Abstract
This paper investigates the scale selection problem for vector-valued nonlinear diffusion scale-spaces. We present a new approach for the localization scale selection, which aims at maximizing the image content’s presence by finding the scale having a maximum correlation with the noise-free image. For scale-space discretization, we propose to address an adaptation of the optimal diffusion stopping time criterion introduced by Mrázek and Navara [1], in such a way that it identifies multiple scales of importance.
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Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. Int. J. of Comp. Vis. 52(2-3), 189–203 (2003)
Lindeberg, T.: Feature detection with automatic scale selection. Int. J. of Comp. Vis. 30(2), 77–116 (1998)
Pratikakis, I., Sahli, H., Cornelis, J.: Low level image partitioning guided by the gradient watershed hierarchy. Signal Processing 75(2), 173–195 (1998)
Vanhamel, I., Pratikakis, I., Sahli, H.: Multi-scale gradient watersheds of color images. IEEE Trans. on IP 12(6), 617–626 (2003)
Petrovic, A., Divorra Escoda, O., Vandergheynst, P.: Multiresolution segmentation of natural images: From linear to non-linear scale-space representations. IEEE Trans. on IP 13(8), 1104–1114 (2004)
Katartzis, A., Vanhamel, I., Sahli, H.: A hierarchical markovian model for multiscale region-based classification of vector-valued images. IEEE Trans. on Geoscience and Remote Sensing 43(3), 548–558 (2005)
Catté, F., et al.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. on Numerical Analysis 29(1), 182–193 (1992)
Whitaker, R.T., Gerig, G.: Vector-valued diffusion. In: Geometry-Driven Diffusion in Computer Vision. Computational Imaging and Vision, vol. 1, pp. 93–134. Kluwer Academic Publishers, Dordrecht (1994)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12(7), 629–639 (1990)
Black, M., et al.: Robust anisotropic diffusion. IEEE Trans. on IP 7(3), 421–432 (1998)
You, Y.-L., et al.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. on IP 5(11), 1539–1553 (1996)
Geman, D., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Trans. on PAMI 14( 3), 367–383 (1992)
Koenderink, J.J.: The structure of images. Biological Cybernetics 50, 363–370 (1984)
Weickert, J.: Coherence-enhancing diffusion of colour images. Image and Vision Computing 17(3-4), 201–212 (1999)
Mrázek, P.: Selection of optimal stopping time for nonlinear diffusion filtering. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 290–298. Springer, Heidelberg (2001)
Lin, Z., Shi, Q.: An anisotropic diffusion PDE for noise reduction and thin edge preservation. In: Int. Conf. on Image Analysis and Processing, pp. 102–107 (1999)
Gilboa, G., Sochen, N., Zeevi, Y.: Estimation of optimal pde-based denoising in the snr sense. CCIT report 499, Technion-Israel (2004)
Hampel, F.R.: The influence curve and its role in robust estimation. J. Amer. Statist. Assoc. 69, 383–393 (1974)
Sporring, J., Colios, C.J., Trahanias, P.E.: Generalized scale-selection. In: IEEE Int. Conf. on Image Processing, vol. 1, pp. 920–923. IEEE Computer Society Press, Los Alamitos (2000)
Sporring, J., Weickert, J.: Information measures in scale-spaces. IEEE Transactions on Information Theory 45, 1051–1058 (1999)
Hadjidemetriou, E., Grossberg, M.D., Nayar, S.K.: Resolution Selection Using Generalized Entropies of Multiresolution Histograms. In: Heyden, A., et al. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 220–235. Springer, Heidelberg (2002)
Vanhamel, I.: Vector valued nonlinear diffusion and its application to image segmentation. PhD thesis, ETRO/IRIS: Vrije Universiteit Brussel, Brussels, Belgium (2006)
Wang, Z., et al.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. on Image Processing 13(4), 600–612 (2004)
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Mihai, C., Vanhamel, I., Sahli, H., Katartzis, A., Pratikakis, I. (2007). Scale Selection for Compact Scale-Space Representation of Vector-Valued Images. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_4
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DOI: https://doi.org/10.1007/978-3-540-72823-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72822-1
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