Abstract
Perona–Malik diffusion is a well-known type of nonlinear diffusion that can be used for image segmentation and denoising. The process itself needs an parameter k to decide which edges will be retained and which can be blurred and a stopping time t S . Although there have been investigations on how to set these parameters, especially for regularized diffusion models, as well as different criteria for the optimal stopping time have been suggested, there is yet no quick and conclusive way to estimate both parameters – or to reduce the search space at least. In this paper, we show that Gaussian noise characteristics of an image and the diffusion parameters for an optimal optical result can be estimated based on the image histogram. We demonstrate the effectiveness of lazy learning in this area and develop a custom feature weighting algorithm.
Chapter PDF
Similar content being viewed by others
Keywords
- Nonlinear Diffusion
- Average Absolute Error
- Lazy Learning
- Estimate Noise Variance
- Nonlinear Anisotropic Diffusion
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Estimation of optimal pde-based denoising in the SNR sense. IEEE Transactions on Image Processing 15(8), 2269–2280 (2006)
Guo, Z., Sun, J., Zhang, D., Wu, B.: Adaptive Perona-Malik model based on the variable exponent for image denoising. IEEE TIP 21(3), 958–967 (2012), http://dx.doi.org/10.1109/TIP.2011.2169272
Halland, M., Frank, E., Holmes, G., Pfahringer, B., Reutemann, P., Witten, I.H.: The WEKA data mining software: An update. In: ACM SIGKDD Explorations, vol. 11, pp. 10–18 (2009)
Kichenassamy, S.: The Perona-Malik method as an edge pruning algorithm. Journal of Mathematical Imaging and Vision 30, 209–219 (2008)
Kuijper, A.: p-Laplacian driven image processing. In: 14th International Conference on Image Processing, ICIP 2007, vol. V, pp. 257–260 (2007)
Kuijper, A.: Geometrical PDEs based on second order derivatives of gauge coordinates in image processing. Image and Vision Computing 27(8), 1023–1034 (2009)
Monteil, J., Beghdadi, A.: A new interpretation and improvement of the nonlinear anisotropic diffusion for image enhancement. IEEE TPAMI 21(9), 940–946 (1999)
Mrázek, P., Navara, M.: Selection of optimal stopping time for nonlinear diffusion filtering. International Journal of Computer Vision 52(2-3), 189–203 (2003)
Ndajah, P., Kikuchi, H., Yukawa, M., Watanabe, H., Muramatsu, S.: An investigation on the quality of denoised images. Circuits, Systems and Signal Processing 5, 423–434 (2011)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 629–639 (1990)
Quinlan, J.R.: Learning with continuous classes. In: Proceedings of the Australian Joint Conference on Artificial Intelligence, pp. 343–348 (1992)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(259-268) (1992)
Schwarzkopf, A., Kalbe, T., Bajaj, C., Kuijper, A., Goesele, M.: Volumetric nonlinear anisotropic diffusion on gpus. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 62–73. Springer, Heidelberg (2012)
Shao, H., Zou, H.: Threshold estimation based on Perona-Malik model. In: Int. Conf. on Computational Intelligence and Software Engineering, pp. 1–4 (2009)
Thuerck, D., Kuijper, A.: Cosine-driven non-linear denoising. In: Kamel, M., Campilho, A. (eds.) ICIAR 2013. LNCS, vol. 7950, pp. 245–254. Springer, Heidelberg (2013)
Voci, F., Eiho, S., Sugimoto, N., Sekibuchi, H.: Estimating the gradient in the Perona-Malik equation. IEEE Signal Processing Magazine 21(3), 39–65 (2004), http://dx.doi.org/10.1109/MSP.2004.1296541
Weickert, J.: Coherence-enhancing diffusion of colour images. Image Vision Comput. 17(3-4), 201–212 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thuerck, D., Kuijper, A. (2013). Lazy Nonlinear Diffusion Parameter Estimation. In: Petrosino, A. (eds) Image Analysis and Processing – ICIAP 2013. ICIAP 2013. Lecture Notes in Computer Science, vol 8156. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41181-6_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-41181-6_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41180-9
Online ISBN: 978-3-642-41181-6
eBook Packages: Computer ScienceComputer Science (R0)