Abstract
When we take a picture through transparent glass the image we obtain is often a linear superposition of two images: the image of the scene beyond the glass plus the image of the scene reflected by the glass. Decomposing the single input image into two images is a massively ill-posed problem: in the absence of additional knowledge about the scene being viewed there are an infinite number of valid decompositions. In this paper we focus on an easier problem: user assisted separation in which the user interactively labels a small number of gradients as belonging to one of the layers.
Even given labels on part of the gradients, the problem is still ill-posed and additional prior knowledge is needed. Following recent results on the statistics of natural images we use a sparsity prior over derivative filters. We first approximate this sparse prior with a Laplacian prior and obtain a simple, convex optimization problem. We then use the solution with the Laplacian prior as an initialization for a simple, iterative optimization for the sparsity prior. Our results show that using a prior derived from the statistics of natural images gives a far superior performance compared to a Gaussian prior and it enables good separations from a small number of labeled gradients.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc. B 39, 1–38 (1977)
Farid, H., Adelson, E.H.: Separating reflections from images by use of independent components analysis. Journal of the optical society of america 16(9), 2136–2145 (1999)
Finlayson, G.D., Hordley, S.D., Drew, M.S.: Removing shadows from images. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2353, pp. 823–836. Springer, Heidelberg (2002)
Irani, M., Peleg, S.: Image sequence enhancement using multiple motions analysis. In: Conf. on Computer Vision and Pattern Recognition, Champaign, Illinois, pp. 216–221 (June 1992)
Levin, A., Zomet, A., Weiss, Y.: Learning to perceive transparency from the statistics of natural scenes. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems 15 (2002)
Mallat, S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. PAMI 11, 674–693 (1989)
Olshausen, B.A., Field, D.J.: Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607–608 (1996)
Shechner, Y., Shamir, J., Kiryati, N.: Polarization-based decorrelation of transparent layers: The inclination angle of an invisible surface. In: Int. Conf. on Computer Vision, pp. 814–819 (1999)
Simoncelli, E.P.: Statistical models for images:compression restoration and synthesis. In: Proc Asilomar Conference on Signals, Systems and Computers, pp. 673–678 (1997)
Simoncelli, E.P.: Bayesian denoising of visual images in the wavelet domain. In: Müller, P., Vidakovic, B. (eds.) Wavelet based models (1999)
Szeliksi, R., Avidan, S., Anandan, P.: Layer extraction from multiple images containing reflections and transparency. In: Conf. on Computer Vision and Pattern Recognition (2000)
Tappen, M., Freeman, W.T., Adelson, E.H.: Recovering intrinsic images from a single image. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems 15 (2002)
Tsin, Y., Kang, S.B., Szeliski, R.: Stereo matching with reflections and translucency. In: Conf. on Computer Vision and Pattern Recognition, pp. 702–709 (2003)
Vanderbei, R.: Loqo (2000), http://www.princeton.edu/rvdb/
Wainwright, M.J., Simoncelli, E.P., Willsky, A.S.: Random cascades of gaussian scale mixtures for natural images. In: Int. Conf. on Image Processing, pp. I:260– 263 (2000)
Weiss, Y.: Deriving intrinsic images from image sequences. In: Proc. Intl. Conf. Computer Vision, pp. 68–75 (2001)
Zibulevsky, M., Kisilev, P., Zeevi, Y., Pearlmutter, B.: Blind source separation via multinode sparse representation. In: Dietterich, T., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems 14 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Levin, A., Weiss, Y. (2004). User Assisted Separation of Reflections from a Single Image Using a Sparsity Prior. In: Pajdla, T., Matas, J. (eds) Computer Vision - ECCV 2004. ECCV 2004. Lecture Notes in Computer Science, vol 3021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24670-1_46
Download citation
DOI: https://doi.org/10.1007/978-3-540-24670-1_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21984-2
Online ISBN: 978-3-540-24670-1
eBook Packages: Springer Book Archive