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Freeform surface filtering using the lifting wavelet transform

Abdul-Rahman, Hussein S., Jiang, Xiangqian and Scott, Paul J. (2012) Freeform surface filtering using the lifting wavelet transform. Precision Engineering, 37 (1). pp. 187-202. ISSN 01416359

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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

Item Type: Article
Additional Information: This is the author’s version of a work that was accepted for publication in Precision Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Precision Engineering Volume 37, Issue 1, January 2013, Pages 187–202
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA76 Computer software
T Technology > T Technology (General)
Schools: School of Computing and Engineering
School of Computing and Engineering > Centre for Precision Technologies > Surface Metrology Group
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Depositing User: Hussein Abdul-Rahman
Date Deposited: 01 Nov 2012 11:59
Last Modified: 28 Aug 2021 20:25


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