Abstract
The Gaussian serves as Green’s function for the linear diffusion equation and as a source for intuitive understanding of the linear difusion process. In general, non-linear difusion equations have no known closed formsolu tions and thereby no equally simple description. This article introduces a simple, intuitive description of these processes in terms of the Difusion Echo. The Difusion Echo offers intuitive visualisations for non-linear difusion processes.
In addition, the Difusion Echo has potential for o?ering simple formulations for grouping problems. Furthermore, the Difusion Echo can be considered a deep structure summary and thereby offers an alternative to multi-scale linking and ?ooding techniques.
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References
The internet brain segmentation repository, 1999. MR brain data set 788⁃6⁃m and its manual segmentation was provided by the Center for Morphometric Analysis at MGH, http://neuro-www.mgh.harvard.edu/cma/ibsr.
F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll. Image selective smoothing and edge detection by nonlinear difusion. SIAM J. of Num. An., 29:182–193, 1992.
Erik Dam. Evaluation of difusion schemes for watershed segmentation. Master#x2019;s thesis, University of Copenhagen, 2000. Technical report 2000/1 on http://www.diku.dk/research/techreports/2000.htm.
Erik Dam and Mads Nielsen. Non-linear difusion for interactive multi-scale watershed segmentation. MICCAI 2000, vol 1935 of LNCS, 216–225. Springer, 2000.
Jan J. Koenderink. The structure of images. Biol. Cybern., 50:363–370, 1984.
Tony Lindeberg. Scale-Space Theory in Computer Vision. Kluwer, 1994.
Pietro Perona and Jitendra Malik. Scale-space and edge detection using anisotropic difusion. IEEE PAMI, 12(7):629–639, July 1990.
H. Scharr and J. Weickert. An anisotropic difusion algorithmwit h optimized rotation invariance. Mustererkennung 2000, DAGM, pp 460–467. Springer, 2000.
Joachim W eickert. Anisotropic Difusion in Image Processing. Teubner, 1998.
Andrew P. Witkin. Scale-space filtering. In Proceedings of International Joint Conference on Artificial Intelligence, pages 1019–1022, Karlsruhe, Germany, 1983.
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Dam, E., Nielsen, M. (2001). Exploring Non-linear Difusion: The Difusion Echo. In: Kerckhove, M. (eds) Scale-Space and Morphology in Computer Vision. Scale-Space 2001. Lecture Notes in Computer Science 2106, vol 2106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47778-0_23
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DOI: https://doi.org/10.1007/3-540-47778-0_23
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