Corrections for systematic boundary effects in pixel-based area counts

Consider digitising a binary pattern on a regular lattice, so that each 'face' of pixel of the lattice is given just one of the two colours in the pattern. If the pixelation algorithm is symmetric, meaning that a pixel which straddles the boundary between two colours inherits the colour that predominates in that particular face, then the systematic errors in pixel counts are generally small. However, they can be significant for asymmetric pixelations. In this paper we provide explicit corrections for systematic errors in area estimates based on asymmetric pixelation algorithms. The corrections are derived by interpreting systematic error as the bias in a statistical estimation problem, and arguing that the pattern was placed into the lattice in a stochastically uniform way. We suggest two sorts of correction: first, a 'local' adjustment based on tracking the boundary and accumulating small amendments along the way; and secondly, a 'global' correction based on parametric knowledge of the type of shape that is being digitised.