User assisted separation of reflections from a single image using a sparsity prior

Anat Levin*, Yair Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

274 Scopus citations


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. This sparsity prior is optimized using the terative reweighted least squares (IRLS) approach. 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 modest number of labeled gradients.

Original languageAmerican English
Pages (from-to)1647-1654
Number of pages8
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number9
StatePublished - Sep 2007


  • Image statistics
  • Interactive image editing
  • Low-level vision
  • Transparency


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