Abstract
This paper investigates the scale selection problem for nonlinear diffusion scale-spaces. This topic comprises the notions of localization scale selection and scale space discretization. For the former, we present a new approach. It aims at maximizing the image content’s presence by finding the scale that has a maximum correlation with the noise-free image. For the latter, we propose to adapt the optimal diffusion stopping time criterion of Mrázek and Navara in such a way that it may identify multiple scales of importance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Black, M., Sapiro, G., Marimont, D., & Heeger, D. (1998). Robust anisotropic diffusion. IEEE Transactions on Image Processing, 7(3), 421–432.
Blomgren, P., & Chan, T. (1998). Color TV: total variation methods for restoration of vector valued images. IEEE Transactions on Image Processing, 7(3), 304–309.
Bresson, X., Vandergheynst, P., & Thiran, J.-P. (2005). Multiscale active contours. In 5th int. conf. on scale space and pde methods in computer vision (pp. 167–178).
Catté, F., Lions, P.-L., Morel, J.-M., & Coll, T. (1992). Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis, 29(1), 182–193.
Charbonnier, P. (1994). Reconstruction d’image: régularisation avec prise en compte desdiscontinuités. PhD, University of Nice-Sophia Antipolis.
Geman, D., & Reynolds, G. (1992). Constrained restoration and the recovery of discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(3), 367–383.
Gilboa, G., Sochen, N., & Zeevi, Y. (2004). Estimation of optimal PDE-based denoising in the SNR sense (CCIT report 499). Technion-Israel.
Hadjidemetriou, E., Grossberg, M., & Nayar, S. (2002). Resolution selection using generalized entropies of multiresolution histograms. In European conference on computer vision (pp. 220–235).
Hampel, F. (1974). The influence curve and its role in robust estimation. Journal of the American Statistical Association, 69, 383–393.
Katartzis, A., Vanhamel, I., & Sahli, H. (2005). A hierarchical Markovian model for multiscale region-based classification of vector-valued images. IEEE Transactions on Geoscience and Remote Sensing, 43(3), 548–558.
Keeling, S., & Stollberger, R. (2002). Nonlinear anisotropic diffusion filtering for multiscale edge enhancement. Inverse Problems, 18(1), 175–190.
Koenderink, J. (1984). The structure of images. Biological Cybernetics, 50, 363–370.
Lin, Z., & Shi, Q. (1999). An anisotropic diffusion PDE for noise reduction and thin edge preservation. In Int. conf. on image analysis and processing (pp. 102–107).
Lindeberg, T. (1998). Feature detection with automatic scale selection. International Journal of Computer Vision, 30(2), 77–116.
Mrázek, P. (2001). Selection of optimal stopping time for nonlinear diffusion filtering. In Scale-space and morphology in computer vision (pp. 290–298).
Mrázek, P., & Navara, M. (2003). Selection of optimal stopping time for nonlinear diffusion filtering. International Journal of Computer Vision, 52(2/3), 189–203.
Mukhopadhyay, S., & Chanda, B. (2003). Multiscale morphological segmentation of gray-scale images. Transactions on Image Processing, 12(5), 533–549.
Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 629–639.
Petrovic, A., Divorra Escoda, O., & Vandergheynst, P. (2004). Multiresolution segmentation of natural images: From linear to non-linear scale-space representations. IEEE Transactions on Image Processing, 13(8), 1104–1114.
Pratikakis, I. (1998). Watershed-driven image segmentation. PhD, Vrije Universiteit Brussel.
Pratikakis, I., Vanhamel, I., Sahli, H., Gatos, B., & Perantonis, S. (2006). Unsupervised watershed-driven region-based image retrieval. IEE Proceedings on Vision, Image and Signal Processing, 153(3), 313–322.
Rudin, L., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Physica D, 60, 259–268.
Sporring, J., & Weickert, J. (1999). Information measures in scale-spaces. IEEE Transactions on Information Theory, 45, 1051–1058.
Sporring, J., Colios, C., & Trahanias, P. (2000). Generalized scale-selection. IEEE International Conference on Image Processing, 1, 920–923.
Vanhamel, I. (2006). Vector valued nonlinear diffusion and its application to image segmentation. PhD thesis, ETRO/IRIS, Vrije Universiteit Brussel, Brussels-Belgium.
Vanhamel, I., Pratikakis, I., & Sahli, H. (2003). Multi-scale gradient watersheds of color images. IEEE Transactions on Image Processing, 12(6), 617–626.
Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 13(4), 600–612.
Weickert, J. (1998). Anisotropic diffusion in image processing. Teubner-Verlag.
Weickert, J. (1999). Coherence-enhancing diffusion of colour images. Image and Vision Computing, 17(3-4), 201–212.
Whitaker, R. (1993). Geometry-limited diffusion. PhD Thesis, The University of North Carolina.
Whitaker, R., & Gerig, G. (1994). Vector-valued diffusion. In Geometry-driven diffusion in computer vision (pp. 93–134).
You, Y.-L., Xu, W., Tannenbaum, A., & Kaveh, M. (1996). Behavioral analysis of anisotropic diffusion in image processing. IEEE Transactions on Image Processing, 5(11), 1539–1553.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vanhamel, I., Mihai, C., Sahli, H. et al. Scale Selection for Compact Scale-Space Representation of Vector-Valued Images. Int J Comput Vis 84, 194–204 (2009). https://doi.org/10.1007/s11263-008-0154-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11263-008-0154-4