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Abstract : |
We address the problem of detecting, and subsequently removing, `line scratch ' distortion in motion picture frames (see gure 4). A model for the lines ' interaction with the im age data is constructed. A sampling based algorithm based on the Reversible Jump Markov chain Monte Carlo frame work is developed which enables automatic determination of both the unknown number of lines present, together with the lines ' parameters. Previous work has not attempted to automatically determine the number of lines present [1]. Our approach is widely applicable in many object recogni tion problems, where the number of objects is unknown. 1. REVERSIBLE JUMP MCMC Recently, Markov chain Monte Carlo (MCMC) methods (e.g. the Gibbs Sampler, the Metropolis-Hastings algorithm [2], [3] ) have come into more widespread use for infer ence tasks, especially in image analysis [4]. They provide a method of exploring a complex probability distribution, usu ally p(`ji), the posterior distribution of the parameters of interest. The Metropolis-Hastings algorithm is constructed by proposing changes to one or more of the components of ` at each iteration. If (dx) is the distribution of interest, and q(x; dx 0) is the proposal distribution for the changes, then accepting the changes with probability A(x; x 0, |
