Nonlocal Image and Movie Denoising
- 2.4k Downloads
Neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels. The first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes. A CCD noise model will be presented justifying the involvement of neighborhood filters. A classification of neighborhood filters will be proposed, including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter, NL-means. In order to compare denoising methods three principles will be discussed. The first principle, “method noise”, specifies that only noise must be removed from an image. A second principle will be introduced, “noise to noise”, according to which a denoising method must transform a white noise into a white noise. Contrarily to “method noise”, this principle, which characterizes artifact-free methods, eliminates any subjectivity and can be checked by mathematical arguments and Fourier analysis. “Noise to noise” will be proven to rule out most denoising methods, with the exception of neighborhood filters. This is why a third and new comparison principle, the “statistical optimality”, is needed and will be introduced to compare the performance of all neighborhood filters.
The three principles will be applied to compare ten different image and movie denoising methods. It will be first shown that only wavelet thresholding methods and NL-means give an acceptable method noise. Second, that neighborhood filters are the only ones to satisfy the “noise to noise” principle. Third, that among them NL-means is closest to statistical optimality. A particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods. It will be pointed out that current movie denoising methods are motion compensated neighborhood filters. This amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory. Unfortunately the aperture problem makes it impossible to estimate ground true trajectories. It will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space-time NL-means preserves more movie details.
KeywordsImage denoising Movie denoising Motion estimation
Unable to display preview. Download preview PDF.
- Awate, S. P. & Whitaker, R. T. (2005). Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering. In Proceedings of the 2005 IEEE computer society conference on computer vision and pattern recognition (CVPR’05) (Vol. 2, pp. 44–51). Google Scholar
- Azzabou, N., Paragios, N., & Guichard, F. (2006). Random walks, constrained multiple hypothesis testing and image enhancement. In ECCV (Vol. 1, pp. 379–390). Google Scholar
- Boulanger, J., Kervrann, C., & Bouthemy, P. (2006). Adaptive space-time patch-based method for image sequence restoration. In Proceedings of the ECCV’06 workshop on statistical methods in multi-image and video processing (SMVP’06), Graz, Austria, May 2006. Google Scholar
- Buades, A., Coll, B., & Morel, J. M. (2005b). A non-local algorithm for image denoising, In IEEE international conference on computer vision and pattern recognition. Google Scholar
- Buades, A., Coll, B., & Morel, J. M. (2005c). Denoising image sequences does not require motion estimation. Preprint, CMLA, N 2005-18, May 2005. http://www.cmla.ens-cachan.fr/Cmla/.
- Colleen Gino, M. (2004). “Noise, noise, noise”. http://www.astrophys-assist.com/educate/noise/noise.htm.
- Cremers, D., & Grady, L. (2006). Statistical priors for efficient combinatorial optimization via graph cuts. In European conference on computer vision. Google Scholar
- Dabov, K., Foi, A., Katkovnik, V., & Egiazarian, K. (2006, submitted). Image denoising by sparse 3D transform-domain collaborative filtering. IEEE Transactions on Image Processing. Google Scholar
- Efros, A., & Leung, T. (1999). Texture synthesis by nonparametric sampling. In Proceedings of the international conference on computer vision (ICCV 99) (Vol. 2, pp. 1033–1038). Google Scholar
- Gilboa, G., & Osher, S. (2006). Nonlocal linear image regularization and supervised segmentation. UCLA CAM Report 06-47. Google Scholar
- Gilboa, G., Darbon, J., Osher, S., & Chan, T. F. (2006). Nonlocal convex functionals for image regularization. UCLA CAM Report 06-57. Google Scholar
- Gonzalez, R. C., & Woods, R. E. (2002). Digital image processing (2nd ed.). New York: Prentice Hall. Google Scholar
- Howell, S. B. (2000). Handbook of CCD astronomy. Cambridge: Cambridge University Press. Google Scholar
- Kervrann, C., & Boulanger, J. (2006). Unsupervised patch-based image regularization and representation. In Proceedings of the European conference on computer vision (ECCV’06), Graz, Austria, May 2006. Google Scholar
- Kokaram, A. C. (1993). Motion picture restoration. PhD thesis, Cambridge University. Google Scholar
- Liu, C., Freeman, W. T., Szeliski, R., & Kang, S. B. (2006). Noise estimation from a single image. In CVPR. Google Scholar
- Martinez, D. M. (1986). Model-based motion estimation and its application to restoration and interpolation of motion pictures. PhD thesis, Massachusetts Institute of Technology. Google Scholar
- Merriman, B., Bence, J., & Osher, S. (1992). Diffusion generated motion by mean curvature. In Proceedings of the geometry center workshop. Google Scholar
- Meyer, Y. (2002). Oscillating patterns in image processing and nonlinear evolution equations. In AMS university lecture series (Vol. 22). Google Scholar
- Nagel, H. H. (1983). Constraints for the estimation of displacement vector fields from image sequences. In Proceedings of the eighth international joint conference on artificial intelligence (IJCAI ’83) (pp. 945–951). Google Scholar
- Samy, R. (1985). An adaptive image sequence filtering scheme based on motion detection. SPIE, 596, 135–144. Google Scholar
- Sezan, M. I., Ozkan, M. K., & Fogel, S. V. (1991). Temporally adaptive filtering of noisy sequences using a robust motion estimation algorithm. In Proceedings of the international conference on acoustics, speech, signal processing (Vol. 91, pp. 2429–2432). Google Scholar
- Tomasi, C., & Manduchi, R. (1998). Bilateral filtering for gray and color images. In Sixth international conference on computer vision (pp. 839–846). Google Scholar
- Weickert, J. (1998). On discontinuity-preserving optic flow. In Proceedings of the computer vision and mobile robotics workshop (pp. 115–122). Google Scholar