1、BSI Standards PublicationBS EN ISO 16610-60:2015Geometrical ProductSpecification (GPS) FiltrationPart 60: Linear areal filters: Basic conceptsBS EN ISO 16610-60:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO16610-60:2015.The UK participation in its pre
2、paration was entrusted to TechnicalCommittee TDW/4, Technical Product Realization.A list of organizations represented on this committee can beobtained on request to its secretary.This publication does not purport to include all the necessaryprovisions of a contract. Users are responsible for its cor
3、rectapplication. The British Standards Institution 2015.Published by BSI Standards Limited 2015ISBN 978 0 580 78865 9ICS 17.040.30Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Policy and Strateg
4、y Committee on 30 November 2015.Amendments/corrigenda issued since publicationDate T e x t a f f e c t e dEUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-60 November 2015 ICS 17.040.30 English Version Geometrical Product Specification (GPS) - Filtration - Part 60: Linear areal filters
5、: Basic concepts (ISO 16610-60:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 60: Filtres surfaciques linaires - Concepts de base(ISO 16610-60:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 60: Lineare Flchenfilter: Grundlegende Konzepte (ISO 16610-60:2015) Thi
6、s 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 referenc
7、es 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 me
8、mber 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, F
9、rance, 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 COMIT EUROPEN DE NORMALISATION EUROPISCHES
10、 KOMITEE FR 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 worldwide for CEN national Members. Ref. No. EN ISO 16610-60:2015 EBS EN ISO 16610-60:2015EN ISO 16610-60:2015 (E) 3 European foreword This d
11、ocument (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
12、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 t
13、hat 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
14、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,
15、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. BS EN ISO 16610-60:2015ISO 16610-60:2015(E)Foreword ivIntroduction vi1 Scope . 12 Normat
16、ive references 13 Terms and definitions . 14 Basic concepts . 34.1 General . 34.2 Separable weighting functions 34.3 Discrete representation of data 44.4 Discrete representation of the linear areal filter . 44.5 Discrete representation of the weighting function 55 Linear areal filters 75.1 Filter eq
17、uations 75.2 Discrete convolution 85.3 Transfer function . 95.4 Separable filter banks 11Annex A (informative) Concept diagram .13Annex B (informative) Relationship to the filtration matrix model .14Annex C (informative) Relationship to the GPS matrix model 15Bibliography .16 ISO 2015 All rights res
18、erved iiiContents PageBS EN ISO 16610-60:2015ISO 16610-60:2015(E)ForewordISO (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 co
19、mmittees. 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 th
20、e 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 t
21、he 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.
22、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 do
23、cument 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 ISOs adherence to the WTO principles in the Technical Barriers to Tra
24、de (TBT) see the following URL: Foreword - Supplementary informationThe 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 (GP
25、S) 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
26、 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
27、 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 filtersiv ISO 2015 All rights reservedBS EN ISO 16610-60:2015ISO 16610-60:2015(E) Part 85: Morphological areal fil
28、ters: SegmentationThe 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: Li
29、near 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 segmen
30、t filters Part 89: Morphological areal filters: Scale space techniques ISO 2015 All rights reserved vBS EN ISO 16610-60:2015ISO 16610-60:2015(E)IntroductionThis 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
31、 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
32、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 f
33、ilters, which include Gaussian filter, Spline filters, and Wavelet filters.vi ISO 2015 All rights reservedBS EN ISO 16610-60:2015INTERNATIONAL STANDARD ISO 16610-60:2015(E)Geometrical product specification (GPS) Filtration Part 60: Linear areal filters Basic concepts1 ScopeThis part of ISO 16610 set
34、s out the basic concepts of linear areal filters.2 Normative referencesThe 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
35、 of the referenced document (including any amendments) applies.ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic conceptsISO 16610-20, Geometrical product specifications (GPS) Filtration Part 20: Linear profile filters: Basic conceptsISO 16610-21:2011, Geome
36、trical product specifications (GPS) Filtration Part 21: Linear profile filters: Gaussian filtersISO/IEC Guide 99:2007, International vocabulary of metrology Basic and general concepts and associated terms (VIM)3 Terms and definitionsFor the purposes of this document, the terms and definitions given
37、in ISO 16610-1, ISO 16610-20, ISO 16610-21, ISO/IEC Guide 99, and the following apply.3.1linear areal filterareal filter which separates surfaces into long wave and short wave components and is also a linear functionNote 1 to entry: If F is a function and X and Y are surfaces then F is a linear func
38、tion 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.3.1.1linear planar filterli
39、near areal filter (3.1) which separates planar surfaces into long wave and short wave components, which applies to nominal planar surfacesNote 1 to entry: A planar surface is open in all directions. ISO 2015 All rights reserved 1BS EN ISO 16610-60:2015ISO 16610-60:2015(E)3.1.2linear cylindrical filt
40、erlinear areal filter (3.1) which separates cylindrical surfaces into long wave and short wave components, which applies to nominal cylindrical surfaceNote 1 to entry: A cylindrical surface is open in the axial direction and closed in the circumferential direction.3.2phase correct areal filterlinear
41、 areal filter (3.1) which does not cause phase shifts leading to asymmetrical surface distortionsNote 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,
42、 which is a phase correct filter.3.3mean surfacelong wave surface component determined from the surface by application of an areal filter3.4weighting functionfunction for calculating the mean surface, which indicates for each point the weight attached by the surface in the vicinity of that point3.5f
43、ilter equationequation for the mathematical description of the filterNote 1 to entry: Filter equations do not necessarily specify an algorithm for the numerical realization of the filter.SOURCE: ISO 16610-1:2015, 3.103.6transmission characteristic of an areal filtercharacteristic that indicates the
44、amount by which the amplitude of a sinusoidal surface is attenuated as a function of its wavelengthsNote 1 to entry: The transmission characteristic is the Fourier transformation of the weighting function.3.7cut-off wavelength (nesting index)wavelength of a sinusoidal surface of which 50 % of the am
45、plitude 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 conv
46、ention.3.8filter bankset of high-pass and low-pass filters, arranged in a specified structureSOURCE: ISO 16610-20:2015, 3.63.9multiresolution analysisdecomposition of a surface by a filter bank (3.8) into portions of different scalesNote 1 to entry: The portions at different scales are also referred
47、 to as resolutions.SOURCE: ISO 16610-20:2015, 3.72 ISO 2015 All rights reservedBS EN ISO 16610-60:2015ISO 16610-60:2015(E)4 Basic concepts4.1 GeneralA filter claiming to comply with this part of ISO 16610 shall exhibit the characteristics described in 4.1, 4.2, 4.3, and 4.4.NOTE A concept diagram fo
48、r linear areal filters is given in Annex A. The relationship to the filtration matrix model is given in Annex B.The most general linear areal filter is defined by Formula (1):wxyKxy zdd(, )(,;,)(,)= (1)wherez (,) is the unfiltered surface;w (x,y) is the filtered surface;K (x, y: , ) is the kernel of
49、 the filter, which is real, symmetric, and spatial invariant.If KxyKxy(, ;,)( ,) = , the filtering is a convolution,wxyKxyzdd(, )(,)(,)= (2)and the kernel is also called the weighting function of the filter.However, extracted data are always discrete. Therefore, the filters described here are also discrete. In cases that the weighting function is not discrete, the discrete nature of the extracted data shall be taken into account (see 4.3).NOTE An alternative approach is t
