Computing and Library Services - delivering an inspiring information environment

Freeform surface filtering using the diffusion equation

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 1364-5021

Metadata 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.

Item Type: Article
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
Related URLs:
Depositing User: Xinfeng Cheng
Date Deposited: 17 Feb 2011 09:35
Last Modified: 28 Aug 2021 11:03


Downloads per month over past year

Repository Staff Only: item control page

View Item View Item

University of Huddersfield, Queensgate, Huddersfield, HD1 3DH Copyright and Disclaimer All rights reserved ©