1、BSI Standards PublicationBS EN ISO 16610-71:2014Geometrical productspecifications (GPS) FiltrationPart 71: Robust areal filters: Gaussianregression filtersBS EN ISO 16610-71:2014 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO16610-71:2014.The UK participati
2、on 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 necessaryprovisions of a contract. Users are responsibl
3、e for its correctapplication. The British Standards Institution 2014. Published by BSI StandardsLimited 2014ISBN 978 0 580 76440 0ICS 17.040.20Compliance with a British Standard cannot confer immunity fromlegal obligations.This British Standard was published under the authority of theStandards Polic
4、y and Strategy Committee on 30 September 2014.Amendments issued since publicationDate Text affectedEUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-71 September 2014 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration - Part 71: Robust areal filters: Gau
5、ssian regression filters (ISO 16610-71:2014) Spcification gomtrique des produits (GPS) - Filtrage - Partie 71: Filtres surfaciques robustes: Filtres de rgression gaussiens (ISO 16610-71:2014) Geometrische Produktspezifikation (GPS) - Filterung - Teil 71: Robuste Flchenfilter: Gausche Regressionsfilt
6、er (ISO 16610-71:2014) This European Standard was approved by CEN on 16 August 2014. 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 a
7、nd 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
8、 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 Yugosl
9、av 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 COMIT EUROPEN D
10、E NORMALISATION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2014 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-71:2014 EBS EN ISO 16610-71:2014EN ISO 16610-71:2014 (E)
11、 3 Foreword This document (EN ISO 16610-71:2014) 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 sec
12、retariat 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 March 2015, and conflicting national standards shall be withdrawn at the latest by March 2015. Attention is draw
13、n 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 followin
14、g 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, Norw
15、ay, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-71:2014 has been approved by CEN as EN ISO 16610-71:2014 without any modification. BS EN ISO 16610-71:2014ISO 16610-71:2014(E) ISO 2014 All rights re
16、served iiiContents PageForeword ivIntroduction vi1 Scope . 12 Normative references 13 Terms and definitions . 14 Robust planar Gaussian regression filter .24.1 General . 24.2 Weighting function 24.3 Filter equation . 34.4 Transmission characteristics 55 Robust cylindrical Gaussian regression filter
17、55.1 General . 55.2 Weighting function 55.3 Filter equation . 65.4 Transmission characteristics 76 Nesting Index for planar and cylinder surfaces . 87 Filter designation. 8Annex A (informative) Regression filter . 9Annex B (informative) Examples .11Annex C (informative) Relationship to the filtratio
18、n matrix model 16Annex D (informative) Relation to the GPS matrix model .18Bibliography .20BS EN ISO 16610-71:2014ISO 16610-71:2014(E)ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of preparing Int
19、ernational 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 w
20、ith 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 Directive
21、s, 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
22、 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 declaration
23、s 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 IS
24、Os adherence to the WTO principles in the Technical Barriers to Trade (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 pa
25、rts, under the general title Geometrical product specifications (GPS) Filtration: Part 1: Overview and basic concepts Technical Specification Part 20: Linear profile filters: Basic concepts Technical Specification Part 21: Linear profile filters: Gaussian filters Part 22: Linear profile filters: Spl
26、ine filters Technical Specification Part 28: Profile filters: End effects Technical Specification Part 29: Linear profile filters: Spline wavelets Technical Specification Part 30: Robust profile filters: Basic concepts Technical Specification Part 31: Robust profile filters: Gaussian regression filt
27、ers Technical Specification Part 32: Robust profile filters: Spline filters Technical Specification Part 40: Morphological profile filters: Basic concepts Technical Specification Part 41: Morphological profile filters: Disk and horizontal line-segment filters Technical Specification Part 49: Morphol
28、ogical profile filters: Scale space techniques Technical Specification Part 60: Linear areal filters Basic concepts Part 61: Linear areal filters Gaussian filters Part 71: Robust areal filters: Gaussian regression filtersiv ISO 2014 All rights reservedBS EN ISO 16610-71:2014ISO 16610-71:2014(E) Part
29、 85: Areal Morphological: 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 42: Morphological profile filters: Moti
30、f filters 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 hor
31、izontal planar segment filters Part 82: Morphological areal filters: Motif filters Part 89: Morphological areal filters: Scale space techniques ISO 2014 All rights reserved vBS EN ISO 16610-71:2014ISO 16610-71:2014(E)IntroductionThis part of ISO 16610 is a Geometrical Product Specification (GPS) sta
32、ndard and is to be regarded as a Global GPS standard (see ISO/TR 14638). It influences the chain links 3 and 5 of all chains of standards.The ISO/GPS Masterplan given in ISO/TR 14638 gives an overview of the ISO/GPS system of which this standard is a part. The fundamental rules of ISO/GPS given in I
33、SO 8015 apply to this standard and the default decision rules given in ISO 14253-1 apply to specifications made in accordance with this standard, unless otherwise indicated.For more detailed information of the relation of this document to the GPS matrix model, see Annex C.This part of ISO 16610 spec
34、ifies the metrological characteristics of robust areal Gaussian regression filters, for the rotationally symmetric filtration of nominal planar surfaces and the filtration of nominal cylindrical surfaces.The filter is insensitive against specific phenomena in the input data (e.g. spike discontinuiti
35、es as well as deep valleys and high peaks, etc.). The boundaries of the measured surface are still usable.vi ISO 2014 All rights reservedBS EN ISO 16610-71:2014INTERNATIONAL STANDARD ISO 16610-71:2014(E)Geometrical product specifications (GPS) Filtration Part 71: Robust areal filters: Gaussian regre
36、ssion filters1 ScopeThis part of ISO 16610 specifies the characteristics of the robust areal Gaussian regression filter for the evaluation of surfaces that may contain spike discontinuities as well as deep valleys and high peaks. It specifies in particular how to separate large scale lateral compone
37、nts and short scale lateral components of a surface.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 edit
38、ion of the referenced document (including any amendments) applies.ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic conceptsISO 16610-30:1), Geometrical product specifications (GPS) Filtration Part 30: Robust profile filters: Basic conceptsISO/IEC Guide 99,
39、International vocabulary of metrology Basic and general concepts and associated terms (VIM)ISO/IEC Guide 98-3, Uncertainty of measurement Part 3: Guide to the expression of uncertainty in measurement (GUM:1995)3 Terms and definitionsFor the purposes of this document, the terms and definitions given
40、in ISO 16610-1, ISO 16610-30, ISO/IEC Guide 99 and ISO/IEC Guide 98-3 and the following apply.3.1robust planar filternon linear areal filter to separate a planar surface with specific phenomena (e.g. spike discontinuities as well as deep valleys and high peaks etc.) into large scale lateral componen
41、ts and short scale lateral components3.2robust cylindrical filternon linear areal filter to separate a cylindrical surface with specific phenomena (e.g. spike discontinuities as well as deep valleys and high peaks etc.) into large scale lateral components and short scale lateral components1) To be p
42、ublished. (Revision of ISO/TS 16610-30:2009) ISO 2014 All rights reserved 1BS EN ISO 16610-71:2014ISO 16610-71:2014(E)3.3biweight functionasymmetric influence function defined byBforforucuucucuc,()=1022(1)where c is the real scale parameter and u is a real numberNote 1 to entry: See ISO 16610-30:, F
43、igure 4.3.4robust areal regression filterweighted Mestimator based on the areal local complete polynomial modelling of the surfaceNote 1 to entry: See ISO 16610-30 for the definition of the weighted M-estimator.Note 2 to entry: See Annex A for the mathematical definition of the robust areal regressi
44、on filter.3.5robust areal Gaussian regression filterrobust areal regression filter based on the areal Gaussian weighting function, the biweight influence function and a local complete polynomial modelling of the surface with the degree p=2 as the default caseNote 1 to entry: to entry:See ISO 16610-6
45、1 for the definition of the areal Gaussian weighting function.Note 2 to entry: to entry:In case of p=2, the robust areal Gaussian regression filter follows a complete polynomial up to second degree.4 Robust planar Gaussian regression filter4.1 GeneralRobust planar Gaussian regression filters complyi
46、ng to this document shall conform to sections 4.2 to 4.4.4.2 Weighting functionThe weighting function of the robust planar Gaussian regression filter depends on the surface values (height to the reference surface) and the location of the weighting function on the surface.2 ISO 2014 All rights reserv
47、edBS EN ISO 16610-71:2014ISO 16610-71:2014(E)4.3 Filter equationThe filter equation is given bywimj nij ijTij ij ijTij=()()=100000 111XSXXSz,., ,., (2)with the surface valuesz =()zzzzmnmnT11 11 (3)The regression function is spanned by the matrix:Xijijij ijmi jmijmi jxyxy xyxyxy xy=111111 121211212 1
48、11112222xyxy xyxyxxyinjinj injmi nj mi nj mi nj (4)wherexkix kmki=()= ,.,1 (5)andyljy lnlj=()= ,.,1 (6)The spatial varying weighting function Sijis given by:Sijijmijmnijnmnij mnssss=11 111111000000midhorizellipsisdownslopeellipsisvertellipsisdownslopeellipsisvertellipsisdownslopeellipsismidhorizelli
49、psis(7)with the Gaussian weighting function:sxykmlklijcki ljc=+=11122 2222piexp , , ,n (8)The constant is given by:pi= 101W12e ,7309 (9)with the branch W()11u of the “Lambert W” function 7. ISO 2014 All rights reserved 3BS EN ISO 16610-71:2014ISO 16610-71:2014(E)The weights ijare derived from the biweight function as follows:ijij ijij i
