Freeform Surface Filtering Using the Lifting Wavelet Transform

Hussein S. Abdul-Rahman, Xiangqian Jane Jiang, Paul J. Scott

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

Texture measurement for simple geometric surfaces is well established. Many surface filtration techniques using Fourier, Gaussian, wavelets, etc., have been proposed over the past decades. These filtration techniques cannot be applied to today's complex freeform surfaces, which have non-Euclidean geometries in nature, without distortion of the results. Introducing the lifting scheme opens the opportunity to extend the wavelet analysis to include irregular complex surface geometries. In this paper, a method of filtering those complex freeform surfaces presented by triangular meshes based on the lifting wavelet has been proposed. The proposed algorithm generalises the traditional lifting scheme to any freeform surface represented by any type of triangular mesh; regular, semi-regular or irregular mesh. This technique consists of five major stages; split, predict, update, simplify (down-sampling) and merge (up-sampling). All of these techniques are discussed and explained in the paper. Results and discussion of the application of this method to simulated and measured data are presented.

LanguageEnglish
Pages187-202
Number of pages16
JournalPrecision Engineering
Volume37
Issue number1
DOIs
Publication statusPublished - Jan 2013

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Wavelet transforms
Sampling
Geometry
Wavelet analysis
Textures

Cite this

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abstract = "Texture measurement for simple geometric surfaces is well established. Many surface filtration techniques using Fourier, Gaussian, wavelets, etc., have been proposed over the past decades. These filtration techniques cannot be applied to today's complex freeform surfaces, which have non-Euclidean geometries in nature, without distortion of the results. Introducing the lifting scheme opens the opportunity to extend the wavelet analysis to include irregular complex surface geometries. In this paper, a method of filtering those complex freeform surfaces presented by triangular meshes based on the lifting wavelet has been proposed. The proposed algorithm generalises the traditional lifting scheme to any freeform surface represented by any type of triangular mesh; regular, semi-regular or irregular mesh. This technique consists of five major stages; split, predict, update, simplify (down-sampling) and merge (up-sampling). All of these techniques are discussed and explained in the paper. Results and discussion of the application of this method to simulated and measured data are presented.",
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Freeform Surface Filtering Using the Lifting Wavelet Transform. / Abdul-Rahman, Hussein S.; Jiang, Xiangqian Jane; Scott, Paul J.

In: Precision Engineering, Vol. 37, No. 1, 01.2013, p. 187-202.

Research output: Contribution to journalArticle

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