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Rotation space random fields with an application to fMRI data. (English) Zbl 1043.92019
The problem of testing for a signal with unknown location and scale in a Gaussian random field defined on \(R^2\) is investigated. The test statistic is the maximum over all filter’s rotations and scales of the rotation space field. The Euler characteristic and the tubes approaches are presented. The obtained results are applied to the problem of searching for activation in brain images.

MSC:
92C55 Biomedical imaging and signal processing
62M40 Random fields; image analysis
60D05 Geometric probability and stochastic geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)
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