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  Randomized algorithms for statistical image analysis based on percolation theory

Davies, P., Langovoy, M., & Wittich, O. (2009). Randomized algorithms for statistical image analysis based on percolation theory. Talk presented at 27th European Meeting of Statisticians (EMS 2009). Toulouse, France.

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Davies, PL, Author
Langovoy, M1, Author              
Wittich, O, Author
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1External Organizations, ou_persistent22              

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 Abstract: We propose a novel probabilistic method for detection of signals and reconstruction of images in the presence of random noise. The method uses results from percolation and random graph theories (see Grimmett (1999)). We address the problem of detection and estimation of signals in situations where the signal-to-noise ratio is particularly low. We present an algorithm that allows to detect objects of various shapes in noisy images. The algorithm has linear complexity and exponential accuracy. Our algorithm substantially diers from wavelets-based algorithms (see Arias-Castro et.al. (2005)). Moreover, we present an algorithm that produces a crude estimate of an object based on the noisy picture. This algorithm also has linear complexity and is appropriate for real-time systems. We prove results on consistency and algorithmic complexity of our procedures.

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 Dates: 2009-07
 Publication Status: Published online
 Pages: -
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 Rev. Type: -
 Identifiers: BibTex Citekey: DaviesL2009
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Title: 27th European Meeting of Statisticians (EMS 2009)
Place of Event: Toulouse, France
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Invited: Yes

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