Molchanov, Ilya
(2004).
*
Applications of random sets in image analysis. How to average a cat and a dog?
*
In:
Soft methodology and random information systems. Advances in intelligent and soft computing: Vol. 26 (pp. 8-18).
Berlin: Springer

The expectation (or average) is one of the basic concepts in probability theory and statistical inference. However, this rather basic concept becomes fairly complicated for random elements in non-linear spaces. The family of compact sets is a typical example of such non-linear space, alongside with numerous possible examples that involve curved spaces. To highlight various complications, it is possible to consider a random compact set that with equal probabilities is the unit interval or its end-points, or a set that is either the circle or the disk bounded by it, or a set that takes values {0} or {0, 1}. Various definitions of expectations respect the shape of the set, its cardinality or measure, or its connectivity properties.

## Item Type: |
Book Section (Review Article) |
---|---|

## Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |

## UniBE Contributor: |
Molchanov, Ilya |

## Subjects: |
500 Science > 510 Mathematics |

## ISSN: |
1867-5662 |

## ISBN: |
978-3-540-44465-7 |

## Series: |
Advances in intelligent and soft computing |

## Publisher: |
Springer |

## Language: |
English |

## Submitter: |
Ilya Molchanov |

## Date Deposited: |
19 Aug 2016 08:03 |

## Last Modified: |
19 Aug 2016 08:03 |

## URI: |
https://boris.unibe.ch/id/eprint/85367 |