1、December 2015 English price group 11No part of this translation may be reproduced without prior permission ofDIN Deutsches Institut fr Normung e. V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).ICS 17.040.30!%IJb“2383963www.din.d
2、eDIN EN ISO 16610-20Geometrical product specifications (GPS) Filtration Part 20: Linear profile filters: Basic concepts (ISO 16610-20:2015);English version EN ISO 16610-20:2015,English translation of DIN EN ISO 16610-20:2015-12Geometrische Produktspezifikation (GPS) Filterung Teil 20: Lineare Profil
3、filter: Grundlegende Konzepte (ISO 16610-20:2015);Englische Fassung EN ISO 16610-20:2015,Englische bersetzung von DIN EN ISO 16610-20:2015-12Spcification gomtrique des produits (GPS) Filtrage Partie 20: Filtres de profil linaires: Concepts de base (ISO 16610-20:2015);Version anglaise EN ISO 16610-20
4、:2015,Traduction anglaise de DIN EN ISO 16610-20:2015-12www.beuth.deDocument comprises 22 pagesDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be considered authoritative.11.15 DIN EN ISO 16610-20:2015-12 2 A comma is used as the decimal marker. National forew
5、ord This document (EN ISO 16610-20:2015) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” (Secretariat: DS, Denmark) in collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical product specification and ve
6、rification” (Secretariat: AFNOR, France). The responsible German body involved in its preparation was DIN-Normenausschuss Technische Grundlagen (DIN Standards Committee Technical Fundamentals), Working Committee NA 152-03-03 AA Oberflchen. The DIN Standards corresponding to the International Standar
7、ds referred to in this document are as follows: ISO 16610-1 DIN EN ISO 16610-1ISO 16610-21 DIN EN ISO 16610-21 ISO/IEC Guide 99 Internationales Wrterbuch der Metrologie (VIM)*)National Annex NA (informative) Bibliography DIN EN ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1:
8、 Overview and basic concepts DIN EN ISO 16610-21, Geometrical product specifications (GPS) Filtration Part 21: Linear profile filters: Gaussian filters DIN V 32950, Geometrical product specification (GPS) Masterplan VIM, International vocabulary of metrology *)Obtainable from: Beuth Verlag GmbH, 107
9、72 Berlin, Order no. 22472, ISBN 978-3-410-22472-3. EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-20 April 2015 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration - Part 20: Linear profile filters: Basic concepts (ISO 16610-20:2015) Spcification gomt
10、rique des produits (GPS) - Filtrage - Partie 20: Filtres de profil linaires: Concepts de base (ISO 16610-20:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 20: Lineare Profilfilter: Grundlegende Konzepte (ISO 16610-20:2015) This European Standard was approved by CEN on 14 February 2
11、015. 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
12、 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-CE
13、NELEC 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, It
14、aly, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION C O M I T EUR O P EN D E NOR M A L I S ATI O N EUR O P I S C HES KOM I T E E F R NOR M UNG CEN-
15、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 E Foreword 3Introduction 51 Scope . 62 Normative references 63 Terms and definitions . 64 Basic con
16、cepts . 74.1 General . 74.2 Discrete representation of data 84.3 Discrete representation of the linear profile filter . 84.4 Discrete representation of the weighting function 85 Linear profile filters . 115.1 Filter equations . 115.2 Discrete convolution . 115.3 Transfer function 125.4 Filter banks
17、. 15Annex A (informative) Concept diagram .16Annex B (informative) Relationship to the filtration matrix model .17Annex C (informative) Relationship to the GPS matrix model 18Bibliography .20Contents PageDIN EN ISO 16610-20:2015-12 EN ISO 16610-20:2015 (E) 2 Foreword This document (EN ISO 16610-20:2
18、015) 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 Eur
19、opean Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2015, and conflicting national standards shall be withdrawn at the latest by October 2015. Attention is drawn to the possibility that some of the el
20、ements 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. ISO 16610 consists of the following parts, under the general title Geometrical product specifications (GPS) Filtration : Part 1: Overview and b
21、asic 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
22、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 techniqu
23、es Part 60: Linear areal filters: Basic concepts Part 61: Linear areal filters: 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 orth
24、ogonal 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 waveletsDIN EN ISO 16610-20:2015-12 EN
25、ISO 16610-20:2015 (E) 3 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 o
26、f 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 16610-20:2015 has been appro
27、ved by CEN as EN ISO 16610-20:2015 without any modification. 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: Mo
28、rphological areal filters: Scale space techniquesDIN EN ISO 16610-20:2015-12 EN ISO 16610-20:2015 (E) 4 IntroductionThis part of ISO 16610 is a geometrical 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 th
29、e 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. 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 spec
30、ifications 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 filters, which include spline filters and
31、 spline wavelets, and the Gaussian filters.DIN EN ISO 16610-20:2015-12 EN ISO 16610-20:2015 (E) 5 1 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 a
32、re 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 conceptsISO
33、/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 in ISO/IEC Guide 99, ISO 16610-1, and the following apply.3.1linear profile filterprofile filter wh
34、ich separates profiles 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 profiles, then F being a linear function implies F(aX + bY) = aF(X) + bF(Y).3.2phase correct profile filterphase correct linear profile filterlinear profil
35、e filter (3.1) which does not cause phase shifts 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 phas
36、e filter which is a phase correct filter.3.3weighting 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
37、 weighting function.DIN EN ISO 16610-20:2015-12 EN ISO 16610-20:2015 (E) 6 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 characteristic i
38、s 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.Note 2 to entry
39、: 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 (3.6) into por
40、tions 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 for linear pr
41、ofile 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 invariant kernel.If K
42、x 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, Example 2), it sh
43、all be converted into a discrete representation.DIN EN ISO 16610-20:2015-12 EN ISO 16610-20:2015 (E) 7 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 sampling is assumed to be uniform, i.e
44、. 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 of this matrix is equal to the
45、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 downslopeellipsisdownslopeellipsisdo
46、wnslopeellipsisdownslopeellipsis 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
47、a symmetrical matrix, the sum of the matrix elements aijof each column j is also constant and equals one, i.e. aiji=1 is also valid.NOTE 2 The relationship between the matrix S, the input data by the vector z, and the output data by the vector w is given in Formula (13).4.4 Discrete representation of the weighting functionGiven that each row of the matrix representation of the filter is identical after being shifted accordingly, the matrix elements may be represented by on
