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Biometrika 1999 86(3):649-660; doi:10.1093/biomet/86.3.649
© 1999 by Biometrika Trust
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Bayesian object identification

H RueA1 and MA HurnA2

A1 Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway E-mail: havard.rue@math.ntnu.no A2 Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK E-mail: m.a.hurn@maths.bath.ac.uk

This paper addresses the task of locating and identifying an unknown number of objects of different types in an image. Baddeley & Van Lieshout (1993) advocate marked point processes as object priors, whereas Grenander & Miller (1994) use deformable template models. In this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types, using reversible jump Markov chain Monte Carlo methods for inference (Green, 1995). The naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this. The first two expand the model space by introducing an additional 'unknown' object type and the idea of a variable resolution template. The third strategy, utilising the first two, augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects.

Key Words: Bayesian inference; Deformable template; Image analysis; Marked point process; Markov chain Monte Carlo; Object recognition; Variable dimension distribution


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