1、December 2015 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!%Ir3“2387916www.din.d
2、eDIN EN ISO 16610-41Geometrical product specifications (GPS) Filtration Part 41: Morphological profile filters: Disk and horizontal line-segment filters (ISO 16610-41:2015);English version EN ISO 16610-41:2015,English translation of DIN EN ISO 16610-41:2015-12Geometrische Produktspezifikation (GPS)
3、Filterung Teil 41: Morphologische Profilfilter: Filter mit Kreisscheibe und horizontaler Strecke (ISO 16610-41:2015);Englische Fassung EN ISO 16610-41:2015,Englische bersetzung von DIN EN ISO 16610-41:2015-12Spcification gomtrique des produits (GPS) Filtrage Partie 41: Filtres de profil morphologiqu
4、es: Filtre disque et filtre segment de droite horizontal(ISO 16610-41:2015);Version anglaise EN ISO 16610-41:2015,Traduction anglaise de DIN EN ISO 16610-41:2015-12www.beuth.deDocument comprises 21 pagesDTranslation by DIN-Sprachendienst.In case of doubt, the German-language original shall be consid
5、ered authoritative.11.15DIN EN ISO 16610-41:2015-12 2 A comma is used as the decimal marker. National foreword This document (EN ISO 16610-41:2015) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” (Secretariat: DS, Denmark) in
6、collaboration with Technical Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” (Secretariat: AFNOR, France). The responsible German body involved in its preparation was DIN-Normenausschuss Technische Grundlagen (DIN Standards Committee Technical Fundamentals),
7、 Working Committee NA 152-03-03 AA Oberflchen. The DIN Standards corresponding to the International Standards referred to in this document are as follows: ISO 14660-1 see DIN EN ISO 14660-1 ISO 16610-1 see DIN EN ISO 16610-1 ISO 16610-40 see DIN EN ISO 16610-40National Annex NA (informative) Bibliog
8、raphy DIN EN ISO 14660-1, Geometrical Product Specifications (GPS) Geometrical features Part 1: General terms and definitions DIN EN ISO 16610-1, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts DIN EN ISO 16610-40, Geometrical product specifications (GPS) Filt
9、ration Part 2: Morphological profile filters: Basic concepts EUROPEAN STANDARD NORME EUROPENNE EUROPISCHE NORM EN ISO 16610-41 June 2015 ICS 17.040.20 English Version Geometrical product specifications (GPS) - Filtration - Part 41: Morphological profile filters: Disk and horizontal line-segment filt
10、ers (ISO 16610-41:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 41: Filtres de profil morphologiques: Filtre disque et filtre segment de droite horizontal (ISO 16610-41:2015) Geometrische Produktspezifikation (GPS) - Filterung - Teil 41: Morphologische Profilfilter: Filter mit
11、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 with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard witho
12、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
13、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
14、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. CEN-CENELEC Manag
15、ement 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 16610-41:2015 E EUROPEAN COMMITTEE FOR STANDARDIZATION COMIT EUROP EN D E NORMAL ISATION EUROP ISCHES KOMITEE FR NORMUNG Conte
16、nts Page European foreword .3Introduction 51 Scope . 62 Normative references 63 Terms and definitions . 64 Morphological filters 64.1 General . 64.2 Discrete representation of input data . 74.3 Discrete representation of structuring element 74.4 Discrete morphological filters . 84.5 Discrete envelop
17、e filters 154.6 End conditions 155 Recommendations .165.1 Circular disk structuring element 165.2 Horizontal line structuring element 165.3 Default morphological filter . 166 Filter designation16Annex A (informative) Relationship to the filtration matrix model 17Annex B (informative) Relationship to
18、 the GPS matrix model 18Bibliography .192 EN ISO 16610-41:2015 (E) DIN EN ISO 16610-41:2015-12European foreword This document (EN ISO 16610-41:2015) has been prepared by Technical Committee ISO/TC 213 “Dimensional and geometrical product specifications and verification” in collaboration with Technic
19、al Committee CEN/TC 290 “Dimensional and geometrical product specification and verification” the secretariat of which 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 December 201
20、5, and conflicting national standards shall be withdrawn at the latest by December 2015. Attention is drawn to the 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 right
21、s. EN 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 filters: Gaussian filters Part 22: Linear profile filters: Spline
22、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: Spline filters Part 40: Morphological profile filters: Basic co
23、ncepts 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 filters Part 71: Robust areal filters: Gaussian regression filt
24、ers Part 85: Morphological areal filters: Segmentation The 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 prof
25、ile filters: Segmentation Part 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
26、: Sphere and horizontal planar segment filters Part 89: Morphological areal filters: Scale space techniques 3EN ISO 16610-41:2015 (E) DIN EN ISO 16610-41:2015-12According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement t
27、his 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, Poland, Portugal, Romania, Slova
28、kia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-41:2015 has been approved by CEN as EN ISO 16610-41:2015 without any modification. 4 EN ISO 16610-41:2015 (E) DIN EN ISO 16610-41:2015-12IntroductionThis part of ISO 16610 is a geometri
29、cal 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 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 f
30、undamental 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 more detailed information about the relation of this part of ISO 16
31、610 to the GPS matrix model, see Annex B.This part of ISO 16610 provides guidelines for computing profile morphological operations and filters with disk and horizontal segment structuring elements. It also describes techniques for applying morphological filters, including envelope filters, for open
32、profiles.5EN ISO 16610-41:2015 (E) DIN EN ISO 16610-41:2015-121 ScopeThis part of ISO 16610 specifies techniques for computing morphological filters with disk and horizontal segment structuring elements, including envelope filters.2 Normative referencesThe following documents, in whole or in part, a
33、re 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 14660-1, Geometrical Product Specifications (GPS) G
34、eometrical 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 Part 40: Morphological profile filters: Basic concepts3 Terms and definitions
35、For 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 using Minkowski sums. There are two primary morphological operations (dil
36、ation 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 can be used to compute closing and opening morphological filters and the r
37、espective 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 ISO 16610 covers general computational techniques; Annexes A and B deal wi
38、th 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, and 5.3.NOTE The relationship of morphological profile filters: disk and
39、horizontal line-segment filters to the filtration matrix model is given in Annex A.6 EN ISO 16610-41:2015 (E) DIN EN ISO 16610-41:2015-124.2 Discrete representation of input dataAn extracted profile is represented as a vector z of finite size n. This is a discrete representation of a profile. For co
40、mputational 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 profile can be obtained by an appropriate interpolation, e.g. a simple linear interpolation p
41、iece 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 representation of structuring elementIn the process of filtering profiles, a circular disk is used, as outl
42、ined 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 horizontal straight line segment, as shown in Figure 3. Again, due to its symmetry about the origin, i
43、t 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 input of vector arrowrightnospz . For ease of computation, input arrowrightnospz and structuring e
44、lement arrowrightnospb are sampled at the same interval .KeyX distance, mY height, mFigure 1 Example of extracted profile graphed after linear interpolation of its discrete representation7EN ISO 16610-41:2015 (E) DIN EN ISO 16610-41:2015-12a) Representation in full form b) Representation in economic
45、 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 the dimensions are in m and the sampling interval is 0,5 m. In Figure 2 b), only the circular arc in the first qu
46、adrant 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
47、length 4 m is arrowrightnospb = 0; 0; 0; 0; 0, where the dimensions are in m and the sampling interval is 0,5 m. In Figure 3 b), only the right half of the line-segment is represented due the symmetry of the line-segment.Figure 3 Example of a horizontal line-segment structuring element4.4 Discrete m
48、orphological filtersA discrete morphological filter takes arrowrightnospz and arrowrightnospb as input and produces a filtered output of the same array length as the input arrowrightnospz . It is a discrete representation of the filtered profile. The basic idea behind the computation of dilation and
49、 erosion is to position the origin of the structuring element at every point of the input and to sum them, as illustrated for a few positions of a circular structuring element for dilation in Figure 4. The extreme value at each sampling point is then collected and these values are reported as the output. For example, in Figure 4, the top-most star in each vertical line is collected after all the disks are positioned, and the array of the vertical coordinates of all the
