
KEITH WORSLEY, Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 2K6, Canada 
The geometry of correlation fields, with an application to functional connectivity of the brain 
Repeated 3D images of brain function, obtained by Positron Emission Tomography (PET) or functional Magnetic Resonance Imaging (fMRI), are now being used to detect pairs of points in 3D that show high functional connectivity. This is defined as the usual sample correlation coefficient measured at the two points in the images, which generates a 6D correlation random field. To detect pairs of regions that are highly correlated, we find tail probabilities of local maxima of the correlation field, and the size of the largest set of connected points in 6D where the correlation field is above a fixed high threshold. The main tool used is the expectation of the Euler characteristic of the excursion set. Results are applied to an experiment to determine which brain regions are functionally connected during an attention task. This is joint work with Jin Cao (Bell Labs, Lucent Technologies).