1、BSI Standards PublicationBS EN ISO 16610-40:2015Geometrical productspecifications (GPS) FiltrationPart 40: Morphological profile filters: BasicconceptsBS EN ISO 16610-40:2015 BRITISH STANDARDNational forewordThis British Standard is the UK implementation of EN ISO 16610-40:2015. It supersedes DD ISO
2、/TS 16610-40:2006 which is withdrawn.The UK participation in its preparation was entrusted to Technical Committee TDW/4, Technical Product Realization.A list of organizations represented on this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 th
3、e 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 77996 1 ICS 17.040.20 Compliance with a British Standard cannot confer immunity from legal obligations.This British St
4、andard 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 16610-40 June 2015 ICS 17.040.20 English Version Geometrical prod
5、uct specifications (GPS) - Filtration - Part 40: Morphological profile filters: Basic concepts (ISO 16610-40:2015) Spcification gomtrique des produits (GPS) - Filtrage - Partie 40: Filtres de profil morphologiques: Concepts de base (ISO 16610-40:2015) Geometrische Produktspezifikation (GPS) - Filter
6、ung - Teil 40: Morphologische Profilfilter: Grundlegende Konzepte (ISO 16610-40:2015) This European Standard was approved by CEN on 21 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
7、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 Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, Germa
8、n). 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 status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia,
9、 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, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and Unite
10、d 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 All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN I
11、SO 16610-40:2015 EBS EN ISO 16610-40:2015EN ISO 16610-40:2015 (E) 3 Foreword This document (EN ISO 16610-40:2015) has been prepared by Technical Committee ISO/TC 213“Dimensional and geometrical product specifications and verification” in collaboration with TechnicalCommittee CEN/TC 290 “Dimensional
12、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, either by publication of an identicaltext or by endorsement, at the latest by December 2015, and conflicting national standards s
13、hall 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 CENELEC shall not be held responsible for identifying any or all such patent rights. According to the CEN-CENELEC Internal
14、Regulations, the national standards 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,
15、Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 16610-40:2015 has been approved by CEN as EN ISO 16610-40:2015 without anymodification. BS EN
16、ISO 16610-40:2015ISO 16610-40:2015(E)Foreword ivIntroduction vi1 Scope . 12 Normative references 13 Terms and definitions . 14 Basic concepts . 34.1 Minkowski sums 34.1.1 General 34.1.2 Minkowski addition . 34.1.3 Minkowski subtraction . 44.2 Morphological operations . 44.2.1 General 44.2.2 Dilation
17、 . 44.2.3 Erosion 54.2.4 Opening 54.2.5 Closing . 64.2.6 Higher order morphological operations . 64.2.7 Properties of morphological operations . 75 Morphological filters 75.1 General . 75.2 Fill transform 75.3 Discrete morphological filters . 85.4 Envelope filters . 85.5 Sampling and reconstruction
18、. 8Annex A (informative) Concept diagram .13Annex B (informative) Relationship to the filtration matrix model .14Annex C (informative) Relationship to the GPS matrix model 15Bibliography .16 ISO 2015 All rights reserved iiiContents PageBS EN ISO 16610-40:2015ISO 16610-40:2015(E)ForewordISO (the Inte
19、rnational 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
20、 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 s
21、tandardization.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 acco
22、rdance 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. Detai
23、ls 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 en
24、dorsement.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 resp
25、onsible for this document is ISO/TC 213, Dimensional and geometrical product specifications and verification.This first edition of ISO 16610-40 cancels and replaces ISO/TS 16610-40:2006 which has been technically revised.ISO 16610 consists of the following parts, under the general title Geometrical
26、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 filters Part 28: Profile filters: End effects Part 29: Linear profile filters: Splin
27、e 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 concepts Part 41: Morphological profile filters: Disk and horizontal line-segment filt
28、ers Part 49: Morphological profile filters: Scale space techniques Part 60: Linear areal filters: Basic conceptsiv ISO 2015 All rights reservedBS EN ISO 16610-40:2015ISO 16610-40:2015(E) Part 61: Linear areal filters: Gaussian filters Part 71: Robust areal filters: Gaussian regression filters Part 8
29、5: Morphological areal 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
30、: 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: Sphere an
31、d horizontal planar segment filters Part 89: Morphological areal filters: Scale space techniques ISO 2015 All rights reserved vBS EN ISO 16610-40:2015ISO 16610-40:2015(E)IntroductionThis part of ISO 16610 is a geometrical product specification (GPS) standard and is to be regarded as a general GPS st
32、andard (see ISO/TR 14638). It influences the chain links 3 and 5 of all chains of standards.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
33、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 16610 to the GPS matrix model, see Annex C.This part of ISO 16610 develops the t
34、erminology and concepts for morphological operations and filters, including envelope filters.vi ISO 2015 All rights reservedBS EN ISO 16610-40:2015INTERNATIONAL STANDARD ISO 16610-40:2015(E)Geometrical product specifications (GPS) Filtration Part 40: Morphological profile filters: Basic concepts1 Sc
35、opeThis part of ISO 16610 sets out the basic concepts and terminology for morphological operations and filters, including envelope filters.2 Normative referencesThe following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For da
36、ted references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.ISO 17450-1:2011, Geometrical product specifications (GPS) Geometrical concepts Part 1: Model for geometrical specification and verificationISO 166
37、10-1:2015, Geometrical product specifications (GPS) Filtration Part 1: Overview and basic concepts3 Terms and definitionsFor the purposes of this document, the terms and definitions given in ISO 16610-1, ISO 17450-1, and the following apply.3.1morphological operationbinary operation involving two ge
38、ometrical objects as sets, resulting in another geometrical objectNote 1 to entry: Dilation and erosion are two primary morphological operations, and closing and opening are two secondary morphological operations.Note 2 to entry: Geometrical objects are point sets, i.e. set of points.3.2morphologica
39、l filtermorphological operation (3.1) that is both monotonically increasing (3.11) and idempotent (3.12)3.3envelope filterclosing (3.10) or opening (3.9) filter, whose output envelops the input profile or surfaceNote 1 to entry: A closing filter generates the upper envelope; an opening filter genera
40、tes the lower envelope.3.4Minkowski additionvector sum of points in two given geometrical sets3.5Minkowski subtractionbinary operation defined using Minkowski addition (3.4) of two setsNote 1 to entry: It is the complement of the Minkowski addition of the complement of the first set with the second
41、set. ISO 2015 All rights reserved 1BS EN ISO 16610-40:2015ISO 16610-40:2015(E)3.6structuring elementmorphological filters second geometrical object used in morphological operations3.7dilationmorphological morphological operation that expands one input set by anotherNote 1 to entry: Dilation is not a
42、 morphological filter because it is not idempotent.3.8erosionmorphological morphological operation that shrinks one input set by anotherNote 1 to entry: Erosion is not a morphological filter because it is not idempotent.3.9openingmorphological filters morphological operation obtained by applying the
43、 erosion (3.8) followed by the dilation (3.7)Note 1 to entry: An opening is both a morphological filter and one of the two basic building blocks for other morphological filters.3.10closingmorphological filters morphological operation obtained by applying the dilation (3.7) followed by the erosion (3
44、.8)Note 1 to entry: A closing is both a morphological filter and one of the two basic building blocks for other morphological filters.3.11monotonically increasingmorphological filters property of an operation that preserves the set containment condition on its operands3.12idempotentproperty of an op
45、eration such that applying the operation more than once does not change the outcome3.13extensivemorphological filters property of an operation that the output of the operation contains the input3.14anti-extensivemorphological filters property of an operation that the output of an operation is contai
46、ned in the input3.15fill transformoperation that converts a profile into a two-dimensional object and a surface into a three-dimensional object3.16umbra transformfill transform (3.15) applicable to open profiles and open surfaces3.17rigid body transformationoperation on a geometric object involving
47、translations and rotations that do not change the distance between any two points in the object2 ISO 2015 All rights reservedBS EN ISO 16610-40:2015ISO 16610-40:2015(E)3.18rigid motion invariantproperty of an operation that does not change under rigid body transformation (3.17)4 Basic concepts4.1 Mi
48、nkowski sums4.1.1 GeneralMinkowski sums refer to Minkowski additions and Minkowski subtractions involving sets of geometric objects in any dimension. Geometric objects are represented by sets of points.NOTE A concept diagram for the concepts for morphological filters is given in Annex A. The relatio
49、nship to the filtration matrix model is given in Annex B.4.1.2 Minkowski additionMinkowski addition of two sets, A and B, is denoted A B, and is defined as the vector additionAB abaAbB=+: , (1)Figure 1 illustrates the Minkowski addition of two sets, A and B, in two dimensions.NOTE 1 Sets A and B can be of any dimensionality. They can also be of mixed dimensionality, e.g. A can be three-dimensional and B can be two-dimensional. Sets in one, two, and three dimensions are of interest.NOTE 2 Minkowsk
