Applications of random sets in image analysis. How to average a cat and a dog?

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

Full text not available from this repository.

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:	05 Dec 2022 14:57
URI:	https://boris.unibe.ch/id/eprint/85367