Jiang, Xiang, Cooper, Philip and Scott, Paul J. (2011) Freeform surface filtering using the diffusion equation. Proceedings of the Royal Society, A, 467 (2127). pp. 841-859. ISSN 1364-5021Metadata only available from this repository.
The measurement of texture for geometric surfaces is well established for surfaces that are of a planar (Euclidean) nature. Gaussian filtering is the fundamental base for scale-limited surfaces used in surface texture, but cannot be applied to non-Euclidean surfaces without distortion of the results. A link exists between Gaussian filtering and solutions of the PDE that models linear isotropic diffusion. In particular, an analytical solution of this diffusion equation over a planar region at a time t is given by the continuous convolution of the initial distribution of the diffused quantity with a Gaussian function of standard deviation Graphic. A practical implementation of the standard Gaussian filter on sampled data can be viewed as a discretization of this process. On a non-Euclidean surface, the diffusion equation is formulated by using the Laplace–Beltrami operator. Using this generalization, a method of Gaussian filtering for freeform surface data is proposed by solving the diffusion equation for approximation residuals defined on a freeform least-squares approximation of the measurement surface data. Results of the application of these methods to simulated and experimental data are presented.
|Subjects:||T Technology > TJ Mechanical engineering and machinery|
|Schools:||School of Computing and Engineering
School of Computing and Engineering > Centre for Precision Technologies > Surface Metrology Group
School of Computing and Engineering > High-Performance Intelligent Computing > Information and Systems Engineering Group
|Depositing User:||Xiang Zhang|
|Date Deposited:||17 Feb 2011 09:35|
|Last Modified:||17 Feb 2011 09:35|
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