EN ISO 16610-60:2015

SLOVENSKI STANDARD
01-februar-2016
6SHFLILNDFLMDJHRPHWULMVNLKYHOLþLQL]GHOND*36)LOWULUDQMHGHO/LQHDUQL
UDYQLILOWULRVQRYQLSRMPL,62
Geometrical Product Specification (GPS) - Filtration - Part 60: Linear areal filters: Basic
concepts (ISO 16610-60:2015)
Geometrische Produktspezifikation (GPS) - Filterung - Teil 60: Lineare Flächenfilter:
Grundlegende Konzepte (ISO 16610-60:2015)
Spécification géométrique des produits (GPS) - Filtrage - Partie 60: Filtres de la ligne
moyenne - Concepts de base (ISO 16610-60:2015)
Ta slovenski standard je istoveten z: EN ISO 16610-60:2015
ICS:
17.040.10 Tolerance in ujemi Limits and fits
17.040.40 6SHFLILNDFLMDJHRPHWULMVNLK Geometrical Product
YHOLþLQL]GHOND*36 Specification (GPS)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 16610-60
EUROPEAN STANDARD
NORME EUROPÉENNE
November 2015
EUROPÄISCHE NORM
ICS 17.040.30
English Version
Geometrical Product Specification (GPS) - Filtration - Part
60: Linear areal filters: Basic concepts (ISO 16610-
60:2015)
Spécification géométrique des produits (GPS) - Filtrage Geometrische Produktspezifikation (GPS) - Filterung -
- Partie 60: Filtres surfaciques linéaires - Concepts de Teil 60: Lineare Flächenfilter: Grundlegende Konzepte
base(ISO 16610-60:2015) (ISO 16610-60:2015)
This European Standard was approved by CEN on 12 March 2015.

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, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2015 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 16610-60:2015 E
worldwide for CEN national Members.

Contents Page
European foreword . 3
European foreword
This document (EN ISO 16610-60:2015) 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 May 2016, and conflicting national standards shall be
withdrawn at the latest by May 2016.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent
rights.
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, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
Endorsement notice
The text of ISO 16610-60:2015 has been approved by CEN as EN ISO 16610-60:2015 without any
modification.
INTERNATIONAL ISO
STANDARD 16610-60
First edition
2015-10-01
Geometrical product specification
(GPS) — Filtration —
Part 60:
Linear areal filters — Basic concepts
Spécification géométrique des produits (GPS) — Filtrage —
Partie 60: Filtres surfaciques linéaires — Concepts de base
Reference number
ISO 16610-60:2015(E)
©
ISO 2015
ISO 16610-60:2015(E)
© ISO 2015, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2015 – All rights reserved

ISO 16610-60:2015(E)
Contents Page
Foreword .iv
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Basic concepts . 3
4.1 General . 3
4.2 Separable weighting functions . 3
4.3 Discrete representation of data . 4
4.4 Discrete representation of the linear areal filter . 4
4.5 Discrete representation of the weighting function . 5
5 Linear areal filters . 7
5.1 Filter equations . 7
5.2 Discrete convolution . 8
5.3 Transfer function . 9
5.4 Separable filter banks .11
Annex A (informative) Concept diagram .13
Annex B (informative) Relationship to the filtration matrix model .14
Annex C (informative) Relationship to the GPS matrix model .15
Bibliography .16
ISO 16610-60:2015(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 on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical
Barriers to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 213, Dimensional and geometrical product
specifications and verification.
ISO 16610 consists of the following parts, under the general title Geometrical product specifications
(GPS) — Filtration:
— Part 1: Overview and basic concepts
— Part 20: Linear profile filters: Basic concepts
— Part 21: Linear profile filters: Gaussian filters
— Part 22: Linear profile filters: Spline filters
— Part 28: Profile filters: End effects
— Part 29: Linear profile filters: Spline wavelets
— Part 30: Robust profile filters: Basic concepts
— Part 31: Robust profile filters: Gaussian regression filters
— Part 32: Robust profile filters: Spline filters
— Part 40: Morphological profile filters: Basic concepts
— Part 41: Morphological profile filters: Disk and horizontal line-segment filters
— Part 49: Morphological profile filters: Scale space techniques
— Part 60: Linear areal filters: Basic concepts
— Part 61: Linear areal filters: Gaussian filters
— Part 71: Robust areal filters: Gaussian regression filters
iv © ISO 2015 – All rights reserved

ISO 16610-60:2015(E)
— Part 85: Morphological areal filters: Segmentation
The following parts are planned:
— Part 26: Linear profile filters: Filtration on nominally orthogonal grid planar data sets
— Part 27: Linear profile filters: Filtration on nominally orthogonal grid cylindrical data sets
— Part 45: Morphological profile filters: Segmentation
— Part 62: Linear areal filters: Spline filters
— Part 69: Linear areal filters: Spline wavelets
— Part 70: Robust areal filters: Basic concepts
— Part 72: Robust areal filters: Spline filters
— Part 80: Morphological areal filters: Basic concepts
— Part 81: Morphological areal filters: Sphere and horizontal planar segment filters
— Part 89: Morphological areal filters: Scale space techniques
ISO 16610-60:2015(E)
Introduction
This part of ISO 16610 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 F of all chains of standards.
The ISO/GPS Matrix model given in ISO 14638 gives an overview of the ISO/GPS system of which this
part of ISO 16610 is a part. The fundamental rules of ISO/GPS given in ISO 8015 apply to this part of
ISO 16610 and the default decision rules given in ISO 14253-1 apply to specifications made in accordance
with this part of ISO 16610, unless otherwise indicated.
For more detailed information about the relation of this part of ISO 16610 to the GPS matrix model, see
Annex C.
This part of ISO 16610 develops the basic concepts of linear areal filters, which include Gaussian filter,
Spline filters, and Wavelet filters.
vi © ISO 2015 – All rights reserved

INTERNATIONAL STANDARD ISO 16610-60:2015(E)
Geometrical product specification (GPS) — Filtration —
Part 60:
Linear areal filters — Basic concepts
1 Scope
This part of ISO 16610 sets out the basic concepts of linear areal filters.
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable for its application. 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
ISO 16610-20, Geometrical product specifications (GPS) — Filtration — Part 20: Linear profile filters:
Basic concepts
ISO 16610-21:2011, Geometrical product specifications (GPS) — Filtration — Part 21: Linear profile filters:
Gaussian filters
ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and
associated terms (VIM)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 16610-1, ISO 16610-20,
ISO 16610-21, ISO/IEC Guide 99, and the following apply.
3.1
linear areal filter
areal filter which separates surfaces into long wave and short wave components and is also a linear
function
Note 1 to entry: If F is a function and X and Y are surfaces then F is a linear function implies
F(aX + bY) = aF(X) + bF(Y).
Note 2 to entry: A linear areal filter is for surfaces in a specified coordinate system, for example, planar and
cylindrical.
Note 3 to entry: Linear areal filter examples include Gaussian, spline, spline wavelet, and complex wavelet.
3.1.1
linear planar filter
linear areal filter (3.1) which separates planar surfaces into long wave and short wave components,
which applies to nominal planar surfaces
Note 1 to entry: A planar surface is open in all directions.
ISO 16610-60:2015(E)
3.1.2
linear cylindrical filter
linear areal filter (3.1) which separates cylindrical surfaces into long wave and short wave components,
which applies to nominal cylindrical surface
Note 1 to entry: A cylindrical surface is open in the axial direction and closed in the circumferential direction.
3.2
phase correct areal filter
linear areal filter (3.1) which does not cause phase shifts leading to asymmetrical surface distortions
Note 1 to entry: Phase correct filters are a particular kind of linear phase filters because any linear phase filter
can be transformed (simply by shifting its weighting function) to a zero phase filter, which is a phase correct filter.
3.3
mean surface
long wave surface component determined from the surface by application of an areal filter
3.4
weighting function
function for calculating the mean surface, which indicates for each point the weight attached by the
surface in the vicinity of that point
3.5
filter equation
equation for the mathematical description of the filter
Note 1 to entry: Filter equations do not necessarily specify an algorithm for the numerical realization of the filter.
[SOURCE: ISO 16610-1:2015, 3.10]
3.6
transmission characteristic of an areal filter
characteristic that indicates the amount by which the amplitude of a sinusoidal surface is attenuated as
a function of its wavelengths
Note 1 to entry: The transmission characteristic is the Fourier transformation of the weighting function.
3.7
cut-off wavelength (nesting index)
wavelength of a sinusoidal surface of which 50 % of the amplitude is transmitted by the linear areal
filter (3.1)
Note 1 to entry: Linear areal filters are identified by the filter type and the cut-off wavelength.
Note 2 to entry: The cut-off value for the linear areal filter is an example of a nesting index.
Note 3 to entry: The cut-off 50 % value is by convention.
3.8
filter bank
set of high-pass and low-pass filters, arranged in a specified structure
[SOURCE: ISO 16610-20:2015, 3.6]
3.9
multiresolution analysis
decomposition of a surface by a filter bank (3.8) into portions o
...