Open AccessREVIEW OF RECENT RESULTS ON EXCURSION SET MODELS
Author(s) -
Richard Wilson,
David J. Nott
Publication year - 2011
Publication title -
image analysis and stereology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.237
H-Index - 27
eISSN - 1854-5165
pISSN - 1580-3139
DOI - 10.5566/ias.v20.p71-78
Subject(s) - excursion , boolean model , set (abstract data type) , computer science , feature (linguistics) , phase (matter) , algorithm , binary number , mathematics , artificial intelligence , discrete mathematics , linguistics , philosophy , chemistry , arithmetic , organic chemistry , political science , law , programming language
Many images consist of two or more "phases", where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed