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Local Maxima and the Expected Euler Characteristic of Excursion Sets of χ 2, F and t Fields

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

K. J. Worsley
K. J. Worsley*
Affiliation:
McGill University
*
* Postal address: Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6.
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Abstract

The maximum of a Gaussian random field was used by Worsley et al. (1992) to test for activation at an unknown point in positron emission tomography images of blood flow in the human brain. The Euler characteristic of excursion sets was used as an estimator of the number of regions of activation. The expected Euler characteristic of excursion sets of stationary Gaussian random fields has been derived by Adler and Hasofer (1976) and Adler (1981). In this paper we extend the results of Adler (1981) to χ2, F and t fields. The theory is applied to some three-dimensional images of cerebral blood flow from a study on pain perception.

Keywords

GAUSSIAN RANDOM FIELDSIMAGE ANALYSIS

MSC classification

Primary: 60G15: Gaussian processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 13 - 42
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This work was supported by the Natural Sciences and Engineering Research Council of Canada, and the Fonds pour la Formation des Chercheurs et l'Aide àla Recherche deQuébec. The author would like to acknowledge the encouragement and assistance of A. C. Evans, S. Marrett and P. Neelin of the Brain Imaging Centre of the Montreal Neurological Institute. The author would like to thank Dr C. Bushnell and Dr G. Duncan for permission to use their data.

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