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Bayesian object recognition with baddeley's delta loss

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Håvard Rue  and
Anne Randi Syversveen
Håvard Rue*
Affiliation:
Norwegian University of Science and Technology
Anne Randi Syversveen*
Affiliation:
Norwegian University of Science and Technology
*
∗ Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034 Trondheim, Norway.
∗ Postal address: Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7034 Trondheim, Norway.
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Abstract

A common problem in Bayesian object recognition using marked point process models is to produce a point estimate of the true underlying object configuration: the number of objects and the size, location and shape of each object. We use decision theory and the concept of loss functions to design a more reasonable estimator for this purpose, rather than using the common zero-one loss corresponding to the maximum a posteriori estimator. We propose to use the squared Δ-metric of Baddeley (1992) as our loss function and demonstrate that the corresponding optimal Bayesian estimator can be well approximated by combining Markov chain Monte Carlo methods with simulated annealing into a two-step algorithm. The proposed loss function is tested using a marked point process model developed for locating cells in confocal microscopy images.

Keywords

Bayesian inferenceunsymmetric loss functionsobject recognitiontemplate modelsMarkov chain Monte Carlo methodsmarked point processesdistance between imagesconfocal microscopy images

MSC classification

Primary: 62M30: Spatial processes
Secondary: 60G35: Signal detection and filtering
Type
Stochatic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 30 , Issue 1 , March 1998 , pp. 64 - 84
Copyright
Copyright © Applied Probability Trust 1998 

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