Size distributions for excursion sets
D J Nott, R. J. Wilson · 1997
By thresholding a random field, excursion set models for binary images can be obtained. For random set models, the behaviour of the size distributions is important. Unfortunately, the study of size distributions for excursion sets of random fields represents a difficult problem. However, there is a connection between Linear size distributions for excursion sets and certain first passage distributions for one dimensional processes and their Palm processes following an upcrossing. There are existing computational methods for rapidly calculating these first passage distributions and these can be exploited for studying excursion set geometry.