1、BSI Standards PublicationBS EN ISO 16610-20:2015Geometrical product specifications (GPS) FiltrationPart 20: Linear profile filters: Basic concepts BS EN ISO 16610-20:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO 16610-20:2015. It supersedes DD ISO/TS
2、16610-20:2006 which is withdrawn.The UK participation in its preparation was entrusted to Technical Committee TDW/4, Technical Product Realization.A list of organizations represented on this committee can be obtained on request to its secretary.This publication does not purport to include all the ne
3、cessary provisions of a contract. Users are responsible for its correct application. The British Standards Institution 2015.Published by BSI Standards Limited 2015ISBN 978 0 580 77993 0 ICS 17.040.20 Compliance with a British Standard cannot confer immunity from legal obligations.This British Standa
4、rd was published under the authority of the Standards Policy and Strategy Committee on 30 April 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 16610-20 April 2015 ICS 17.040.20 English Version Geometrical produc
5、t specifications (GPS) - Filtration - Part 20: Linear profile filters: Basic concepts (ISO 16610-20:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 20: Filtres de profil linaires: Concepts de base (ISO 16610-20:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 20:
6、Lineare Profilfilter: Grundlegende Konzepte (ISO 16610-20:2015) This European Standard was approved by CEN on 14 February 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
7、 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 o
8、ther 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 Republi
9、c, 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 CO
10、MMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES 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 16610-20:2015 EBS E
11、N ISO 16610-20:2015EN ISO 16610-20:2015 (E) 3 Foreword This document (EN ISO 16610-20:2015) has been prepared by Technical Committee ISO/TC 213“Dimensional and geometrical product specifications and verification“ in collaboration with TechnicalCommittee CEN/TC 290 “Dimensional and geometrical produc
12、t specification and verification” the secretariat ofwhich is held by AFNOR. This European Standard shall be given the status of a national standard, either by publication of an identicaltext or by endorsement, at the latest by October 2015, and conflicting national standards shall be withdrawn atthe
13、 latest by October 2015. Attention is drawn to the possibility that some of the elements of this document may be the subject of patentrights. 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 nationa
14、l standards organizations of the followingcountries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, CzechRepublic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece,Hungary, Iceland, Ireland, Italy, Latvia, Lithuania
15、, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-20:2015 has been approved by CEN as EN ISO 16610-20:2015 without anymodification. BS EN ISO 16610-20:2015ISO 166
16、10-20:2015(E)Foreword ivIntroduction vi1 Scope . 12 Normative references 13 Terms and definitions . 14 Basic concepts . 24.1 General . 24.2 Discrete representation of data 34.3 Discrete representation of the linear profile filter . 34.4 Discrete representation of the weighting function 35 Linear pro
17、file filters 65.1 Filter equations 65.2 Discrete convolution 65.3 Transfer function . 75.4 Filter banks . 10Annex A (informative) Concept diagram .11Annex B (informative) Relationship to the filtration matrix model .12Annex C (informative) Relationship to the GPS matrix model 13Bibliography .15 ISO
18、2015 All rights reserved iiiContents PageBS EN ISO 16610-20:2015ISO 16610-20:2015(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 throu
19、gh 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 collabora
20、tes 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 cr
21、iteria 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
22、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 nam
23、e used in this document is information given for the convenience of users and does not constitute an endorsementFor 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
24、 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.This first edition cancels and replaces ISO/TS 16610-20:2006 which has been technically
25、revised.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: Spli
26、ne 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
27、 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 filtersiv ISO 2015 All rights reservedBS EN ISO 16610-20:201
28、5ISO 16610-20:2015(E) Part 71: Robust areal filters: Gaussian regression filters Part 85: Morphological areal filters: 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
29、 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: Morp
30、hological areal filters: Basic concepts Part 81: Morphological areal filters: Sphere and horizontal planar segment filters Part 89: Morphological areal filters: Scale space techniques ISO 2015 All rights reserved vBS EN ISO 16610-20:2015ISO 16610-20:2015(E)IntroductionThis part of ISO 16610 is a geo
31、metrical product specification (GPS) standard and is to be regarded as a general GPS standard (see ISO/TR 14638). It influences chain links 3 and 5 in the GPS matrix structure.The ISO/GPS Masterplan given in ISO 14638 gives an overview of the ISO/GPS system of which this part of ISO 16610 is a part.
32、 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 the specifications made in accordance with this part of ISO 16610, unless otherwise indicated.For more detailed information about the relation of this part
33、 of ISO 16610 to the GPS matrix model, see Annex C.This part of ISO 16610 develops the basic concepts of linear filters, which include spline filters and spline wavelets, and the Gaussian filters.vi ISO 2015 All rights reservedBS EN ISO 16610-20:2015Geometrical product specifications (GPS) Filtratio
34、n Part 20: Linear profile filters: Basic concepts1 ScopeThis part of ISO 16610 describes the basic concepts of linear profile 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 r
35、eferences, 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 conceptsISO/IEC Guide 99:2007, International vocabulary of m
36、etrology Basic and general concepts and associated terms (VIM)3 Terms and definitionsFor the purposes of this document, the terms and definitions given in ISO/IEC Guide 99, ISO 16610-1, and the following apply.3.1linear profile filterprofile filter which separates profiles into long wave and short w
37、ave components and is also a linear functionNote 1 to entry: If F is a function and X and Y are profiles, then F being a linear function implies F(aX + bY) = aF(X) + bF(Y).3.2phase correct profile filterphase correct linear profile filterlinear profile filter (3.1) which does not cause phase shifts
38、leading to asymmetrical profile distortionsNote 1 to entry: Phase correct filters are a particular kind of the so called 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.3.3weigh
39、ting functionfunction for calculating the mean line which indicates, for each point, the weight attached by the profile in the vicinity of that pointNote 1 to entry: The transmission characteristic of the mean line is the Fourier transformation of the weighting function.INTERNATIONAL STANDARD ISO 16
40、610-20:2015(E) ISO 2015 All rights reserved 1BS EN ISO 16610-20:2015ISO 16610-20:2015(E)3.4transmission characteristic of a filtercharacteristic that indicates the amount by which the amplitude of a sinusoidal profile is attenuated as a function of its wavelengthNote 1 to entry: The transmission cha
41、racteristic is the Fourier transformation of the weighting function.3.5cut-off wavelengthwavelength of a sinusoidal profile of which 50 % of the amplitude is transmitted by the profile filterNote 1 to entry: Linear profile filters are identified by the filter type and the cut-off wavelength value.No
42、te 2 to entry: The cut-off wavelength is the recommended nesting index for linear profile filters.3.6filter bankset of high-pass and low-pass filters arranged in a specified structureNote 1 to entry: See 5.4 for further details.3.7multiresolution analysisdecomposition of a profile by a filter bank (
43、3.6) into portions of different scalesNote 1 to entry: The portions at different scales are also referred to as resolutions.4 Basic concepts4.1 GeneralFor a filter to conform with this part of ISO 16610, it shall exhibit the characteristics described in 5.1, 5.2, 5.3, and 5.4.NOTE A concept diagram
44、for linear profile filters is given in Annex A. The relationship to the filtration matrix model is given in Annex B.The most general linear profile filter is defined byyx Kx z() (,)( )=d (1)wherez() is the unfiltered profile;yx() is the filtered profile;Kx(,) is a real symmetric and spatial invarian
45、t kernel.If Kx Kx(,)( )=, the filtering is a convolution,yx Kx z() ()()=d (2)and the kernel is called the weighting function of the filter.However, extracted data are always discrete. Consequently, the filters described here are also discrete. If the weighting function is not discrete (see 4.4, Exam
46、ple 2), it shall be converted into a discrete representation.2 ISO 2015 All rights reservedBS EN ISO 16610-20:2015ISO 16610-20:2015(E)4.2 Discrete representation of dataAn extracted profile can be represented by a vector. The length n of this vector is equal to the number of data points. The samplin
47、g is assumed to be uniform, i.e. the sampling interval is constant. The ith data point of the profile is therefore the ith component of the vector.zaaaaainn=( . . )12 1(3)4.3 Discrete representation of the linear profile filterA linear profile filter is represented by a square matrix. The dimension
48、of this matrix is equal to the number of data points to be filtered. If the filter is non-periodic, the matrix is a constant diagonal (Toeplitz) matrix:Sabcbccbabccbcba= (4)Otherwise, if the filter is periodic, the matrix is a circulant matrix:Sabccbbabc ccbabccbabcccbabbc cb=downslopeellipsis downs
49、lopeellipsisdownslopeellipsisdownslopeellipsisdownslopeellipsis a(5)If the filter is phase correct, the matrix representing the filter is symmetrical, i.e. bbcc= = , (generally aaij ji= ) is valid. The sum of the matrix elements aijof each row i is constant and for low-pass filters equals one, i.e.aijj=1 (6)NOTE 1 In the case of a symmetrical matrix, the sum of the matrix elements aijof each column j is also constant and equals o
