Abstract
Iterative smoothing algorithms are frequently applied in image restoration tasks. The result depends crucially on the optimal stopping (scale selection) criteria. An attempt is made towards the unification of the two frequently applied model selection ideas: (i) the earliest time when the ‘entropy of the signal’ reaches its steady state, suggested by J. Sporring and J. Weickert (1999), and (ii) the time of the minimal ‘correlation’ between the diffusion outcome and the noise estimate, investigated by P. Mrázek and M. Navara (2003). It is shown that both ideas are particular cases of the marginal likelihood inference. Better entropy measures are discovered and their connection to the generalized signal-to-noise ratio is emphasized.
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
Barry, R.P., Pace, R.K.: Monte Carlo estimates of the log determinant of large sparse matrices. Lin. Alg. Appl. 289, 41–54 (1999)
Carasso, A.S.: Linear and nonlinear image deblurring: A documented study. SIAM J. Numer. Anal. 36(6), 1659–1689 (1999)
D’Almeida, F.: Nonlinear diffusion toolbox. MATLAB Central (2003)
Fischer, B., Modersitzki, J.: Inverse Problems, Image Analysis, and Medical Imaging. In: Fast Diffusion Registration. AMS Contemporary Mathematics, vol. 313, pp. 117–129 (2002)
Gilboa, G., Sochen, N., Zeevi, Y.Y.: Estimation of optimal PDE-based denoising in the SNR sense. IEEE Trans. Im. Proc. 15(8), 2269–2280 (2006)
Girdziušas, R., Laaksonen, J.: When is a discrete diffusion a scale-space. In: Int. Conf. Comp. Vis.
Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications. Academic Press, London (1979)
Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. Int. Journal of Computer Vision 52(2), 189–203 (2003)
Perona, P., Malik, J.: Scale–space and edge detection using anisotropic diffusion. IEEE Trans. on PAMI 12(7), 629–639 (1990)
Sporring, J., Weickert, J.: Information measures in scale spaces. IEEE Trans. Inf. Theory 45(3), 1051–1058 (1999)
Weickert, J., ter Haar Romeny, B.M., Viergever, M.A.: Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans. on Image Processing 7(3), 398–410 (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Girdziušas, R., Laaksonen, J. (2007). How Marginal Likelihood Inference Unifies Entropy, Correlation and SNR-Based Stopping in Nonlinear Diffusion Scale-Spaces. In: Yagi, Y., Kang, S.B., Kweon, I.S., Zha, H. (eds) Computer Vision – ACCV 2007. ACCV 2007. Lecture Notes in Computer Science, vol 4843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76386-4_77
Download citation
DOI: https://doi.org/10.1007/978-3-540-76386-4_77
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76385-7
Online ISBN: 978-3-540-76386-4
eBook Packages: Computer ScienceComputer Science (R0)