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Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.745732January 1999 (vol. 21 no. 1) pp. 42-48
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Abstract—Nonlinear anisotropic diffusion algorithms provide significant improvement in image enhancement as compared to linear filters. However, the excessive computational cost of solving nonlinear PDEs precludes their use in real-time vision applications. In the present paper, we show that two orders of magnitude speed improvement is provided by a new image filtering paradigm in which an adaptively determined vector field specifies nonlocal application points for an image filter.

[1] 42 H. Blum, "A New Model of Global Brain Function," Perspectives in Biology and Medicine, vol. 10, pp. 381-407, 1967.
[2] H. Blum, "Biological Shape and Visual Science: Part I," J. Theoretical Biology, vol., 38, pp. 205-287, 1973.
[3] H. Blum and R.N. Nagel, "Shape Description Using Weighted Symmetric Axis Features," Pattern Recognition, vol. 10, no. 3, pp. 167-180, 1978.
[4] C.A. Burbeck and S.M. Pizer, "Object Representation by Cores: Identifying and Representing Primitive Spatial Regions," Vision Research, vol. 35, no. 13, pp. 1,917-1,930, 1995.
[5] P.J. Burt and E.H. Adelson, “The Laplacian Pyramid as a Compact Image Code,” IEEE Trans. Comm., vol. 31, no. 4, pp. 532-540, 1983.
[6] J. Canny, “A Computational Approach to Edge Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, June 1986.
[7] F. Catté, P.L. Lions, J.M. Morel, and T. Coll, “Image Selective Smoothing and Edge Detection by Nonlinear Diffusion,” SIAM J. Numerical Analysis, vol. 29, no. 1, pp. 182-193, 1992.
[8] M.A. Cohen and S. Grossberg, "Neural Dynamics of Brightness Perception: Features, Boundaries, Diffusion, and Resonance," Perception and Psychophysics, vol. 36, pp. 428-456, 1984.
[9] P.-E. Danielsson, "Getting the Median Faster," Computer Graphics, and Image Processing, vol. 17, pp. 71-78, 1981.
[10] A.I. El-Fallah and G.E. Ford, "Nonlinear Adaptive Image Filtering Based on Inhomogeneous Diffusion and Differential Geometry," SPIE Image and Video Processing II, vol. 2,182, pp. 49-63, 1994.
[11] B. Fischl and E. Schwartz, "Learning an Integral Equation Approximation to Nonlinear Anisotropic Diffusion in Image Processing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 4, pp. 342-352, 1997.
[12] B. Fischl and E.L. Schwartz, "Learned Adaptive Nonlinear Filtering for Anisotropic Diffusion Approximation in Image Processing," Int'l Conf. Pattern Recognition,Vienna, Austria, 1996.
[13] F.S. Frome, "A Psychophysical Study of Shape," Technical Report TR-198, Univ. of Maryland, Computer Science Center, College Park, Md., 1972.
[14] S. Grossberg and E. Mingolla, "Neural Dynamics of Form Perception: Boundary Completion, Illusory Figures, and Neon Color Spreading," Psychological Rev., vol. 92, no. 2, pp. 173-211, 1985.
[15] T. Huang, G. Yang, and G. Tang, "A Fast Two-Dimensional Median Filtering Algorithm," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 27, pp. 13-18, 1979.
[16] A. Hummel, "Representations Based on Zero-Crossings in Scale-Space," M. Fischler, and O. Firschein, eds., Readings in Computer Vision: Issues, Problems, Principles and Paradigms.Los Angeles, Calif.: Morgan Kaufmann, 1986.
[17] J. Koenderink, "The Structure of Images," Biological Cybernetics, vol. 50, pp. 363-370, 1984.
[18] I. Kovács and B. Julesz, "Perceptual Sensitivity Maps Within Globally Defined Visual Shapes," Nature, vol. 370, pp. 644-646, 1994.
[19] V.A.F. Lamme, "The Neurophysiology of Figure-Ground Segregation in Primary Visual Cortex," J. Neuroscience, vol. 15, no. 2, pp. 1,605-1,615, 1995.
[20] T.S. Lee, "Neurophysiological Evidence for Image Segmentation and Medial Axis Computation in Primate V1," J. Bower, ed., Advances in Computational Neuroscience. Proc. Fourth Ann. Computational Neuroscience Conf. Plenum Press, 1995.
[21] T.S. Lee, V.A.F. Lamme, and D. Mumford, "The Role of V1 in Scene Segmentation and Shape Representation," Nature, 1996.
[22] R. Malladi and J.A. Sethian, "Image Processing Via Level Set Curvature Flow," Proc. Nat'l Academy of Sciences, vol. 92, pp. 7,046-7,050, 1995.
[23] D. Marr and E. Hildreth, "Theory of Edge Detection," Proc. Royal Soc. London, B-207, pp. 187-217, 1980.
[24] M. Nitzberg, D. Mumford, and T. Shiota, “Filtering, Segmentation and Depth Filtering, Segmentation and Depth,” Lecture Notes in Computer Science, vol. 662, 1993.
[25] M. Nitzberg and T. Shiota, “Nonlinear Image Filtering with Edge and Corner Enhancement,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, pp. 826-833, 1992.
[26] S. Osher and J.A. Sethian, “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations,” J. Computing in Physics, vol. 79, pp. 12-49, 1988.
[27] P. Perona and J. Malik, "Scale Space and Edge Detection Using Anisotropic Diffusion," Proc. IEEE CS Workshop Computer Vision, pp. 16-27,Miami, Fla., 1987.
[28] P. Perona and J. Malik, "Scale-Space and Edge Detection Using Anisotropic Diffusion," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629639, July 1990.
[29] A.S. Rojer and E.L. Schwartz, "Design Considerations for a Space-Variant Visual Sensor With Complex-Logarithmic Geometry," Proc. Int'l Conf. Pattern Recognition, ICPR-10, vol. 2, pp. 278-285, 1990.
[30] Geometry-Driven Diffusion in Computer Vision, B.M. ter Haar Romeny, ed. Kluwer, 1994.
[31] J. Weickert, "Recursive Separable Schemes for Nonlinear Diffusion Filters," B.M. ter Haar Romeny, L. Florack, J. Koenderink, and M. Viergever, eds., Lecture Notes in Computer Science, vol. 1,252, pp. 260-271. Springer, 1997.
[32] J. Weickert, B.M. ter Haar Romeny, and M. Viergener, Efficient and Reliable Scheme for Non-Linear Diffusion and Filtering IEEE Trans. Image Processing, vol. 7, pp. 398-410, 1998.
[33] J. Weickert, K. Zuiderveld, B.M. ter Haar Romeny, and W. Niessen, "Parallel Implementations of AOSÕSchemes: A Fast Way of Nonlinear Diffusion Filtering," Proc. 1997 IEEE Int'l Conf. Image Processing ICIP-97.Santa Barbara, Calif.: Springer, 1997.
[34] R.T. Whitaker and S.M. Pizer, “A Multi-Scale Approach to Non Uniform Diffusion,” CVGIP: Image Understanding, vol. 57, no. 1, pp. 99-110, 1993.
[35] A. Witkin, "Scale-Space Filtering," Int'l Joint Conf. Artificial Intelligence, pp. 1,019-1,021,Karlsruhe, West Germany, 1983.

Index Terms:
Segmentation, diffusion, scale-space, anisotropic diffusion, nonlinear diffusion, filtering, permutation filter, nonlocal filter.
Citation:
Bruce Fischl, Eric L. Schwartz, "Adaptive Nonlocal Filtering: A Fast Alternative to Anisotropic Diffusion for Image Enhancement," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 1, pp. 42-48, Jan. 1999, doi:10.1109/34.745732
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