Comparison of discrete Laplacian-Beltrami operators and their applications in surface metrology

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Abstract

In addition to computer image processing, mesh smoothing can also be used in surface metrology to remove noise from free-form surfaces, which are widely represented by triangular meshes. The diffusion equation, also known as the heat equation, is generalised and applied to smooth meshes. The Laplacian operator in the equation is generalised to the Laplacian-Beltrami operator so the equation can be used not only on scalar functions defined in Euclidean space but also on
functions defined on non-Euclidean manifolds. The triangular meshes are piecewise linear approximations of a free-form surface. Therefore, the LaplacianBeltrami operator needs to be discrete.
There are three kinds of discretisation methods widely used currently: uniform graph Laplacian, distance Laplacian and cotangent formula. Their algorithms will be briefly introduced and their performance will be compared in four aspects: smoothness, shrinkage degree, computation time and edge distortion degree. Tests will be conducted on simulated surfaces and measured surfaces. Then, recommendations will be given regarding the requirements of measurement and
characteristics of samples.
Original languageEnglish
Title of host publicationLaser Metrology and Machine Performance XV
Subtitle of host publication15th International Conference and Exhibition on Laser Metrology, Machine Tool, CMM & Robotic Performance: LAMDAMAP 2023
EditorsAndrew Longstaff, Nan Yu
Publishereuspen
Pages257-260
Number of pages13
ISBN (Electronic)9781998999125
Publication statusPublished - 15 Mar 2023
Event15th International Conference and Exhibition on Laser Metrology, Coordinate Measuring Machine and Machine Tool Performance - Edinburgh, United Kingdom
Duration: 14 Mar 202315 Mar 2023

Conference

Conference15th International Conference and Exhibition on Laser Metrology, Coordinate Measuring Machine and Machine Tool Performance
Abbreviated titleLamdamap 2023
Country/TerritoryUnited Kingdom
CityEdinburgh
Period14/03/2315/03/23

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