EN ISO 16610-29:2015
(Main)Geometrical product specifications (GPS) - Filtration - Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015)
Geometrical product specifications (GPS) - Filtration - Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015)
ISO 16610-29:2015 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.
Geometrische Produktspezifikation (GPS) - Filterung - Teil 29: Lineare Profilfilter: Spline-Wavelets (ISO 16610-29:2015)
Spécification géométrique des produits (GPS) - Filtrage - Partie 29: Filtres de profil linéaires: Ondelettes splines (ISO 16610-29:2015)
ISO 16610-29:2015 spécifie les caractéristiques des filtres à ondelettes splines utilisés pour les profils ainsi que les concepts pertinents Elle définit la terminologie de base pour les filtres ondelette spline compactes ainsi que leur usage.
Specifikacija geometrijskih veličin izdelka (GPS) - Filtriranje - 29. del: Linearni profilni filtri: utorni valjčki (ISO 16610-29:2015)
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2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Geometrische Produktspezifikation (GPS) - Filterung - Teil 29: Lineare Profilfilter: Spline-Wavelets (ISO 16610-29:2015)Spécification géométrique des produits (GPS) - Filtrage - Partie 29: Filtres de profil linéaires: Ondelettes splines (ISO 16610-29:2015)Geometrical product specifications (GPS) - Filtration - Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015)17.040.20Lastnosti površinProperties of surfacesICS:Ta slovenski standard je istoveten z:EN ISO 16610-29:2015SIST EN ISO 16610-29:2015en,fr01-julij-2015SIST EN ISO 16610-29:2015SLOVENSKI
STANDARD
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
EN ISO 16610-29
May 2015 ICS 17.040.20 English Version
Geometrical product specifications (GPS) - Filtration - Part 29: Linear profile filters: Spline wavelets (ISO 16610-29:2015)
Spécification géométrique des produits (GPS) - Filtrage - Partie 29: Filtres de profil linéaires: Ondelettes splines (ISO 16610-29:2015)
Geometrische Produktspezifikation (GPS) - Filterung - Teil 29: 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 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, 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 status 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, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
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CEN-CENELEC Management Centre:
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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 ESIST EN ISO 16610-29:2015
Part 29: Linear pro Ðile
Ðiltersã Spline wavelets
Partie
x ã Filtres de pro Ôil linéairesã Ondelettes splinesINTERNATIONAL STANDARDISO16610-29First edition2015-05-01Reference numberISO 16610-29:2015(E)SIST EN ISO 16610-29:2015
ii © ISO 2015 – All rights reservedCOPYRIGHT PROTECTED DOCUMENT©
ISO 2015All rights reservedä Unless otherwise speci Ðiedá no part of this publication may be reproduced or utilized otherwise in any form or by any meansá electronic or mechanicalá including photocopyingá or posting on the internet or an intranetá without prior written permissionä Permission can be requested from either ISO at the address below or ISOïs member body in the country of the requester.ISO copyright of ÐiceCase postale 56 • CH-1211 Geneva 20Tel. + 41 22 749 01 11Fax + 41 22 749 09 47Eæmail copyright 7isoäorgWeb www.iso.orgPublished in SwitzerlandSIST EN ISO 16610-29:2015
Foreword .ivIntroduction .vi1 Scope .1 t Normative references .1 u Terms and de Ðinitions .1 v 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 .5 w Recommendations . w5.1 Spline wavelet .5 x Filter designation. wAnnex 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
Ðiltration matrix model . s wAnnex E (informative) Relation to the GPS matrix model.16Bibliography .18© ISO 2015 – All rights reserved iiiContents PageSIST EN ISO 16610-29:2015
Forewordthrough ISO technical committeesä 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 organizationsá governmental and nonægovernmentalá in liaison with ISOá also take part in the workä electrotechnical standardizationäThe procedures used to develop this document and those intended for its further maintenance are
In particular the different approval criteria needed for the different types of ISO documents should be notedä
This document was drafted in accordance with the
Directivesá Part
www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rightsä ISO shall not be held responsible for identifying any or all such patent rightsä
Details of 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 endorsement.For an explanation on the meaning of ISO speci Ðic terms and expressions related to conformity assessmentá as well as information about ISOïs adherence to the WTO principles in the Technical Barriers to Trade (TBT) see the following URL:
Foreword æ Supplementary information
t s uá Dimensional and geometrical product speci Ôications and veri Ôication.
s x x s ræ t {ã t r r x which has been technically revisedäISO
s x x s r consists of the following partsá under the general title Geometrical product speci Ôications
:— Part
wã Overview and basic concepts— Part
x vã Linear pro Ôile
Ôiltersã Basic concepts— Part
x wã Linear pro Ôile
Ôiltersã Gaussian
Ôilters— Part
x xã Linear pro Ôile
Ôiltersã Spline
Ôilters— Part
x ~ã Pro Ôile
Ôiltersã End effects— Part
x ã Linear pro Ôile
Ôiltersã Spline wavelets— Part
y vã Robust pro Ôile
Ôiltersã Basic concepts— Part
y wã Robust pro Ôile
Ôiltersã Gaussian regression
Ôilters— Part
y xã Robust pro Ôile
Ôiltersã Spline
Ôilters— Part
z vã Morphological pro Ôile
Ôiltersã Basic concepts— Part
z wã Morphological pro Ôile
Ôiltersã Disk and horizontal lineæsegment
Ôilters— Part
z ã Morphological pro Ôile
Ôiltersã Scale space techniques— Part
| vã Linear areal
Ôiltersã Basic concepts— Part
| wã Linear areal
Ôiltersã Gaussian
Ôilters iv © ISO 2015 – All rights reservedSIST EN ISO 16610-29:2015
— Part
} wã Robust areal
Ôiltersã Gaussian regression
Ôilters— Part
~ {ã Morphological areal
Ôiltersã SegmentationThe following parts are planned:— Part 26: Linear pro Ôile
Ôiltersã Filtration on nominally orthogonal grid planar data sets— Part 27: Linear pro Ôile
Ôiltersã Filtration on nominally orthogonal grid cylindrical data sets— Part 45: Morphological pro Ôile
Ôiltersã Segmentation— Part 62: Linear areal
Ôiltersã Spline
Ôilters— Part 69: Linear areal
Ôiltersã Spline wavelets— Part 70: Robust areal
Ôiltersã Basic concepts— Part 72: Robust areal
Ôiltersã Spline
Ôilters— Part 80: Morphological areal
Ôiltersã Basic concepts— Part 81: Morphological areal
Ôiltersã Sphere and horizontal planar segment
Ôilters— Part 89: Morphological areal
Ôiltersã Scale space techniques © ISO 2015 – All rights reserved vSIST EN ISO 16610-29:2015
IntroductionThis part of ISO
spart of ISO
s
z r s w apply to this part of ISO
s x x s r and the default decision rules given in ISO
s v t w uæ s apply to speci Ðications made in accordance with this part of ISO
s x x s rá unless otherwise indicatedäFor more detailed information of the relation of this part of ISO 16610 to the GPS matrix modelá see Annex E.This part of ISO
s x x s r develops the terminology and concepts for spline waveletsä vi © ISO 2015 – All rights reservedSIST EN ISO 16610-29:2015
Part 29: Linear pro Ðile
Ðiltersã Spline wavelets1 ScopeThis part of ISO
s x x s r speci Ðies spline wavelets for pro Ðiles and contains the relevant conceptsä It gives the basic terminology for spline wavelets of compact supportá together with their usageä t Normative referencesThe following documentsá in whole or in partá are normatively referenced in this document and are indispensable for its applicationä For dated referencesá only the edition cited appliesä For undated ISO 16610-1á
wã Overview and basic terminologyISO 16610-20á
x vã Linear pro Ôile
Ôiltersã Basic conceptsISO 16610-22á
x xã Linear pro Ôile
Ôiltersã Spline
ÔiltersISO/IEC Guide
{ {ã t r r yá International vocabulary of metrology Basic and general concepts and
u Terms and de Ðinitions
{ {á ISO
s x x s ræ sá ISO
s x x s ræ t rá ISO
s x x s ræ t tá and the following applyä3.1mother waveletfunction of one or more variables which forms the basic building block for wavelet analysisá related to a scalar functionNote
s to entryã A mother waveletá which usually integrates to zeroá is localized in space and has a
Ðinite bandwidthä Figure 1 provides an example of a real-valued mother wavelet.INTERNATIONAL STANDARD © ISO 2015 – All rights reserved 1SIST EN ISO 16610-29:2015
xs(x)Figure
s 3.2wavelet familygaábfamily of functions generated from the mother wavelet (3.1Note
s to entryã If g(xs the mother waveletá then the wavelet family gaáb(x) is generated as follows: (1)where ais the dilation parameter; bis the translation parameter.3.2.1dilationCÃwaveletCÄ transformation which scales the spatial variable x by a factor aNote
s to entryã This transformation takes the function g(x) to a « rá wg(x/aa.Note
t to entryã The factor a « rá w keeps the area under the function constant.3.2.2translationtransformation which shifts the spatial position of a function by a real numb
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