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Stochastic annealing for nearest-neighbour point processes with application to object recognition

Part of: Geometric probability and stochastic geometry Artificial intelligence (68Txx) Markov processes Parametric inference

Published online by Cambridge University Press:  01 July 2016

M. N. M. Van Lieshout
M. N. M. Van Lieshout*
Affiliation:
University of Warwick
*
* Present address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

We study convergence in total variation of non-stationary Markov chains in continuous time and apply the results to the image analysis problem of object recognition. The input is a grey-scale or binary image and the desired output is a graphical pattern in continuous space, such as a list of geometric objects or a line drawing. The natural prior models are Markov point processes found in stochastic geometry. We construct well-defined spatial birth-and-death processes that converge weakly to the posterior distribution. A simulated annealing algorithm involving a sequence of spatial birth-and-death processes is developed and shown to converge in total variation to a uniform distribution on the set of posterior mode solutions. The method is demonstrated on a tame example.

Keywords

CONVERGENCE IN TOTAL VARIATIONHOUGH TRANSFORMLIKELIHOOD RATIOMAXIMUM A POSTERIORI ESTIMATIONNEAREST-NEIGHBOUR MARKOV PROCESSESSPATIAL BIRTH-AND-DEATH PROCESSESSTOCHASTIC ANNEALING

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 62F15: Bayesian inference 68T10: Pattern recognition, speech recognition
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 281 - 300
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research carried out at the Free University, Amsterdam, and CWI, Amsterdam.

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