2004 | OriginalPaper | Chapter
User Assisted Separation of Reflections from a Single Image Using a Sparsity Prior
Authors : Anat Levin, Yair Weiss
Published in: Computer Vision - ECCV 2004
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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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.