Abstract
This paper addresses the problem of edge-preserving smoothing of natural images. A novel adaptive approach as a preprocessing stage in feature extraction and/or image segmentation. It performs a weighted convolution by combining both spatial and tonal information in a single similarity measure based on the local calculation of geodesic time functions. Two different strategies are derived for smoothing heterogeneous areas while preserving relevant structures.
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References
Jähne, B.: Digital Image Processing: Concepts, Algorithms and Scientific Applications, 4th edn. Springer, Heidelberg (1997)
Saint-Marc, P., Chen, J., Medioni, G.: Adaptive smoothing: A general tool for early vision. IEEE Trans. Patt. Ana. Mach. Intel. 13, 514–529 (1991)
Winkler, G., Aurich, V., Hahn, K., Martin, A.: Noise reduction in images: some recent edge-preserving methods. Patt. Recogn. Im. Ana. 9, 749–766 (1999)
Mrázek, P., Weickert, J., Bruhn, A.: On robust estimation and smoothing with spatial and tonal kernels. In: Klette, R., Kozera, R., Noakes, L., Weickert, J. (eds.) Geometric Properties from Incomplete Data, pp. 335–352. Springer, Heidelberg (2006)
Sun, T., Neuvo, Y.: Detail-preserving median based filters in image processing. Patt. Recogn. Lett. 15, 341–347 (1994)
Nitzberg, M., Shiota, T.: Nonlinear image filtering with edge and corner enhancement. IEEE Trans. Patt. Ana. Mach. Intel. 14, 826–833 (1992)
Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proc. of ICCV, pp. 839–846 (1998)
Barash, D.: A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation. IEEE Trans. Patt. Ana. Mach. Intel. 24, 844–847 (2002)
Buades, A., Coll, B., Morel, J.M.: Neighborhood filters and PDE’s. Numer. Math. 105, 1–34 (2006)
Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Patt. Ana. Mach. Intel. 12, 629–639 (1990)
van den Boomgaard, R., van de Weijer, J.: On the equivalence of local-mode finding, robust estimation and mean-shift analysis as used in early vision tasks. In: Proc. of ICPR, vol. 3, pp. 927–930 (2002)
Comaniciu, D., Meer, P.: Mean shift: a robust approach toward feature space analysis. IEEE Trans. Patt. Ana. Mach. Intel. 24, 603–619 (2002)
Lantuéjoul, C., Maisonneuve, F.: Geodesic methods in image analysis. Patt. Recogn. 17, 177–187 (1984)
Soille, P.: Generalized geodesy via geodesic time. Patt. Recogn. Lett. 15, 1235–1240 (1994)
Verwer, B., Verbeek, P., Dekker, S.: An efficient uniform cost algorithm applied to distance transforms. IEEE Trans. Patt. Ana. Mach. Intel. 11, 425–429 (1989)
Soille, P.: Morphological Image Analysis: Principles and Applications, 2nd edn. Springer, Heidelberg (2004)
Levi, G., Montanari, U.: A grey-weighted skeleton. Inform. Cont. 17, 62–91 (1970)
Ikonen, L., Toivanen, P.: Distance and nearest neighbor transforms on gray-level surfaces. Patt. Recogn. Lett. 28, 604–612 (2007)
Sethian, J.: A fast marching level set method for monotonically advancing fronts. Proc. of Nat. Acad. Sci. 93, 1591–1595 (1996)
Borgefors, G.: Distance transformations in digital images. Comp. Vis. Graph. Im. Proc. 34, 344–371 (1986)
Sumengen, B., Bertelli, L., Manjunath, B.: Fast and adaptive pairwise similarities for graph cuts-based image segmentation. In: Proc. of IEEE POCV (2006)
Di Zenzo, S.: A note on the gradient of a multi-image. Comp. Vis. Graph. Im. Proc. 33, 116–125 (1986)
Scheunders, P., Sijbers, J.: Multiscale anisotropic filtering of color images. In: Proc. of IEEE ICIP, vol. 3, pp. 170–173 (2001)
Lerallut, R., Decencière, E., Meyer, F.: Image filtering using morphological amoebas. Im. Vis. Comput. 25, 395–404 (2007)
Soille, P., Grazzini, J.: Advances in constrained connectivity. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 423–433. Springer, Heidelberg (2008)
Gomez, G.: Local smoothness in terms of variance. In: Proc. of BMVC, vol. 2, pp. 815–824 (2000)
Spira, A., Kimmel, R., Sochen, N.: A short time Beltrami kernel for smoothing images and manifolds. IEEE Trans. Im. Proc. 16, 1628–1636 (2007)
Barash, D., Comaniciu, D.: A common framework for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift. Im. Vis. Comput. 22, 73–81 (2004)
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Grazzini, J., Soille, P. (2009). Image Filtering Based on Locally Estimated Geodesic Functions. In: Ranchordas, A., Araújo, H.J., Pereira, J.M., Braz, J. (eds) Computer Vision and Computer Graphics. Theory and Applications. VISIGRAPP 2008. Communications in Computer and Information Science, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10226-4_10
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DOI: https://doi.org/10.1007/978-3-642-10226-4_10
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