Distribution of the global maximum of a Gaussian random field and performance of matched filter detectors

A simple model is developed that successfully captures the point statistics of the global maximum of a Gaussian random field of reasonably large suppo rt. Tractable expressions for the probability that the global maximum of th e field exceeds an arbitrary threshold are provided; this probability is sh own to be completely insensitive to the fine details of the correlation fun ction of the random field. The validity of these results is assessed by com parison with computer simulation, where excellent agreement is obtained. Th ese results are potentially most valuable for the assessment of the perform ance of matched filters for large-scale feature detection in images.