Abstract
Techniques based on the Well-Balanced Flow Equation have been employed as efficient tools for edge preserving noise removal. Although effective, this technique demands high computational effort, rendering it not practical in several applications. This work aims at proposing a multigrid like technique for speeding up the solution of the Well-Balanced Flow equation. In fact, the diffusion equation is solved in a coarse grid and a coarse-to-fine error correction is applied in order to generate the desired solution. The transfer between coarser and finer grids is made by the Mitchell-Filter, a well known interpolation scheme that is designed for preserving edges. Numerical results are compared quantitative and qualitatively with other approaches, showing that our method produces similar image quality with much smaller computational time.
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References
Acton, S.T.: Multigrid anisotropic diffusion. IEEE Transaction on Image Processing 7(3), 280–291 (1998)
Alvarez, L., Lions, P., Morel, J.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(3), 182–193 (1992)
Barcelos, C.A.Z., Boaventura, M., Castro Silva Jr., E.: Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters. Computational and Applied Mathematics 24(1), 131–150 (2005)
Barcelos, C.A.Z., Boaventura, M., Castro Silva Jr., E.: A well-balanced flow equation for noise removal and edge detection. IEEE Transaction on Image Processing 12(7), 751–763 (2003)
Briggs, W.L.: A Multigrid Tutorial. Society for Industrial and Applied Mathematics (1987)
Duff, T.: Splines in Animation and Modeling. State of the Art in Image Synthesis. In: SIGGRAPH 1986 Course Notes (1986)
Hou, H.S., Andrews, H.C.: Cubic splines for image interpolation and digital filtering. IEEE Trans. Acoust., Speech, Signal Processing ASSP-26, 508–517 (1978)
Keys, R.: Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust., Speech, Signal Processing ASSP-29, 1153–1160 (1981)
Koenderink, J.: The structure of images. Biol. Cybernet 50, 363–370 (1984)
Marr, D., Hildreth, E.: Theory of edge detection. Proc. Roy. Soc. 207, 187–217 (1980)
McCormick, S.F. (ed.): Multigrid methods. Frontiers in Applied Mathematics, vol. 3. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1987)
Mitchell, D., Netravali, A.: Reconstruction filters in computer graphics. Computer Graphics 22(4), 221–228 (1988)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transaction on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)
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© 2006 Springer-Verlag Berlin Heidelberg
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Ferraz, C.T., Nonato, L.G., Cuminato, J.A. (2006). An Edge-Preserving Multigrid-Like Technique for Image Denoising. In: Campilho, A., Kamel, M.S. (eds) Image Analysis and Recognition. ICIAR 2006. Lecture Notes in Computer Science, vol 4141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11867586_12
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DOI: https://doi.org/10.1007/11867586_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44891-4
Online ISBN: 978-3-540-44893-8
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