### Abstract

Condensation is a popular algorithm for sequential inference that resamples a sampled representation of the posterior. The algorithm is known to be asymptotically correct as the number of samples tends to infinity. However, the resampling phase involves a loss of information. The sequence of representations produced by the algorithm is a Markov chain, which is usually inhomogeneous. We show simple discrete examples where this chain is homogeneous and has absorbing states. In these examples, the representation moves to one of these states in time apparently linear in the number of samples and remains there. This phenomenon appears in the continuous case as well, where the algorithm tends to produce \clumpy" representations. In practice, this means that different runs of a tracker on the same data can give very different answers, while a particular run of the tracker will look stable. Furthermore, the state of the tracker can collapse to a single peak | which has non-zero probability of being the wrong peak | within time linear in the number of samples, and the tracker can appear to be following tight peaks in the posterior even in the absence of any meaningful measurement. This means that, if theoretical lower bounds on the number of samples are not available, experiments must be very carefully designed to avoid these effects.

Original language | English (US) |
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Title of host publication | Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings |

Editors | David Vernon |

Publisher | Springer-Verlag |

Pages | 695-709 |

Number of pages | 15 |

ISBN (Print) | 3540676856 |

State | Published - Jan 1 2000 |

Externally published | Yes |

Event | 6th European Conference on Computer Vision, ECCV 2000 - Dublin, Ireland Duration: Jun 26 2000 → Jul 1 2000 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1842 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 6th European Conference on Computer Vision, ECCV 2000 |
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Country | Ireland |

City | Dublin |

Period | 6/26/00 → 7/1/00 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings*(pp. 695-709). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1842). Springer-Verlag.

**How does CONDENSATION behave with a finite number of samples?** / King, O.; Forsyth, D. A.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1842, Springer-Verlag, pp. 695-709, 6th European Conference on Computer Vision, ECCV 2000, Dublin, Ireland, 6/26/00.

}

TY - GEN

T1 - How does CONDENSATION behave with a finite number of samples?

AU - King, O.

AU - Forsyth, D. A.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - Condensation is a popular algorithm for sequential inference that resamples a sampled representation of the posterior. The algorithm is known to be asymptotically correct as the number of samples tends to infinity. However, the resampling phase involves a loss of information. The sequence of representations produced by the algorithm is a Markov chain, which is usually inhomogeneous. We show simple discrete examples where this chain is homogeneous and has absorbing states. In these examples, the representation moves to one of these states in time apparently linear in the number of samples and remains there. This phenomenon appears in the continuous case as well, where the algorithm tends to produce \clumpy" representations. In practice, this means that different runs of a tracker on the same data can give very different answers, while a particular run of the tracker will look stable. Furthermore, the state of the tracker can collapse to a single peak | which has non-zero probability of being the wrong peak | within time linear in the number of samples, and the tracker can appear to be following tight peaks in the posterior even in the absence of any meaningful measurement. This means that, if theoretical lower bounds on the number of samples are not available, experiments must be very carefully designed to avoid these effects.

AB - Condensation is a popular algorithm for sequential inference that resamples a sampled representation of the posterior. The algorithm is known to be asymptotically correct as the number of samples tends to infinity. However, the resampling phase involves a loss of information. The sequence of representations produced by the algorithm is a Markov chain, which is usually inhomogeneous. We show simple discrete examples where this chain is homogeneous and has absorbing states. In these examples, the representation moves to one of these states in time apparently linear in the number of samples and remains there. This phenomenon appears in the continuous case as well, where the algorithm tends to produce \clumpy" representations. In practice, this means that different runs of a tracker on the same data can give very different answers, while a particular run of the tracker will look stable. Furthermore, the state of the tracker can collapse to a single peak | which has non-zero probability of being the wrong peak | within time linear in the number of samples, and the tracker can appear to be following tight peaks in the posterior even in the absence of any meaningful measurement. This means that, if theoretical lower bounds on the number of samples are not available, experiments must be very carefully designed to avoid these effects.

UR - http://www.scopus.com/inward/record.url?scp=0007997129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007997129&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0007997129

SN - 3540676856

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 695

EP - 709

BT - Computer Vision - ECCV 2000 - 6th European Conference on Computer Vision, Proceedings

A2 - Vernon, David

PB - Springer-Verlag

ER -