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Automatic Range Image Registration in the Markov Chain
January 2010 (vol. 32 no. 1)
pp. 12-29
Yonghuai Liu, Aberystwyth University, Ceredigion
In this paper, a novel entropy that can describe both long and short-tailed probability distributions of constituents of a thermodynamic system out of its thermodynamic limit is first derived from the Lyapunov function for a Markov chain. We then maximize this entropy for the estimation of the probabilities of possible correspondences established using the traditional closest point criterion between two overlapping range images. When we change our viewpoint to look carefully at the minimum solution to the probability estimate of the correspondences, the iterative range image registration process can also be modeled as a Markov chain in which lessons from past experience in estimating those probabilities are learned. To impose the two-way constraint, outliers are explicitly modeled due to the almost ubiquitous occurrence of occlusion, appearance, and disappearance of points in either image. The estimated probabilities of the correspondences are finally embedded into the powerful mean field annealing scheme for global optimization, leading the camera motion parameters to be estimated in the weighted least-squares sense. A comparative study using real images shows that the proposed algorithm usually outperforms the state-of-the-art ICP variants and the latest genetic algorithm for automatic overlapping range image registration.

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Index Terms:
Automatic registration, range image, Markov chain, Lyapunov function, entropy maximization, mean field annealing.
Yonghuai Liu, "Automatic Range Image Registration in the Markov Chain," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 1, pp. 12-29, Jan. 2010, doi:10.1109/TPAMI.2008.280
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