Summary
Based on image processsing methodology and the theory of geometric evolution problems a novel multiscale method on textured surfaces is presented. The aim is fairing of parametric noisy surfaces coated by a noisy texture. Simultaneously features in the texture and on the surface are enhanced. Considering an appropriate coupling of the two fairing processes one can take advantage of the frequently present strong correlations between edge features in the texture and on the surface edges.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Desbrun, M. Meyer, P. Schroeder, and A. Barr, “Implicit fairing of irregular meshes using diffusion and curvature flow,” in Computer Graphics (SIGGRAPH ‘89 Proceedings), 1999, pp. 317–324.
L. Kobbelt, “Discrete fairing,” in Proceedings of the 7th IMA Conference on the Mathematics of Surfaces 1997, pp. 101–131.
L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel, “Interactive multi-resolution modeling on arbitrary meshes,” in Computer Graphics (SIGGRAPH ‘88 Proceedings), 1998, pp. 105–114.
G. Taubin, “A signal processing approach to fair surface design,” in Computer Graphics (SIGGRAPH ‘85 Proceedings) 1995, pp. 351–358.
B. Curless and M. Levoy, “A volumetric method for building complex models from range images,” in Computer Graphics (SIGGRAPH ‘86 Proceedings), 1996, pp. 303–312.
W.E. Lorensen and H.E. Cline, “Marching cubes: A high resolution 3d surface construction algorithm,” Computer Graphics, vol. 21, no. 4, pp. 163–169, 1987.
M. P. do Carmo, Riemannian Geometry, Birkhäuser, Boston- Basel-Berlin, 1993.
I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, 1984.
I. Guskov, W. Sweldens, and P. Schroeder, “Multiresolution signal processing for meshes,” in Computer Graphics (SIGGRAPH ‘89 Proceedings), 1999.
U. Dierkes, S. Hildebrandt, A. Küster, and O. Wohlrab, Minimal Surfaces, Grundlehren der Mathematischen Wissenschaften. 295. Berlin: Springer- Verlag, 1992.
G. Dziuk, “An algorithm for evolutionary surfaces,” Numer. Math., vol. 58, pp. 603–611, 1991.
P. Perona and J. Malik, “Scale space and edge detection using anisotropic diffusion,” in IEEE Computer Society Workshop on Computer Vision, 1987.
F. Catté, P. L. Lions, J. M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal., vol. 29, pp. 182–193, 1992.
J. Weickert, “Foundations and applications of nonlinear anisotropic diffusion filtering,” Z. Angew. Math. Mech., vol. 76, pp. 283–286, 1996.
U. Diewald, U. Clarenz, and M. Rumpf, “Nonlinear anisotropic diffusion in surface processing,” in Proceedings of IEEE Visualization 2000, 2000, pp. 397 405.
T. Preußer and M. Rumpf, “A level set method for anisotropic geometric diffusion in 3D image processing,” To appear in SIAM J. Appl., 2002.
R. Kimmel, “Intrinsic scale space for images on surfaces: The geodesic curvature flow,” Graphical Models and Image Processing, vol. 59 (5), pp. 365–372, 1997.
J. Weickert, “Coherence-enhancing diffusion of colour images,” Image and Vision Computing, vol. 17, pp. 201–212, 1999.
J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer Graphics: Principles and Practice, Addison-Wesley, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clarenz, U., Diewald, U., Rumpf, M. (2003). A Multiscale Fairing Method for Textured Surfaces. In: Hege, HC., Polthier, K. (eds) Visualization and Mathematics III. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05105-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-662-05105-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05682-6
Online ISBN: 978-3-662-05105-4
eBook Packages: Springer Book Archive