1、DD ISO/TS16610-32:2009ICS 17.040.20NO COPYING WITHOUT BSI PERMISSION EXCEPT AS PERMITTED BY COPYRIGHT LAWDRAFT FOR DEVELOPMENTGeometrical productspecifications (GPS) FiltrationPart 32: Robust profile filters: SplinefiltersThis Draft for Developmentwas published under theauthority of the StandardsPol
2、icy and StrategyCommittee on 30 April2009 BSI 2009ISBN 978 0 580 57487 0Amendments/corrigenda issued since publicationDate CommentsDD ISO/TS 16610-32:2009National forewordThis Draft for Development is the UK implementation of ISO/TS16610-32:2009.This publication is not to be regarded as a British St
3、andard.It is being issued in the Draft for Development series of publications andis of a provisional nature. It should be applied on this provisional basis,so that information and experience of its practical application can beobtained.Comments arising from the use of this Draft for Development arere
4、quested so that UK experience can be reported to the internationalorganization responsible for its conversion to an international standard.A review of this publication will be initiated not later than 3 years afterits publication by the international organization so that a decision can betaken on it
5、s status. Notification of the start of the review period will bemade in an announcement in the appropriate issue of Update Standards.According to the replies received by the end of the review period,the responsible BSI Committee will decide whether to support theconversion into an international Stan
6、dard, to extend the life of theTechnical Specification or to withdraw it. Comments should be sent tothe Secretary of the responsible BSI Technical Committee at BritishStandards House, 389 Chiswick High Road, London W4 4AL.The UK participation in its preparation was entrusted to TechnicalCommittee TD
7、W/4, Technical product realization (TPR).A list of organizations represented on this committee can be obtained onrequest to its secretary.This publication does not purport to include all the necessary provisionsof a contract. Users are responsible for its correct application.Compliance with a Britis
8、h Standard cannot confer immunityfrom legal obligations.DD ISO/TS 16610-32:2009Reference numberISO/TS 16610-32:2009(E)ISO 2009TECHNICAL SPECIFICATION ISO/TS16610-32First edition2009-03-15Geometrical product specifications (GPS) Filtration Part 32: Robust profile filters: Spline filters Spcification
9、gomtrique des produits (GPS) Filtrage Partie 32: Filtres de profil robustes: Filtres splines DD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall not be edi
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14、opyrightiso.org Web www.iso.org Published in Switzerland ii ISO 2009 All rights reservedDD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) ISO 2009 All rights reserved iiiContents Page Foreword iv Introduction . vi 1 Scope . 1 2 Normative references . 1 3 Terms and definitions. 1 4 Robust spline filters
15、 . 2 4.1 Weighting function . 2 4.2 Filter equations . 2 4.2.1 General. 2 4.2.2 Filter equation of the robust spline filter for open profiles 2 4.2.3 Filter equation of the robust spline filter for closed profiles . 3 4.3 Transmission characteristic 3 5 Recommendations 4 5.1 Nesting index (cut-off v
16、alue c). 4 5.2 Tension parameter () 4 5.3 Implementation . 4 5.4 Filter designation 4 Annex A (informative) Examples 5 Annex B (informative) Relationship to the filtration matrix model 8 Annex C (informative) Relation to the GPS matrix model 9 Bibliography . 10 DD ISO/TS 16610-32:2009ISO/TS 16610-32
17、:2009(E) iv ISO 2009 All rights reservedForeword ISO (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 committees. Each member bo
18、dy 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 International Electrot
19、echnical Commission (IEC) on all matters of electrotechnical standardization. International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2. The main task of technical committees is to prepare International Standards. Draft International Standards adopted b
20、y the technical committees are circulated to the member bodies for voting. Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote. In other circumstances, particularly when there is an urgent market requirement for such documents, a technical
21、committee may decide to publish other types of normative document: an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in an ISO working group and is accepted for publication if it is approved by more than 50 % of the members of the parent committee ca
22、sting a vote; an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting a vote. An ISO/PAS or ISO/TS is reviewed after three years in order to decide wh
23、ether it will be confirmed for a further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an International Standard or be withdrawn. Attent
24、ion 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. ISO/TS 16610-32 was prepared by Technical Committee ISO/TC 213, Dimensional and geometrical product specifi
25、cations and verification. ISO 16610 consists of the following parts, 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 profil
26、e filters: Gaussian filters Part 22: Linear profile filters: Spline filters Technical Specification Part 29: Linear profile filters: Spline wavelets Technical Specification Part 30: Robust profile filters: Basic concepts Technical Specification Part 32: Robust profile filters: Spline filters Technic
27、al Specification DD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) ISO 2009 All rights reserved v Part 40: Morphological profile filters: Basic concepts Technical Specification Part 41: Morphological profile filters: Disk and horizontal line-segment filters Technical Specification Part 49: Morphologica
28、l profile filters: Scale space techniques Technical Specification The following parts are under preparation: Part 28: Profile filters: End effects Technical Specification Part 31: Robust profile filters: Gaussian regression filters Technical Specification The following parts are planned: Part 26: Li
29、near 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: Motif filters Part 60: Linear areal filters: Basic concepts Part 61: Linear areal filt
30、ers: Gaussian filters Part 62: Linear areal filters: Spline filters Part 69: Linear areal filters: Spline wavelets Part 70: Robust areal filters: Basic concepts Part 71: Robust areal filters: Gaussian regression filters Part 72: Robust areal filters: Spline filters Part 80: Morphological areal filte
31、rs: Basic concepts Part 81: Morphological areal filters: Sphere and horizontal planar segment filters Part 82: Morphological areal filters: Motif filters Part 89: Morphological areal filters: Scale space techniques DD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) vi ISO 2009 All rights reservedIntrodu
32、ction This part of ISO 16610 is a geometrical product specification (GPS) standard 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. For more detailed information of the relation of this part of ISO 16610 to the GPS m
33、atrix model, see Annex C. This part of ISO 16610 develops the terminology and concepts of robust spline filters. The robust spline filter has the advantage over a conventional phase correct filter that the edges of the measured profile are still usable. This is important especially in the case of fo
34、rm filtering. Moreover, the robust spline filter is tolerant against outliers. DD ISO/TS 16610-32:2009TECHNICAL SPECIFICATION ISO/TS 16610-32:2009(E) ISO 2009 All rights reserved 1Geometrical product specifications (GPS) Filtration Part 32: Robust profile filters: Spline filters 1 Scope This part of
35、 ISO 16610 specifies the characteristics of robust spline filters for surface profiles. It specifies in particular how to separate the long and short wave content of a surface profile. 2 Normative references The following referenced documents are indispensable for the application of this document. F
36、or dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 4287:1997, Geometrical Product Specifications (GPS) Surface texture: Profile method Terms, definitions and surface texture parameters ISO
37、/TS 16610-1:2006, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts ISO/TS 16610-22:2006, Geometrical product specifications (GPS) Filtration Part 22: Linear profile filters: Spline filters ISO/TS 16610-30:2009, Geometrical product specifications (GPS) Filtratio
38、n Part 30: Robust profile filters: Basic concepts ISO/IEC Guide 99:2007, International vocabulary of metrology Basic and general concepts and associated terms (VIM) 3 Terms and definitions For the purposes of this document, the terms and definitions given in ISO/IEC Guide 99, ISO 4287, ISO/TS 16610-
39、1, ISO/TS 16610-22, ISO/TS 16610-30 and the following apply. DD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) 2 ISO 2009 All rights reserved3.1 robust spline filter robust filter based on splines NOTE 1 The result of the low-pass filtering (the mean line) is a spline. NOTE 2 The degree of the spline i
40、s equal to the degree of the polynomial of highest degree used, e.g. a cubic spline is made of cubic polynomials. NOTE 3 Robust spline filters are non-linear filters. 4 Robust spline filters 4.1 Weighting function The weighting function of a robust spline filter does not exist because this filter is
41、 non-linear. 4.2 Filter equations 4.2.1 General Filter equations for robust spline filters may be constructed for any degree, but only those based on cubic splines are given here. 4.2.2 Filter equation of the robust spline filter for open profiles The filter equation is given by ()24sgn( )(1 )z wPQw
42、z w + =(1) with the matrix 11 12112 1 2 5 4 112 1 1 4 6 4 112 1 1 4 6 4 112 1 1 4 5 211 1 2 1PQ = % % (2) with n rows and n columns and the parameters c12sinx=and 0 1uu (3) where n is the number of measured values of the profile; z is the vector of dimension n of the profile values before filtering;
43、 w is the vector of dimension n of this profiles values in the reference line; cis the limiting wavelength of the profile filter; DD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) ISO 2009 All rights reserved 3x is the sampling interval ()1if 0sgn1if 0ttt+=WNOTE 1 The vector w gives the profile values
44、of the long wave component (reference line). The short wave component, r, may be obtained by the difference vector rzw= , i.e. by subtracting the mean line values obtained by the filtering process from the measured profile values. NOTE 2 The value of 0,625 242 gets the spline filter as close as poss
45、ible to the Gaussian filter. 4.2.3 Filter equation of the robust spline filter for closed profiles The filter equation is given by 24sgn( )(1 )()z wPQwz w + =(4) with the matrix 21 1 641 1412 1 4 6 4 1 112 1 1 4 6 4 112 1 1 4 6 4 112 1 1 1 4 6 41124PQ = % % (5) with n rows and n columns and the para
46、meters c12sinx=and 0 1uu (6) where n is the number of measured values of the profile; z is the vector of dimension n of the profile values before filtering; w is the vector of dimension n of this profiles values in the mean line; cis the limiting wavelength of the profile filter; x is the sampling i
47、nterval. NOTE The vector z gives the profile values of the long wave component (mean line). The short wave component, r , may be obtained by the difference vector rzw= , i.e. by subtracting the mean line values obtained by the filtering process from the measured profile values. 4.3 Transmission char
48、acteristic The transmission characteristic of a robust spline filter does not exist because this filter is non-linear, i.e. no weighting function exists. DD ISO/TS 16610-32:2009ISO/TS 16610-32:2009(E) 4 ISO 2009 All rights reservedNOTE The transmission characteristic of a linear filter is given as the Fourier transformation of the weighting function. This is not possible with non-linear filters. 5 Recommendations 5.1 Nesting index (cut-off value c) It is recommended that the nesting index (the cut-off value c) be chosen
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