BS EN ISO 16610-29-2020 Geometrical product specifications (GPS)一Filtration Part 29: Linear profile filters: Wavelets.
4.4 Biorthogonal wavelets
4.4.1 General
The application addressed with this document is to recognize features of differing scales (resolutions) by smoothing accordingly. The biorthogonal wavelets specified in this document are all symmetrical wavelets and the decomposed signal can be reconstructed without loss.
4.4.2 Cubic prediction wavelets
A fast implementation of the wavelet decomposition and reconstruction has been employed using a lifting scheme with three stages: splitting, prediction and updating, originally introduced by Sweldens, in which the Neville polynomials are employed to implement the prediction stage by interpolating between sampling positions[6.Z1. The cubic prediction wavelets in Annex A using Sweldens’ lifting schemel6] has been validated as an efficient tool for fast and in-place wavelet transform for geometrical products applications, for example surface metrologyl2].
4.4.3 Cubic b-spline wavelets
Spline wavelets are based on the spline function. In this document a cubic b-spline function is used, which has a compact support. The particular cubic spline wavelets used are the biorthogonal wavelets
CDF 9/7 with four vanishing moments, detailed in Annex B. This was original introduced by Cohen et al.[8] and has been used in geometrical products applications, for example multiscale analysis. The cubic spline wavelet transform can be implemented using both the Fourier method and the lifting scheme (however, it is a five-stage process) with relevant precision.
5 Filter designation
Lifting schemes using cubic interpolation for the wavelet transform in conformity with this document are designated:
CDF 9/7 Spline wavelets in conformity with this document are designated:
See also ISO 16610-1:2015, Clause 5.BS EN ISO 16610-29 pdf download.