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In order to estimate the specific intrinsic volumes of a planar Boolean modelfrom a binary image, we consider local digital algorithms based on weightedsums of $2\times 2$ configuration counts. For Boolean models with balls asgrains, explicit formulas for the bias of such algorithms are derived,resulting in a set of linear equations that the weights must satisfy in orderto minimize the bias in high resolution. These results generalize to largerclasses of random sets, as well as to the design based situation, where a fixedset is observed on a stationary isotropic lattice. Finally, the formulas forthe bias obtained for Boolean models are applied to existing algorithms inorder to compare their accuracy.

Local digital estimators of intrinsic volumes for Boolean models and in the design based setting