We are interested in creating methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the perimeter of excursion sets of random fields. The parsimonious estimator acts on binary digital images of the excursions and computes the length of a piecewise linear approximation of the boundary. Consistency and asymptotic normality results are obtained for decreasing pixel size and growing domain, without the restrictive assumption of isotropy of the underlying random field. We conduct several numerical studies that suggest our asymptotic results are well approximated in the finite data setting.