1、BSI Standards PublicationBS EN ISO 16610-22:2015Geometrical productspecifications (GPS) FiltrationPart 22: Linear profile filters: Spline filtersBS EN ISO 16610-22:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO16610-22:2015. It supersedes DD ISO/TS 166
2、10-22:2006 which iswithdrawn.The UK participation in its preparation 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 necessar
3、yprovisions of a contract. Users are responsible for its correctapplication. The British Standards Institution 2015. Published by BSI StandardsLimited 2015ISBN 978 0 580 77994 7ICS 17.040.20Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was publ
4、ished under the authority of theStandards Policy and Strategy Committee on 31 July 2015.Amendments issued since publicationDate Text affectedEUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-22 July 2015 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration
5、 - Part 22: Linear profile filters: Spline filters (ISO 16610-22:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 22: Filtres de profil linaires: Filtres splines (ISO 16610-22:2015) This European Standard was approved by CEN on 7 May 2015. CEN members are bound to comply with the
6、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
7、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
8、 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, Net
9、herlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2015 CEN All r
10、ights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-22:2015 EBS EN ISO 16610-22:2015EN ISO 16610-22:2015 (E) 3 European foreword This document (EN ISO 16610-22:2015) has been prepared by Technical Committee ISO/TC 213 “Dimensional and
11、 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 b
12、y publication of an identical text or by endorsement, at the latest by January 2016, and conflicting national standards shall be withdrawn at the latest by January 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 C
13、ENELEC 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 Rep
14、ublic, 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. End
15、orsement notice The text of ISO 16610-22:2015 has been approved by CEN as EN ISO 16610-22:2015 without any modification. BS EN ISO 16610-22:2015ISO 16610-22:2015(E)Foreword ivIntroduction vi1 Scope . 12 Normative references 13 Terms and definitions . 14 Spline profile filters . 24.1 General . 24.2 W
16、eighting function 24.3 Filter equations 24.3.1 General 24.3.2 Filter equation for the non-periodic spline profile filter . 34.3.3 Filter equation for the periodic spline profile filter 44.4 Transmission characteristics 44.4.1 General 44.4.2 Transmission characteristic of the long-wave profile compon
17、ent . 54.4.3 Transmission characteristic of the short-wave profile component . 55 Recommendations 65.1 Nesting index (cut-off values) 65.2 Tension parameter () 65.3 Implementation 66 Filter designation. 7Annex A (informative) Influence of the sampling interval 8Annex B (informative) Comparison of sp
18、line profile filter and Gaussian filter . 9Annex C (informative) Illustrative examples.10Annex D (informative) Concept diagram .14Annex E (informative) Relationship to the filtration matrix model 15Annex F (informative) Relationship to the GPS matrix model 16Bibliography .18 ISO 2015 All rights rese
19、rved iiiContents PageBS EN ISO 16610-22:2015ISO 16610-22:2015(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 com
20、mittees. 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
21、 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 th
22、e 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. IS
23、O 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 docum
24、ent 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 Trade
25、(TBT) see the following URL: Foreword - Supplementary informationThe committee responsible for this document is ISO/TC 213, Dimensional and geometrical product specifications and verification.This first edition of ISO 16610-22 cancels and replaces ISO/TS 16610-22:2006, which has been technically rev
26、ised.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
27、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 co
28、ncepts 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 conceptsiv ISO 2015 All rights reservedBS EN ISO 16610-22:2015ISO 16610-22:2015(E) Part 61: Linear areal filters
29、: Gaussian filters 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 no
30、minally 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: Morphol
31、ogical 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 16610-22:2015ISO 16610-22:2015(E)IntroductionThis part of ISO 16610 is a geomet
32、rical product specification (GPS) standard and is to be regarded as a general GPS standard (see ISO/TR 14638). It influences the feature characteristics and measurement chain links 3 and 5 in the GPS matrix structure.The ISO/GPS Masterplan given in ISO/TR 14638 gives an overview of the ISO/GPS syste
33、m 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 inf
34、ormation about the relation of this part of ISO 16610 to the GPS matrix model, see Annex F.This part of ISO 16610 develops the terminology and concepts of spline filters.The spline filter has an advantage over a conventional phase correct filter in that for open profiles, the ends of the measured pr
35、ofile are still usable.vi ISO 2015 All rights reservedBS EN ISO 16610-22:2015INTERNATIONAL STANDARD ISO 16610-22:2015(E)Geometrical product specifications (GPS) Filtration Part 22: Linear profile filters: Spline filters1 ScopeThis part of ISO 16610 specifies spline filters for the filtration of prof
36、iles. It specifies in particular how to separate the long- and short-wave component of a profile.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 app
37、lies. 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 terminologyISO 16610-20:2015, Geometrical product specifications (GPS) Filtration Part 20: L
38、inear profile filters: Basic conceptsISO/IEC Guide 99:2007, International vocabulary of metrology Basic and general concepts and associated terms (VIM)ISO/IEC Guide 98-3:2008, Uncertainty of measurement Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)3 Terms and definitionsFo
39、r the purposes of this document, the terms and definitions given in ISO/IEC Guide 99:2007 (VIM), ISO 16610-1, and ISO 16610-20 and the following apply.3.1splinelinear combination of piecewise polynomials, with a smooth fit between the piecesNote 1 to entry: The degree of the spline is equal to the d
40、egree of the polynomial of the highest degree used, e.g. a cubic spline is made of cubic polynomials.3.2cardinal splinebasic function of the space of splines (3.1) with infinite support3.3natural splinespline (3.1) which is a straight line beyond the end points3.4spline profile filterlinear profile
41、filter based on splines (3.1)Note 1 to entry: For the purposes of this part of ISO 16610, the result of the low-pass filtering is a spline. ISO 2015 All rights reserved 1BS EN ISO 16610-22:2015ISO 16610-22:2015(E)4 Spline profile filters4.1 GeneralFor a spline filter to conform with this part of ISO
42、 16610, it shall satisfy the filter equations given in 4.3.2, for open profiles, and 4.3.3, for closed profiles.NOTE A comparison with Gaussian filters is given in Annex B, and illustrative examples are given in Annex C. A concept diagram for the concepts of spline filters is given in Annex D, and t
43、he relationship to the filtration matrix model is given in Annex E.4.2 Weighting functionThe weighting function of a spline profile filter cannot be given by a simple closed formula. Filter equations are therefore used instead of weighting functions to describe the spline profile filters. However, w
44、here necessary, a numerical calculation of the weighting function for a spline profile filter is always possible. If the sampling interval x is small enough, and the spline profile filter is based on cardinal cubic splines, the weighting function sx(), with a default value of = 0, can be approximate
45、d by the continuous functionsx xx()=+pipipipiCC Csin|exp |242 (1)NOTE This is the weighting function of the ideal spline profile filter, based on cardinal cubic splines. A graph of this function is shown in Figure 1.Figure 1 Weighting function of the ideal spline profile filter, based on cardinal cu
46、bic splines4.3 Filter equations4.3.1 GeneralThe following filter equations for spline profile filters are based on cardinal cubic splines (for more details, see Reference 4).2 ISO 2015 All rights reservedBS EN ISO 16610-22:2015ISO 16610-22:2015(E)4.3.2 Filter equation for the non-periodic spline pro
47、file filterNon-periodic spline profile filters should be used in cases of filtering open profiles. The filter equation for the non-periodic spline profile filter is given by1P Q+()= 241 wz (2)where 1 is the identity matrix and PQ=1112 112 112 112 11112125downslopeellipsisdownslopeellipsisdownslopeel
48、lipsis4114641146411452121downslopeellipsisdownslopeellipsisdownslopeellipsisdownslopeellipsisdownslopeellipsis (3)with n rows, n columns, and the parameterspi=12sinCxand 0 1 (4)wheren is the number of extracted data values of the profile;z is the vector of dimension n of the profile values before fi
49、ltering;w is the vector of dimension n of the profile values in the filtered profile;cis the cut-off wavelength of the profile filter;x is the sampling interval.NOTE 1 The vector w gives the profile values of the long-wave component. The short-wave component r can be obtained by the difference vector r = z w, i.e. by subtracting the long wave-component values obtained by the filtering process from the extracted
