Abstract
A discrete regularization framework on graphs is proposed and studied for color image filtering purposes when images are represented by grid graphs. Image filtering is considered as a variational problem which consists in minimizing an appropriate energy function. In this paper, we propose a general discrete regularization framework defined on weighted graphs which can be seen as a discrete analogue of classical regularization theory. With this formulation, we propose a family of fast and simple anisotropic linear and nonlinear filters. The parameters of the proposed discrete regularization are estimated to have a parameterless filtering.
This research work was partially supported by the ANR foundation under grant ANR-06-MDCA-008-01/FOGRIMMI.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing. Springer, Heidelberg (2002)
Chan, T., Shen, J.: Image Processing and Analysis - Variational, PDE, wavelet, and stochastic methods. SIAM (2005)
Tang, B., Sapiro, G., Caselles, V.: Color image enhancement via chromaticity diffusion. IEEE Transactions on Image Processing 10, 701–707 (2001)
Tschumperlé, D., Deriche, R.: Vector-valued image regularization with PDEs: A common framework for different applications. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(4), 506–517 (2005)
Weickert, J.: Coherence-enhancing diffusion of colour images. Image Vision Comput. 17(3-4), 201–212 (1999)
Zhou, D., Scholkopf, B.: A regularization framework for learning from graph data. In: ICML Workshop on Statistical Relational Learning and Its Connections to Other Fields, pp. 132–137 (2004)
Lezoray, O., Bougleux, S., Elmoataz, A.: Graph regularization for color image processing. Computer Vision and Image Understading (in press) (2007)
Bensoussan, A., Menaldi, J.L.: Difference equations on weighted graphs. Journal of Convex Analysis 12, 13–44 (2005)
Diestel, R.: Graph Theory, vol. 173. Springer, Heidelberg (2005)
Chan, T., Osher, S., Shen, J.: The digital TV filter and nonlinear denoising. IEEE Transactions on on Image Processing 10, 231–241 (2001)
Chambolle, A., Lions, P.L.: Image recovery via total variation minimization and related problems. Numerische Mathematik 76(2), 167–188 (1997)
Chan, T., Kang, S., Shen, J.: Total variation denoising and enhancement of color images based on the CB and HSV color models. J. of Visual Communication and Image Representation 12, 422–435 (2001)
Buades, A., Coll, B., Morel, J.: A non local algorithm for image denoising. In: IEEE Int. Conf. on Computer Vision and Pattern Recognition, vol. 2, pp. 60–65. IEEE Computer Society Press, Los Alamitos (2005)
Brook, A., Kimmel, R., Sochen, N.: Variational restoration and edge detection for color images. Journal of Mathematical Imaging and Vision 18, 247–268 (2003)
Buades, A., Coll, B., Morel, J.: A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation (SIAM interdisciplinary journal) 4(2), 490–530 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lezoray, O., Bougleux, S., Elmoataz, A. (2007). Parameterless Discrete Regularization on Graphs for Color Image Filtering. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2007. Lecture Notes in Computer Science, vol 4633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74260-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-74260-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74258-6
Online ISBN: 978-3-540-74260-9
eBook Packages: Computer ScienceComputer Science (R0)