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

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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