Abstract
The Perona-Malik model is an effective but ill-posed model for denoising digital images by anisotropic diffusion. Instead of complex regularizations, we propose a new continuous model which is well-posed and show that it is nevertheless effective for denoising. In addition, an extension of our model offers the possibility of inducing a convergence for the discretization. A comparison to the original Perona-Malik model is carried out using an human vision-centered quality index which shows the improvements of our model when it comes to denoising.
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References
Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner, Stuttgart (1998)
Kuijper, A.: p-Laplacian driven image processing. In: ICIP, vol. V, pp. 257–260 (2007)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. In: Proceedings of IEEE Computer Society Workshop on Computer Vision, pp. 16–22 (1987)
Kuijper, A.: Geometrical PDEs based on second order derivatives of gauge coordinates in image processing. Image and Vision Computing 27(8), 1023–1034 (2009)
Wielgus, M.: Perona-Malik equation and its numerical properties. Master’s thesis, Uniwersytet Warszawski (2010)
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, 2nd edn. Springer (2006)
Catté, F., Lions, P.L., Morel, J.M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)
Benhamouda, B.: Parameter adaptation for nonlinear diffusion in image processing. Master’s thesis, Kaiserslautern (1996)
Weickert, J., ter Haar Romeny, B.M., Viergever, M.A.: Efficient and reliable schemes for nonlinear diffusion filtering. IEEE TIP 7, 398–410 (1998)
Robert, L., Deriche, R.: Dense depth map reconstruction: A minimization and regularization approach which preserves discontinuities. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1065, pp. 439–451. Springer, Heidelberg (1996)
Wei, G.: Generalized Perona-Malik equation for image restoration. IEEE Signal Processing Letters 6, 165–167 (1997)
Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)
Vogel, C.R., Oman, M.E.: Fast, robust total variation-based reconstruction of noisy, blurred images. IEEE TIP 7(6), 813–824 (1998)
Guo, Z., Sun, J., Zhang, D., Wu, B.: Adaptive Perona and Malik Model Based on the Variable Exponent for Image Denoising. IEEE TIP 21(3), 958–967 (2012)
Thuerck, D.: A weakened Perona Malik inspired model for effective denoising. Technical Report, TU Darmstadt (2013)
Kuijper, A., Schwarzkopf, A., Kalbe, T., Bajaj, C., Roth, S., Goesele, M.: 3D anisotropic diffusion on GPUs by closed-form local tensor computations. Numerical Mathematics: Theory, Methods and Applications 6(1), 72–94 (2013)
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)
Wang, Z., Lu, L., Bovik, A.C.: Foveation scalable video coding with automatic fixation selection. IEEE TIP 12(2), 243–254 (2003)
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Thuerck, D., Kuijper, A. (2013). Cosine-Driven Non-linear Denoising. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2013. Lecture Notes in Computer Science, vol 7950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39094-4_28
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DOI: https://doi.org/10.1007/978-3-642-39094-4_28
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