The exact probability density for a windowed observation of a discrete one-dimensional Boolean process having convex grains is found via recursive probability expressions. This observation density is used as the likelihood function for the process and numerically yields the maximum-likelihood estimator for the process intensity and the parameters governing the distribution of the grain lengths. The only restriction on the derivation is that the length distribution not be too heavy tailed. Maximum-likelihood estimation is applied in the cases of uniformly and Poisson distributed lengths. The entire approach applies to unions of independent Boolean processes.
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