1、BSI Standards PublicationBS EN ISO 16610-41:2015Geometrical productspecifications (GPS) FiltrationPart 41: Morphological profile filters: Diskand horizontal line-segment filtersBS EN ISO 16610-41:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO 16610-41:
2、2015. It supersedes DD ISO/TS 16610-41:2006 which is withdrawn.The UK participation in its preparation was entrusted to Technical Committee TDW/4, Technical Product Realization.A list of organizations represented on this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
3、 purport to include all the necessary 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 77997 8 ICS 17.040.20 Compliance with a British Standard cannot confer immunity from legal o
4、bligations.This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 June 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 16610-41 June 2015 ICS 17.040.20 Englis
5、h Version Geometrical product specifications (GPS) - Filtration - Part 41: Morphological profile filters: Disk and horizontal line-segment filters (ISO 16610-41:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 41: Filtres de profil morphologiques: Filtre disque et filtre segment d
6、e droite horizontal (ISO 16610-41:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 41: Morphologische Profilfilter: Filter mit Kreisscheibe und horizontaler Strecke (ISO 16610-41:2015) This European Standard was approved by CEN on 14 February 2015. CEN members are bound to comply wit
7、h 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-CENELEC Manag
8、ement 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 same sta
9、tus 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, Luxembourg, Malt
10、a, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom. EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROPEN DE NORMALISATION EUROPISCHES KOMITEE FR NORMUNG CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels 2015 CEN
11、 All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN ISO 16610-41:2015 EBS EN ISO 16610-41:2015EN ISO 16610-41:2015 (E) 3 European foreword This document (EN ISO 16610-41:2015) has been prepared by Technical Committee ISO/TC 213“Dimensiona
12、l and geometrical product specifications and verification” in collaboration with TechnicalCommittee CEN/TC 290 “Dimensional and geometrical product specification and verification” the secretariat ofwhich is held by AFNOR. This European Standard shall be given the status of a national standard, eithe
13、r by publication of an identicaltext or by endorsement, at the latest by December 2015, and conflicting national standards shall be withdrawnat the latest by December 2015. Attention is drawn to the possibility that some of the elements of this document may be the subject of patentrights. CEN and/or
14、 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 followingcountries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, CzechRep
15、ublic, Denmark, 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 the United Kingdom. Endor
16、sement notice The text of ISO 16610-41:2015 has been approved by CEN as EN ISO 16610-41:2015 without anymodification. BS EN ISO 16610-41:2015ISO 16610-41:2015(E)Foreword ivIntroduction vi1 Scope . 12 Normative references 13 Terms and definitions . 14 Morphological filters 14.1 General . 14.2 Discret
17、e representation of input data . 24.3 Discrete representation of structuring element 24.4 Discrete morphological filters . 34.5 Discrete envelope filters 104.6 End conditions 105 Recommendations .115.1 Circular disk structuring element 115.2 Horizontal line structuring element 115.3 Default morpholo
18、gical filter . 116 Filter designation11Annex A (informative) Relationship to the filtration matrix model .12Annex B (informative) Relationship to the GPS matrix model .13Bibliography .14 ISO 2015 All rights reserved iiiContents PageBS EN ISO 16610-41:2015ISO 16610-41:2015(E)ForewordISO (the Internat
19、ional 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 bee
20、n 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 stand
21、ardization.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 accordan
22、ce 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. Details o
23、f 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 endors
24、ement.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 responsi
25、ble for this document is ISO/TC 213, Dimensional and geometrical product specifications and verification.This first edition cancels and replaces ISO/TS 16610-41:2006 which has been technically revised.ISO 16610 consists of the following parts, under the general title Geometrical product specificatio
26、ns (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 30:
27、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: Morphol
28、ogical profile filters: Scale space techniques Part 60: Linear areal filters: Basic concepts Part 61: Linear areal filters: Gaussian filtersiv ISO 2015 All rights reservedBS EN ISO 16610-41:2015ISO 16610-41:2015(E) Part 71: Robust areal filters: Gaussian regression filters Part 85: Morphological are
29、al filters: 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 45: Morphological profile filters: Segmentation Part
30、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 horizontal planar
31、segment filters Part 89: Morphological areal filters: Scale space techniques ISO 2015 All rights reserved vBS EN ISO 16610-41:2015ISO 16610-41:2015(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 1
32、4638). It influences chain links 3 and 5 in the GPS matrix structureThe 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
33、 rules given in ISO 14253-1 apply to specifications 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 B.This part of ISO 16610 provides guidelines for computing prof
34、ile morphological operations and filters with disk and horizontal segment structuring elements. It also describes techniques for applying morphological filters, including envelope filters, for open profiles.vi ISO 2015 All rights reservedBS EN ISO 16610-41:2015INTERNATIONAL STANDARD ISO 16610-41:201
35、5(E)Geometrical product specifications (GPS) Filtration Part 41: Morphological profile filters: Disk and horizontal line-segment filters1 ScopeThis part of ISO 16610 specifies techniques for computing morphological filters with disk and horizontal segment structuring elements, including envelope fil
36、ters.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 edition of the referenced document (including any a
37、mendments) applies.ISO 14660-1, Geometrical Product Specifications (GPS) Geometrical features Part 1: General terms and definitionsISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic conceptsISO 16610-40, Geometrical product specifications (GPS) Filtration Par
38、t 40: Morphological profile filters: Basic concepts3 Terms and definitionsFor the purposes of this document, the terms and definition givens in ISO 14660-1, ISO 16610-1, and ISO 16610-40 apply.4 Morphological filters4.1 GeneralThe morphological filters described in this part of ISO 16610 are defined
39、 using Minkowski sums. There are two primary morphological operations (dilation and erosion) and two secondary morphological operations (opening and closing). The opening and closing operators are also called morphological filters. Any technique that can compute Minkowski additions and subtractions
40、can be used to compute closing and opening morphological filters and the respective envelope filters. Computation of morphological filters can be greatly simplified by using with discrete morphological filters, which are described in the rest of this part of ISO 16610. The main body of this part of
41、ISO 16610 covers general computational techniques; Annexes A and B deal with specific implementations of discrete morphological operations and filters for profiles.A morphological filter conforming to this part of ISO 16610 shall exhibit the characteristics described in 4.3, 4.4, 4.5, 4.6, 5.1, 5.2,
42、 and 5.3.NOTE The relationship of morphological profile filters: disk and horizontal line-segment filters to the filtration matrix model is given in Annex A. ISO 2015 All rights reserved 1BS EN ISO 16610-41:2015ISO 16610-41:2015(E)4.2 Discrete representation of input dataAn extracted profile is repr
43、esented as a vector z of finite size n. This is a discrete representation of a profile. For computational convenience, the sampling is assumed to be uniform with a sampling interval . zi, the ith component of z, is the value of the function evaluated at i.A continuous representation of the extracted
44、 profile can be obtained by an appropriate interpolation, e.g. a simple linear interpolation piece by piece of the discrete data. Figure 1 illustrates the graph of this kind of continuous representation, starting with a discrete representation using vector arrowrightnospz .4.3 Discrete representatio
45、n of structuring elementIn the process of filtering profiles, a circular disk is used, as outlined in Figure 2. Due to its symmetry about the origin, it is sufficient to consider only its first quadrant form and represent it discretely as the vector arrowrightnospb . The same applies with a horizont
46、al straight line segment, as shown in Figure 3. Again, due to its symmetry about the origin, it is sufficient to consider only its right half and represent it discretely as the vector arrowrightnospb . The length of the structuring element vector arrowrightnospb is much smaller than that of the inpu
47、t of vector arrowrightnospz . For ease of computation, input arrowrightnospz and structuring element arrowrightnospb are sampled at the same interval .KeyX distance, mY height, mFigure 1 Example of extracted profile graphed after linear interpolation of its discrete representation2 ISO 2015 All righ
48、ts reservedBS EN ISO 16610-41:2015ISO 16610-41:2015(E)a) Representation in full form b) Representation in economic form in the first quadrant due to its symmetryNOTE 1 For example, an economic representation of a circular disk of radius 2 m is arrowrightnospb = 2,00; 1,93; 1,732 1; 1,32; 0,00, where
49、 the dimensions are in m and the sampling interval is 0,5 m. In Figure 2 b), only the circular arc in the first quadrant is represented due the symmetry of the circular disk.Figure 2 Example of a circular disk structuring elementa) Representation in full form b) Representation in economic form showing only its right half due to its symmetryNOTE 2 An economic representation of a horizontal line-segment of total length 4 m is arrowrightnospb = 0; 0; 0; 0; 0, where the dimensions are in m and the sam
