### Abstract

Original language | English |
---|---|

Place of Publication | Amsterdam |

Publisher | Centrum voor Wiskunde en Informatica |

Number of pages | 14 |

Publication status | Published - 2009 |

### Publication series

Name | CWI Report |
---|---|

Volume | PNA-E0906 |

### Fingerprint

### Cite this

*A note on pooling of labels in random fields*. (CWI Report; Vol. PNA-E0906). Amsterdam: Centrum voor Wiskunde en Informatica.

}

*A note on pooling of labels in random fields*. CWI Report, vol. PNA-E0906, Centrum voor Wiskunde en Informatica, Amsterdam.

**A note on pooling of labels in random fields.** / Lieshout, van, M.N.M.; Stoica, R.S.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - A note on pooling of labels in random fields

AU - Lieshout, van, M.N.M.

AU - Stoica, R.S.

PY - 2009

Y1 - 2009

N2 - ABSTRACT This paper studies the effect on the interaction structure of merging labels in random field models. INTRODUCTION In image segmentation, often Markov random field models are employed in which neighbouring (blocks) of pixels have a similar texture [11]. Generally, the number of different textures is unknown. To overcome this problem, a number of Bayesian approaches have been suggested in which the unknown number is treated as a random variable. See for example [4, 7]. A practical problem with such approaches is that most Markov random field densities are known only up to a normalising constant. When updating the number of labels in a Monte Carlo method, the normalising constants do not cancel out and have to be approximated. A more fundamental problem is that the interaction structure may change dramatically if two labels are pooled together, in other words, the class of Markov random fields is not closed under merging labels, making them unnatural models in an unsupervised image segmentation algorithm. In contrast, we show that the class of Markov connected component models [10] is closed under the above mentioned operation, and hence may provide more natural prior distributions for image segmentation with an unknown number of different textures. The plan of this note is as follows. First we review some random field theory in Section 2, the main Section 3 studies the effect on the interaction structure of changes in the number of labels and compares the results to their counterparts in a continuous point process set-up [2, 9]. The paper closes with a short discussion.

AB - ABSTRACT This paper studies the effect on the interaction structure of merging labels in random field models. INTRODUCTION In image segmentation, often Markov random field models are employed in which neighbouring (blocks) of pixels have a similar texture [11]. Generally, the number of different textures is unknown. To overcome this problem, a number of Bayesian approaches have been suggested in which the unknown number is treated as a random variable. See for example [4, 7]. A practical problem with such approaches is that most Markov random field densities are known only up to a normalising constant. When updating the number of labels in a Monte Carlo method, the normalising constants do not cancel out and have to be approximated. A more fundamental problem is that the interaction structure may change dramatically if two labels are pooled together, in other words, the class of Markov random fields is not closed under merging labels, making them unnatural models in an unsupervised image segmentation algorithm. In contrast, we show that the class of Markov connected component models [10] is closed under the above mentioned operation, and hence may provide more natural prior distributions for image segmentation with an unknown number of different textures. The plan of this note is as follows. First we review some random field theory in Section 2, the main Section 3 studies the effect on the interaction structure of changes in the number of labels and compares the results to their counterparts in a continuous point process set-up [2, 9]. The paper closes with a short discussion.

M3 - Report

T3 - CWI Report

BT - A note on pooling of labels in random fields

PB - Centrum voor Wiskunde en Informatica

CY - Amsterdam

ER -