentation properties
can be found in Reference [8].
3.2.3
first segmentation property
property where each event is allocated to the set of significant events or the set of insignificant
events but not both
Note 1 to entry: This property can also be given as a mathematical equation as follows:
P1 ∀⊆AE , ΨΦ()AA∪ () =AAandΨΦ() ∩ ()A = ∅
where
P1 is a first segmentation property;
E is the set of all events;
A is a subset of E;
Ψ . maps events onto the set of significant events;
()
Φ(). maps events onto the set of insignificant events (see Figure 3).
Figure 3 — Venn diagram of first segmentation property
Note 2 to entry: (.), and throughout this document, the dot is a placeholder for any set of events.
3.2.4
second segmentation property
property where a significant event is removed from the set of events, then the remaining significant
events are contained in the new set of significant events
Note 1 to entry: This property can also be given as a mathematical equation as follows:

ISO 16610-45:2025(en)
P2 ∀⊆AB⊆EA, ΦΦ⊆ B
() ()
where
P2 is a second segmentation property;
E is the set of all events;
A and B are subsets of E;
Φ(). maps events onto the set of insignificant events (see Figure 4).
NOTE The shaded areas are the significant events for subset A.
Figure 4 — Venn diagram of second segmentation property
3.2.5
third segmentation property
property where an insignificant event is removed from the set of events, then the same set of
significant events is obtained
Note 1 to entry: This property can also be given as a mathematical equation as follows:
∀⊆AB⊆EB, ΨΨ⊆⇒AA =Ψ B
P3 () () ()
where
P3 is a third segmentation property;
E is the set of all events;
A and B are subsets of E;
Ψ (). maps events onto the set of significant events (see Figure 5).
Figure 5 — Venn diagram of third segmentation property

ISO 16610-45:2025(en)
3.3 Terms related to pruning
3.3.1
hill change tree
graph which describes the relationships between peaks and pits sorted by their hill local heights (3.3.5.1)
Note 1 to entry: Peaks are represented on a hill change tree by the ends of lines. Pits are represented on a hill change
tree by joining lines.
Note 2 to entry: See Figure 6.
Key
X X-axis (reference line)
Y height
P peak
V pit
NOTE The filled areas indicate hills for watershed segmentation.
Figure 6 — Hill change tree
3.3.2
dale change tree
graph which describes the relationships between pits and peaks sorted by their dale local depths (3.3.5.4)
Note 1 to entry: Pits are represented on a dale change tree by the ends of lines. Peaks are represented on a dale change
tree by joining lines.
Note 2 to entry: See Figure 7.

ISO 16610-45:2025(en)
Key
X X-axis (reference line)
Y height
P peak
V pit
NOTE The filled areas indicate dales for watershed segmentation.
Figure 7 — Dale change tree
3.3.3
change tree
hill change tree or dale change tree
3.3.4
profile pruning
method to simplify a change tree in which lines from peaks (or pits) to t
...