Applications of random sets in image analysis. How to average a cat and a dog?
Abstract
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.
Date Issued
2004
Publication Type
Book Section
Subject(s)
Language(s)
en
Additional Credits
Publisher
Springer
ISSN
1867-5662
ISBN
978-3-540-44465-7
Access(Rights)
metadata.only