1、BSI Standards PublicationBS EN ISO 16610-29:2015Geometrical product specifications (GPS) FiltrationPart 29: Linear profile filters: Spline wavelets BS EN ISO 16610-29:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO 16610-29:2015. It supersedes DD ISO/TS
2、 16610-29:2006 which is withdrawn.The UK participation in its preparation was entrusted to Technical Committee TDW/4, Technical Product Realization.A list of organizations represented on this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 n
3、ecessary 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 77995 4 ICS 17.040.20 Compliance with a British Standard cannot confer immunity from legal obligations.This British Stand
4、ard was published under the authority of the Standards Policy and Strategy Committee on 31 May 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 16610-29 May 2015 ICS 17.040.20 English Version Geometrical product s
5、pecifications (GPS) - Filtration - Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 29: Filtres de profil linaires: Ondelettes splines (ISO 16610-29:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 29:
6、Lineare Profilfilter: Spline-Wavelets (ISO 16610-29:2015) 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 witho
7、ut 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 other l
8、anguage 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 Republic, Den
9、mark, 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 COMMITTE
10、E 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 16610-29:2015 EBS EN ISO
11、16610-29:2015EN ISO 16610-29:2015 (E) 3 Foreword This 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 TechnicalCommittee CEN/TC 290 “Dimensional and geometrical product spec
12、ification 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 November 2015, and conflicting national standards shall be withdrawnat the late
13、st by November 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 national st
14、andards 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, Lu
15、xembourg, Malta, Netherlands, Norway, Poland, 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 anymodification. BS EN ISO 16610-29:2015ISO 16610-2
16、9:2015(E)Foreword ivIntroduction vi1 Scope . 12 Normative references 13 Terms and definitions . 14 General wavelet description . 34.1 General . 34.2 Basic usage of wavelets 34.3 Wavelet transform 44.4 Spline wavelets . 44.5 Nested mathematical models . 55 Recommendations 55.1 Spline wavelet 56 Filte
17、r designation.5Annex A (normative) Family of interpolating spline wavelets 6Annex B (informative) Examples of the application of cubic of interpolating spline wavelets 10Annex C (informative) Concept diagram 14Annex D (informative) Relationship to the filtration matrix model .15Annex E (informative)
18、 Relation to the GPS matrix model16Bibliography .18 ISO 2015 All rights reserved iiiContents PageBS EN ISO 16610-29:2015ISO 16610-29:2015(E)ForewordISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies). The work of prepari
19、ng International 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 lia
20、ison with 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 Dir
21、ectives, 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
22、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. 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 decl
23、arations 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
24、about ISOs 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.This first edition cancels and
25、 replaces ISO/TS 16610-29:2006 which has been technically 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 filte
26、rs: 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 31: Robust profile filters: Gaussian regression filters Part 32: Robust profile filters: Sp
27、line 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 techniques Part 60: Linear areal filters: Basic concepts Part 61: Linear areal filters: Gaussian fi
28、ltersiv ISO 2015 All rights reservedBS EN ISO 16610-29:2015ISO 16610-29:2015(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 plana
29、r 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 wavelets Part 70: Robust areal filters: Basic concepts P
30、art 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: Morphological areal filters: Scale space techniques ISO 2015 All rights reserved vBS EN ISO 16610-29:2015ISO 1
31、6610-29:2015(E)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 the GPS matrix structure.The ISO/GPS Masterplan given in ISO 14638 gives an overview of the
32、 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 specifications made in accordance with this part of ISO 16610, unless otherwise indicated.For mor
33、e 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.vi ISO 2015 All rights reservedBS EN ISO 16610-29:2015Geometrical product specifications (GPS) Filtration Part 29: Li
34、near profile filters: Spline wavelets1 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
35、 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 edition of the referenced document (including any amendments) applies.ISO 16610-1, Geometrical product specifications
36、 (GPS) 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 99:2
37、007, 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
38、 one 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.INTERNATIO
39、NAL STANDARD ISO 16610-29:2015(E) ISO 2015 All rights reserved 1BS EN ISO 16610-29:2015ISO 16610-29:2015(E)xs (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 th
40、e mother wavelet, then the wavelet family ga,b(x) is generated as follows: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(
41、x) to a0,5g(x/a) for an arbitrary positive real number a.Note 2 to entry: 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)
42、for an arbitrary real number b.3.3discrete wavelet transformunique decomposition 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 e
43、ntry: The dilation parameters are usually powers of 2.Note 2 to entry: Throughout the rest of this part of ISO 16610, the discrete wavelet transform is referred to as the wavelet transform.2 ISO 2015 All rights reservedBS EN ISO 16610-29:2015ISO 16610-29:2015(E)3.4multiresolution analysisdecompositi
44、on of a profile by a filter bank into portions of different scalesNote 1 to entry: The portions 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 reconstru
45、ct 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 a decimationNote 1 to
46、 entry: The weighting function of the difference filter is defined by the wavelet from a particular family of wavelets, with a particular dilation parameter and no translation.3.4.3multiresolution ladder structurestructure consisting of all the orders of the difference components and the highest ord
47、er smooth component3.4.4scalar functionfunction which defines the weighting function of the smoothing filter used to obtain the smooth componentNote 1 to entry: In order to avoid loss of information on the multiresolution ladder structure, the wavelet and scaling function are matched.3.4.5decimation
48、wavelet action which samples every kth point in a sampled profile, where k is a positive integerNote 1 to entry: Typically, k is equal to 2.3.5spline waveletwavelet family (3.2) whose corresponding reconstructing scalar functions (3.4.4) are splines4 General wavelet description4.1 GeneralA spline wa
49、velet claiming to comply with this part of ISO 16610 shall satisfy the equations given in Annex A.Note Examples of the application of cubic of interpolating spline wavelets are given in Annex B. A concept diagram for the concepts for spline wavelet filters is given in Annex C, and the relationship to the filtration matrix model is given in Annex D.4.2 Basic usage of waveletsWavelet analysis consists of decomposing a profile into a linear combination of wavelets ga,b(x), all generated from a s
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