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 support. Tractable expressions for the probability that the global maximum of the field exceeds an arbitrary threshold are provided; this probability is shown to be completely insensitive to the fine details of the correlation function of the random field. The validity of these results is assessed by comparison with computer simulation, where excellent agreement is obtained. These results are potentially most valuable for the assessment of the performance of matched filters for large-scale feature detection in images