ISO/TR 16610-32:2023

Geometrical product specifications (GPS) — Filtration — Part 32: Robust profile filters: Spline filters

This document provides information on a generalized version of the linear spline filter for uniform and non-uniform sampling and the robust spline filters for surface profiles. It supplements ISO 16610-22, ISO 16610-30 and ISO 16610-31. This document provides information on how to apply the robust estimation to the spline filter as specified in ISO 16610-22, as well as its generalized form for non-uniform sampling. The weight function chosen for the M-estimator is the Tukey biweight influence function as specified in ISO 16610-31.

Spécification géométrique des produits (GPS) — Filtrage — Partie 32: Filtres de profil robustes: Filtres splines

Le présent document fournit des informations sur une version généralisée du filtre spline linéaire pour un échantillonnage uniforme et non uniforme et des filtres splines robustes pour des profils de surface. Il complète les ISO 16610‑22, ISO 16610‑30 et ISO 16610‑31. Le présent document fournit des informations sur la manière d’appliquer l’estimation robuste au filtre spline tel que spécifié dans l’ISO 16610‑22, ainsi que sa forme généralisée pour un échantillonnage non uniforme. La fonction de pondération choisie pour l’estimateur M est la fonction d’influence à double pondération de Tukey telle que spécifiée dans l’ISO 16610‑31.

General Information

• Status: Published
• Publication Date: 25-Oct-2023
• ICS: 17.040.20 - Properties of surfaces
• ICS: 17.040.40 - Geometrical Product Specification (GPS)
• Technical Committee: ISO/TC 213 - Dimensional and geometrical product specifications and verification
• Drafting Committee: ISO/TC 213 - Dimensional and geometrical product specifications and verification
• Current Stage: 6060 - International Standard published
• Start Date: 26-Oct-2023
• Completion Date: 26-Oct-2023

Relations

• Revises: ISO/TS 16610-32:2009 - Geometrical product specifications (GPS) — Filtration — Part 32: Robust profile filters: Spline filters
• Effective Date: 06-Jun-2022

Standards Content (Sample)

TECHNICAL ISO/TR
REPORT 16610-32
First edition
2023-10
Geometrical product specifications
(GPS) — Filtration —
Part 32:
Robust profile filters: Spline filters
Spécification géométrique des produits (GPS) — Filtrage —
Partie 32: Filtres de profil robustes: Filtres splines
Reference number
ISO/TR 16610-32:2023(E)
© ISO 2023

---------------------- Page: 1 ----------------------
ISO/TR 16610-32:2023(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
  © ISO 2023 – All rights reserved

---------------------- Page: 2 ----------------------
ISO/TR 16610-32:2023(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Spline filter for uniform and non-uniform sampling . 2
4.1 General . 2
4.2 Filter equation for cubic spline filter . 2
4.2.1 General . 2
4.2.2 Regularization parameter . 3
4.2.3 Tension parameter . 4
4.2.4 Matrix V for linear cubic spline filter . 4
4.2.5 Matrix V for robust cubic spline filter . 4
4.2.6 Termination of the iteration of robust estimation . 5
4.2.7 Matrices of differentiation P and Q . 5
4.3 Transmission characteristics . 7
4.4 Alternative robust spline filter . 7
4.4.1 General . 7
4.4.2 Objective function with L2-norm without tension energy for the linear
filter equation . 8
4.4.3 Objective function with L1-norm without tension energy for robust
filtration .
...

RAPPORT ISO/TR
TECHNIQUE 16610-32
Première édition
2023-10
Spécification géométrique des
produits (GPS) — Filtrage —
Partie 32:
Filtres de profil robustes: Filtres
splines
Geometrical product specifications (GPS) — Filtration —
Part 32: Robust profile filters: Spline filters
Numéro de référence
ISO/TR 16610-32:2023(F)
© ISO 2023

---------------------- Page: 1 ----------------------
ISO/TR 16610-32:2023(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2023
Tous droits réservés. Sauf prescription différente ou nécessité dans le contexte de sa mise en œuvre, aucune partie de cette
publication ne peut être reproduite ni utilisée sous quelque forme que ce soit et par aucun procédé, électronique ou mécanique,
y compris la photocopie, ou la diffusion sur l’internet ou sur un intranet, sans autorisation écrite préalable. Une autorisation peut
être demandée à l’ISO à l’adresse ci-après ou au comité membre de l’ISO dans le pays du demandeur.
ISO copyright office
Case postale 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Genève
Tél.: [phone]
E-mail: [e-mail]
Web: www.iso.org
Publié en Suisse
ii
  © ISO 2023 – Tous droits réservés

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ISO/TR 16610-32:2023(F)
Sommaire Page
Avant-propos .iv
Introduction .v
1 Domaine d'application .1
2 Références normatives .1
3 Termes et définitions .1
4 Filtre spline pour un échantillonnage uniforme et non uniforme .2
4.1 Généralités . 2
4.2 Équation de filtre pour un filtre spline cubique . 3
4.2.1 Généralités . 3
4.2.2 Paramètre de régularisation . 4
4.2.3 Paramètre de tension . 4
4.2.4 Matrice V pour un filtre spline cubique linéaire . 4
4.2.5 Matrice V pour un filtre spline cubique robuste . 5
4.2.6 Terminaison de l’itération d’une estimation robuste . 5
4.2.7 Matrices de différenciation P et Q . 5
4.3 Caractéristiques de transmission . . 8
4.4 Autre filtre spline robuste . . 8
4.4.1 Généralités . 8
4.4.2 Fonction objectif avec la norme L2 sans énergie de tension pour l’équation
de filtre linéaire . . . 9
4.4.3 Fonction objectif avec la norme L1 sans énergie de tension pour un filtrage
robuste .
...

TECHNICAL ISO/TR
REPORT 16610-32
First edition
Geometrical product specifications
(GPS) — Filtration —
Part 32:
Robust profile filters: Spline filters
Spécification géométrique des produits (GPS) — Filtrage —
Partie 32: Filtres de profil robustes: Filtres splines
PROOF/ÉPREUVE
Reference number
ISO/TR 16610-32:2023(E)
© ISO 2023

---------------------- Page: 1 ----------------------
ISO/TR 16610-32:2023(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
PROOF/ÉPREUVE © ISO 2023 – All rights reserved

---------------------- Page: 2 ----------------------
ISO/TR 16610-32:2023(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Spline filter for uniform and non-uniform sampling . 2
4.1 General . 2
4.2 Filter equation for cubic spline filter . 2
4.2.1 General . 2
4.2.2 Regularization parameter . 3
4.2.3 Tension parameter . 4
4.2.4 Matrix V for linear cubic spline filter . 4
4.2.5 Matrix V for robust cubic spline filter . 4
4.2.6 Termination of the iteration of robust estimation . 5
4.2.7 Matrices of differentiation P and Q . 5
4.3 Transmission characteristics . 8
4.4 Alternative robust spline filter . 8
4.4.1 General . 8
4.4.2 Objective function with L2-norm without tension energy for the linear
filter equation . 9
4.4.3 Objective function with L1-norm without tension energy for robust
filtration .
...

© ISO 2023 – All rights reserved
ISO/PRF TR 16610-32:2023(E)
ISO/TC 213/WG 15
Secretariat: BSI
Date: 2023-07-24
Geometrical product specifications (GPS) — Filtration —
Part 32:
Robust profile filters: Spline filters

Technical Report

Warning for WDs and CDs
This document is not an ISO International Standard. It is distributed for review and comment. It is subject to
change without notice and may not be referred to as an International Standard.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of
which they are aware and to provide supporting documentation.

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ISO #####-#:####(X)
Spécification géométrique des produits (GPS) — Filtrage —
Partie 32: Filtres de profil robustes: Filtres splines
FDIS stage
2 © ISO #### – All rights reserved

---------------------- Page: 2 ----------------------
ISO/PRF TR 16610-32:(E)
© ISO 2023, Published in Switzerland
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this
publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical,
including photocopying, or posting on the internet or an intranet, without prior written permission. Permission can
be requested from either ISO at the address below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. Phone: + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail: [e-mail]
Website: www.iso.org
Published in Switzerland
www.iso.org
© ISO 2023 – All rights reserved iii

---------------------- Page: 3 ----------------------
ISO/PRF TR 16610-32:(E)
Contents
Foreword . v
Introduction . vii
Part 32: Robust profile filters: Spline filters. 1
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Spline filter for uniform and non-uniform sampling . 2
4.1 General . 2
4.2 Filter equation for cubic spline filter . 3
4.2.1 General . 3
4.2.2 Regularization parameter . 4
4.2.3 Tension parameter . 4
4.2.4 Matrix V for linear cubic spline filter . 5
4.2.5 Matrix V for robust cubic spline filter . 5
4.2.6 Termination of the iteration of robust estimation . 6
4.2.7 Matrices of differentiation P and Q . 6
4.3 Transmission characteristics . 9
4.4 Alternative robust spline filter . 9
...