1、April 2016 English price group 12No 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!%Q;“2469724www.din.deDIN
2、 EN ISO 16610-29Geometrical product specifications (GPS) Filtration Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015);English version EN ISO 16610-29:2015,English translation of DIN EN ISO 16610-29:2016-04Geometrische Produktspezifikation (GPS) Filterung Teil 29: Lineare Profilfil
3、ter: Spline-Wavelets (ISO 16610-29:2015);Englische Fassung EN ISO 16610-29:2015,Englische bersetzung von DIN EN ISO 16610-29:2016-04Spcification gomtrique des produits (GPS) Filtrage Partie 29: Filtres de profil linaires: Ondelettes splines (ISO 16610-29:2015);Version anglaise EN ISO 16610-29:2015,T
4、raduction anglaise de DIN EN ISO 16610-29:2016-04www.beuth.deDocument comprises 26 pagesDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be considered authoritative.04.16DIN EN ISO 16610-29:2016-04 2 A comma is used as the decimal marker. National foreword This
5、 document (EN ISO 16610-29:2015) 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 verificati
6、on” (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 Standards refer
7、red to in this document are as follows: ISO 16610-1 DIN EN ISO 16610-1ISO 16610-20 DIN EN ISO 16610-20 ISO 16610-22 DIN EN ISO 16610-22 ISO/IEC Guide 99 International vocabulary of metrology (VIM)*)National Annex NA (informative) Bibliography DIN EN ISO 14638, Geometrical product specifications (GPS
8、) Matrix model DIN EN ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts DIN EN ISO 16610-20, Geometrical product specifications (GPS) Filtration Part 20: Linear profile filters: Basic concepts DIN EN ISO 16610-21, Geometrical product specifications
9、(GPS) Filtration Part 21: Linear profile filters: Gaussian filters DIN EN ISO 16610-22, Geometrical product specifications (GPS) Filtration Part 22: Linear profile filters: Spline filters VIM, International vocabulary of metrology *)Obtainable from: Beuth Verlag GmbH, 10772 Berlin, Order no. 22472,
10、ISBN 978-3-410-22472-3. EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-29 May 2015 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration - Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015) Spcification gomtrique des produits (GPS) - Fi
11、ltrage - Partie 29: Filtres de profil linaires: Ondelettes splines (ISO 16610-29:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 29: Lineare Profilfilter: Spline-Wavelets (ISO 16610-29:2015) This European Standard was approved by CEN on 14 February 2015. CEN members are bound to com
12、ply 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 on application to the CEN-CENELE
13、C 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-CENELEC Management Centre has the s
14、ame 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, Italy, Latvia, Lithuania, Luxembour
15、g, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. 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 M
16、embers. Ref. No. EN ISO 16610-29:2015 E EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROP EN D E NORMAL ISATION EUROP ISCHES KOMITEE FR NORMUNG Foreword .4Introduction .61 Scope .72 Normative references 73 Terms and definitions . 74 General wavelet description . 94.1 General .94.2 Basic usage of wa
17、velets 94.3 Wavelet transform. 104.4 Spline wavelets 104.5 Nested mathematical models 115 Recommendations .115.1 Spline wavelet . 116 Filter designation11Annex A (normative) Family of interpolating spline wavelets . 12Annex B (informative) Examples of the application of cubic of interpolating spline
18、 wavelets 16Annex C (informative) Concept diagram 20Annex D (informative) Relationship to the filtration matrix model .21Annex E (informative) Relation to the GPS matrix model22Bibliography .24Contents PageEuropean foreword .32 EN ISO 16610-29:2015 (E) DIN EN ISO 16610-29:2016-04European foreword Th
19、is document (EN ISO 16610-29:2015) 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 wh
20、ich 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 November 2015, and conflicting national standards shall be withdrawn at the latest by November 2015. Attention is drawn to the
21、 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 following countr
22、ies 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, Norway, Pola
23、nd, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-29:2015 has been approved by CEN as EN ISO 16610-29:2015 without any modification. 3EN ISO 16610-29:2015 (E)DIN EN ISO 16610-29:2016-04ForewordISO (the Inter
24、national 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 committees. Each member body interested in a subject for which a technical committee has
25、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 International Electrotechnical Commission (IEC) on all matters of electrotechnical st
26、andardization.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 the different types of ISO documents should be noted. This document was drafted in accor
27、dance 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. ISO shall not be held responsible for identifying any or all such patent rights. Detail
28、s 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 document is information given for the convenience of users and does not constitute an end
29、orsement.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 (TBT) see the following URL: Foreword - Supplementary informationThe committee respo
30、nsible for this document is ISO/TC 213, Dimensional and geometrical product specifications and verification.This first edition cancels and replaces ISO/TS 16610-29:2006 which has been technically revised.ISO 16610 consists of the following parts, under the general title Geometrical product specifica
31、tions (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 filters Part 28: Profile filters: End effects Part 29: Linear profile filters: Spline wavelets Part 3
32、0: 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 concepts Part 41: Morphological profile filters: Disk and horizontal line-segment filters Part 49: Morp
33、hological profile filters: Scale space techniques Part 60: Linear areal filters: Basic concepts Part 61: Linear areal filters: Gaussian filters4 EN ISO 16610-29:2015 (E) DIN EN ISO 16610-29:2016-04 Part 71: Robust areal filters: Gaussian regression filters Part 85: Morphological areal filters: Segme
34、ntationThe 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: Linear areal
35、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 segment filters P
36、art 89: Morphological areal filters: Scale space techniques5EN ISO 16610-29:2015 (E)DIN EN ISO 16610-29:2016-04IntroductionThis 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
37、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. 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 s
38、pecifications made in accordance with this part of ISO 16610, unless otherwise indicated.For more detailed information of the relation of this part of ISO 16610 to the GPS matrix model, see Annex E.This part of ISO 16610 develops the terminology and concepts for spline wavelets.6 EN ISO 16610-29:201
39、5 (E) DIN EN ISO 16610-29:2016-041 ScopeThis part of ISO 16610 specifies spline wavelets for profiles and contains the relevant concepts. It gives the basic terminology for spline wavelets of compact support, together with their usage.2 Normative referencesThe following documents, in whole or in par
40、t, 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 of the referenced document (including any amendments) applies.ISO 16610-1, Geometrical product specifications (GP
41、S) Filtration Part 1: Overview and basic terminologyISO 16610-20, Geometrical product specifications (GPS) Filtration Part 20: Linear profile filters: Basic conceptsISO 16610-22, Geometrical product specifications (GPS) Filtration Part 22: Linear profile filters: Spline filtersISO/IEC Guide 99:2007,
42、 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, ISO 16610-20, ISO 16610-22, and the following apply.3.1mother waveletfunction of one
43、 or more variables which forms the basic building block for wavelet analysis, related to a scalar functionNote 1 to entry: A mother wavelet, which usually integrates to zero, is localized in space and has a finite bandwidth. Figure 1 provides an example of a real-valued mother wavelet.7EN ISO 16610-
44、29:2015 (E)DIN EN ISO 16610-29:2016-04xs (x )Figure 1 Example of a real-valued mother wavelet3.2wavelet familyga,bfamily of functions generated from the mother wavelet (3.1) by dilation and translationNote 1 to entry: If g(x) is the mother wavelet, then the wavelet family ga,b(x) is generated as fol
45、lows:gxagxbaab,(),=05(1)wherea is the dilation parameter;b is the translation parameter.3.2.1dilationwavelet transformation which scales the spatial variable x by a factor aNote 1 to entry: This transformation takes the function g(x) to a0,5g(x/a) for an arbitrary positive real number a.Note 2 to en
46、try: The factor a0,5keeps the area under the function constant.3.2.2translationtransformation which shifts the spatial position of a function by a real number bNote 1 to entry: This transformation takes the function g(x) to g(x b) for an arbitrary real number b.3.3discrete wavelet transformunique de
47、composition of a profile into a linear combination of a wavelet family (3.2) where the translation (3.2.2) parameters are integers and the dilation (3.2.1) parameters are powers of a fixed positive integer greater than 1Note 1 to entry: The dilation parameters are usually powers of 2.Note 2 to entry
48、: Throughout the rest of this part of ISO 16610, the discrete wavelet transform is referred to as the wavelet transform.8 EN ISO 16610-29:2015 (E) DIN EN ISO 16610-29:2016-043.4multiresolution analysisdecomposition of a profile by a filter bank into portions of different scalesNote 1 to entry: The p
49、ortions at different scales are also referred to as resolutions (see ISO 16610-20).Note 2 to entry: See Figure 2.Note 3 to entry: Since there is, by definition, no loss of information, it is possible to reconstruct the original profile from the multiresolution ladder structure.3.4.1low-pass componentcomponent obtained after convolution with a smoothing filter (low pass) and a decimation3.4.2high-pass componentcomponent obtained after convolution with a difference filter (high pass) and
