Freeform surface filtering using the diffusion equation

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 467, Issue 2127, 2011, Pages 841-859

  Jiang, X ^a   Cooper, P ^a   Scott, P J ^a  

^a UNIVERSITY OF HUDDERSFIELD   (United Kingdom)

Author keywords

Diffusion filtering; Freeform surfaces; Gaussian scale space; Surface metrology

Indexed keywords

CONVOLUTION; GAUSSIAN DISTRIBUTION; LAPLACE EQUATION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL OPERATORS; TEXTURES; UNITS OF MEASUREMENT;

ANALYTICAL SOLUTIONS; DIFFUSION EQUATIONS; DIFFUSION FILTERING; DISCRETIZATIONS; EUCLIDEAN; EXPERIMENTAL DATA; FREE-FORM SURFACE; FREEFORM SURFACES; FREEFORMS; GAUSSIAN FILTERING; GAUSSIAN FILTERS; GAUSSIAN FUNCTIONS; GAUSSIAN SCALE SPACE; GEOMETRIC SURFACES; ISOTROPIC DIFFUSION; LAPLACE-BELTRAMI OPERATOR; NON-EUCLIDEAN; PLANAR REGION; PRACTICAL IMPLEMENTATION; SAMPLED DATA; STANDARD DEVIATION; SURFACE DATA; SURFACE METROLOGY; SURFACE TEXTURES;

DIFFUSION;

EID: 79952328801     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2010.0307     Document Type: Article

References (21)

1. Bajaj, C. & Xu, G. 2003 Anisotropic diffusion of surfaces and functions on surfaces. ACM Trans. Graph. 22, 4-32. (doi:10.1145/588272.588276) (Pubitemid 44769056)
2. Clarenz, U., Diewald, U. & Rumpf, M. 2000 Anisotropic geometric diffusion in surface processing. In IEEE Visualization, Salt Lake City, Utah, pp. 397-405. Los Alamitos, CA: IEEE Computer Society Press.
3. Clayor, N. E., Combs, D. M., Lechuga, O. M., Mader, J. J. & Udayasankaran, J. 2004 An overview of freeform optics production. In Proc. of ASPE Winter Topical Meeting: Free-Form Optics: Design, Fabrication, Metrology, Assembly, North Carolina, USA, 4-5 February. Raleigh, NC: APSE.
4. Desbrun, M., Meyer, M., Schröder, P. & Barr, A. H. 1999 Implicit fairing of irregular meshes using diffusion and curvature flow. In SIGGRAPH '99: Proc. of the 26th Annual Conf. on Computer Graphics and Interactive Techniques, 1999, pp. 317-324. New York, NY: ACM Press/Addison- Wesley Publishing Co.
5. do Carmo, M. P. 1993 Riemannian geometry. Boston, MA: Birkhäuser.
6. ISO 11562. 1996 Geometric product specification (GPS) -surface texture: Profile method- metrological characteristics of phase correct filters. Geneva, Switzerland: International Standards Organization.
7. ISO/CD 16610-61. 2010 Geometrical product specifications (GPS) -filtration-part 61: Linear areal filters: Gaussian filters. Geneva, Switzerland: International Standards Organization.
8. ISO/FDIS 16610-21 Series. 2010 Geometrical product specifications (GPS) - filtration-part 21: Linear profile filters: Gaussian filters. Geneva, Switzerland: International Standards Organization.
9. ISO/FDIS 25178-2. 2010 Geometrical product specification (GPS) -surface texture: Areal-part 2: Terms, definitions and surface texture parameters. Geneva, Switzerland: International Standards Organization.
10. ISO/TS 16610 Series. 2010 Geometrical product specification (GPS) -filtration. Geneva, Switzerland: International Standards Organization.
11. Jiang, X., Scott, P. J., Whitehouse, D. J. & Blunt, L. 2007a Paradigm shifts in surface metrology. Part I. Historical philosophy. Proc. R. Soc. A 463, 2049-2070. (doi:10.1098/rspa.2007.1874)
12. Jiang, X., Scott, P. J., Whitehouse, D. J. & Blunt, L. 2007b Paradigm shifts in surface metrology. Part II. The current shift. Proc. R. Soc. A 463, 2071-2099. (doi:10.1098/rspa.2007.1873)
13. Jiang, X., Zhang, X. & Scott, P. 2010 Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology. Meas. Sci. Technol. 21, 045101. (doi:10.1088/0957- 0233/21/4/045101)
14. Liu, D., Xu, G. & Zhang, Q. 2008 A discrete scheme of Laplace-Beltrami operator and its convergence over quadrilateral meshes. Comput. Math. Appl. 55, 1081-1093. (doi:10.1016/j.camwa.2007.04.047) (Pubitemid 351199986)
15. Meyer, M., Desbrun, M., Schröder, P. & Barr, A. H. 2002 Discrete differential geometry operators for triangulated 2-manifolds. In Int. Workshop on Visualization and Mathematics, Berlin, Germany, 2002, pp. 35-57.
16. NIST. 2010 Surface metrology algorithm testing system, USA. See http://syseng.nist.gov/VSC/jsp/index.jsp.
17. Perona, P. & Malik, J. 1987 Scale space and edge detection using anisotropic diffusion. In Proc. IEEE Computer Society Workshop on Computer Vision, Miami Beach, FL, 30 November to 2 December 1987, pp. 16-22. Washington, DC: IEEE Computer Society. (Pubitemid 18569199)
18. Piegl, L. & Tiller, W. 1997 The NURBS book, 2nd edn. New York, NY: Springer.
19. Weickert, J. 1998 Anisotropic diffusion in image processing. Stuttgart, Germany: B.G. Teubner.
20. Witkin, A. P. 1983 Scale-space filtering. In Proc. 8th Int. Joint Conf. on Artificial Intelligence, Karlsruhe, West Germany, August, 1983, pp. 1019-1022. San Francisco, CA: Morgan Kaufman Publishers Inc.
21. Xu, G. 2004 Convergence of discrete Laplace-Beltrami operators over surfaces Comput. Math. Appl. 48, 347-360. (doi:10.1016/j.camwa.2004.05.001)