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Multigrid Bilateral Filter

Authors: Zongqing Lu

Abstract:

It has proved that nonlinear diffusion and bilateral filtering (BF) have a closed connection. Early effort and contribution are to find a generalized representation to link them by using adaptive filtering. In this paper a new further relationship between nonlinear diffusion and bilateral filtering is explored which pays more attention to numerical calculus. We give a fresh idea that bilateral filtering can be accelerated by multigrid (MG) scheme which likes the nonlinear diffusion, and show that a bilateral filtering process with large kernel size can be approximated by a nonlinear diffusion process based on full multigrid (FMG) scheme.

Keywords: Bilateral filter, multigrid

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1086029

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[1] Z. Lin, , and Q. Shi. An anisotropic diffusion PDE for noise reduction and thin edge preservation. In Proc. 10th Int. Conf. Image Analysis and Processing, IEEE Computer Society, Los Alamitos, CA, 102-107, 1999.
[2] N. Sochen, R. Kimmel, and R. Malladi. A geometrical framework for low level vision. IEEE Trans. Image Processing, 7(3):310-318, 1998.
[3] J. Weickert. Anisotropic Diffusion in Image Processing, ser. ECMI Series. Stuttgart, Germany: Teubner, 1998.
[4] G. Sapiro and D. L. Ringach. Anisotropic diffusion of color images. Proc. SPIE, 471:382-2657, 1996.
[5] P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE Trans on PAMI. 12(7):629-639, 1990.
[6] R. L. Lagendijk, J. Biemond, and D. E. Boekee. Regularized iterative image restoration with ringing reduction. IEEE Trans. Acoust., Speech, Signal Processing, 36(12):1874-1887, 1988.
[7] M. E. Zervakis. Nonlinear image restoration techniques. Ph.D. dissertation, Univ. Toronto, Toronto, ON, Canada, 1990.
[8] M. J. Black and G. Sapiro. Edges as outliers: Anisotropic smoothing using local image statistics. In Scale-Space Theories in Computer Vision, Second International Conference, Scale-Space. Proceedings (Lecture Notes in Computer Science), 1682: 259-270, 1999.
[9] M. Black and A. Rangarajan. On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. Int. J. Comput. Vis., 19(1): 57-92, 1996.
[10] C. Tomasi and R. Manduchi. Bilateral filtering for gray and color images. In Proc. 6th Int. Conf. Computer Vision, New Delhi, India, 839-846, 1998.
[11] D. Adalsteinsson and J. A. Sethian. A fast level set method for propagating interfaces. Journal of Computational Physics, 118(2):269-277, 1995.
[12] S. M. Smith and J. M. Brady. SUSAN - a new approach to low level image processing. International Journal of Computer Vision, 23(1):45-78, 1997(b).
[13] J. H. Bramble, Multigrid Methods. New York: Wiley, 1993.
[14] W. L. Briggs. A Multigrid Tutorial. Philadelphia, PA: SIAM, 1988.
[15] W. Hackbush and U. Trottenberg, Eds., Multigrid Methods. New York: Springer-Verlag, 1982.
[16] S. F. McCormick, Ed., Multigrid Methods. Philadelphia, PA: SIAM, 1987.
[17] P. Saint-Marc, J. Chen, and G. Medioni. Adaptive smoothing: A general tool for early vision. IEEE Trans on PAMI. 13(6):514-529, 1991.
[18] D. Terzopoulos. Image analysis using multigrid relaxation methods. IEEE Trans on PAMI. 8(2):129-139, 1986.
[19] Danny Barash. A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing and the Nonlinear Diffusion Equation. IEEE Trans on PAMI, 24(6):1-5, 2002.
[20] S. Paris, F. Durand. A fast approximation of the bilateral filter using a signal processing approach. J. Comput. Vis., 81(1):24-52, 2009.
[21] Ming Zhang, Gunturk. B. K. Multiresolution Bilateral Filtering for Image Denoising. IEEE Trans on Image processing. 17(12):2324-2333, 2008.
[22] B. Weiss. Fast median and bilateral filtering. Proc. SIGGRAPH, 25(3):519-526, 2006.
[23] F. Porikli. Constant Time O (1) Bilateral Filtering. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), 1-8, 2008.
[24] Van E. H. Multigrid methods nonlinear problems: an overview. Proc. SPIE, 5016:36-38, 2003.