Abstract

This paper presents an adaptive image decomposition method based on the newly proposed texture descriptor, which combines contrast variation and structure correlation. By incorporating it into the classical edge-preserving bilateral filter, we construct an adaptive nonlinear filter capable of preserving edges and removing texture parts effectively. We derive the variational formulation of the proposed filter and explore its relationship with robust statistics. Comparative experiments against other state-of-the-art decomposition approaches show that better separation results of geometric structure from texture are obtained.

References

• M. Bertalmio, L. Vese, G. Sapiro, and S. Osher, “Simultaneous structure and texture image inpainting,” IEEE Trans. Image Process., vol. 12, no. 8, pp. 882–889, 2003.
• T. Saito, Y. Ishii, H. Aizawa, D. Yamada, and T. Komatsu, “Image-processing approach via nonlinear image decomposition for a digital color camera,” in 15th IEEE International Conference on Image Processing (ICIP), 2008, pp. 905-908.
• D. Paquin, D. Levy, E. Schreibmann, and L. Xing, “Multiscale image registration,” Math. Biosci. Eng., vol. 3, pp. 389–418, 2006.
• Y. Meyer, “Oscillating patterns in image processing and nonlinear evolution equations,” Volume 22 of University Lecture Series. American Mathematical Society, Providence, RI, 2001. The fifteenth Dean Jacqueline B. Lewis memorial lectures.
• L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D., vol. 60, pp. 259–268, 1992.
• L. Vese and S. Osher, “Modeling textures with total variation minimization and oscillating patterns in image processing,” Journal of Scientific Computing, vol. 19, no. 1, pp. 553–572, 2003.
• S.J. Osher, A. Sole, and L.A. Vese, “Image decomposition and restoration using total variation minimization and the H-1 norm,” SIAM Multiscale Modeling and Simulation, vol. 1, no. 3, pp. 349-370, 2003.
• J. Garnett, T. Le, Y. Meyer, and L. Vese, “Image decompositions using bounded variation and homogeneous Besov spaces,” Tech. Rep. CAM Report 05-57, UCLA, 2005.
• C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color images,” in Proc. IEEE Int. Conf. Computer Vision, 1998, pp. 839–846.
• F. Durand and J. Dorsey, “Fast bilateral filtering for the display of high-dynamic-range images,” ACM Trans. Graphics, vol. 21, no. 3, pp. 257–266, 2002.
• S. Bae, S. Paris, and F. Durand, “Two-scale tone management for photographic look,” ACM Trans. Graphics, vol. 25, no. 3, pp. 637–645, 2006.
• Z. Farbman, R. Fattal, D. Lischinski, and R. Szeliski, “Edge-preserving decompositions for multi-scale tone and detail manipulation,” ACM Trans. Graphics, vol. 27, no. 3, pp. 1-10, 2008.
• M.W. Tao, M.K. Johnson, and S. Paris, “Error-tolerant Image Compositing,” Computer Vision, vol. 20, no. 63, pp. 31-44, 2010.
• A. Baudes, T. Le, J.M. Morel, and L. Vese, “Fast cartoon + texture image filters,” IEEE Trans. Image Process., vol. 19, no. 8, pp. 1978-1986, 2010.
• Z. Wang, A.C. Bovik, H.R. Sheikh, and E. P. Simoncelli, “Image Quality Assessment: From Error Measurement to Structural Similarity,” IEEE Trans. Image Process., Vol. 13, No. 4, pp. 600-613, April 2004.
• F.R. Hampel, E.M. Ronchettl, P.J. Rousseeuw, and W.A. Stahel, “Robust statistics: The approach based on influence functions,” Wiley, New York, 1986.