STATISTICAL PROPERTIES OF LOCAL EXTREMA IN 2-DIMENSIONAL GAUSSIAN RANDOM-FIELDS

This paper is concerned with the statistical properties of the local e xtrema and local maxima of two-dimensional (2-D) Gaussian random field s (GRF's). A GRF may be represented by a linear filtering operation on a white noise field; the spatial properties of the GRF are then deter mined by the shape of the filter kernel function, New expressions are derived for the mean spatial density of local extrema and for the dist ribution of local extrema in a 2-D random field, The work is motivated by the problem of detecting known structures in images using 2-D matc hed filters. The new results enable accurate performance predictions t o be made of the reliability of such filters in the presence of noise, Case studies are presented for several well-known 2-D filter kernel f unctions.