## 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.

Original language | English (US) |
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Pages (from-to) | 64-84 |

Number of pages | 21 |

Journal | Advances in Applied Probability |

Volume | 30 |

Issue number | 1 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

## Keywords

- Bayesian inference
- Confocal microscopy images
- Distance between images
- Marked point processes
- Markov chain Monte Carlo methods
- Object recognition
- Template models
- Unsymmetric loss functions

## ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics