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Quantised binary images are formed by projecting the binary intensity silhouette or line edge of a shape onto a spatial quantisation grid. The quantised shape depends on the orientation and translation of the object's image. Different complexities in the borders, due to the quantisation effects, are part of the error arising in a binary template-match process. The letter suggests a model to approximate the variation statistics as a result of uncertainty in translation only. To isolate the quantisation effects, noise-free images are considered.