Optimally small operator supports for fully parallel thinning algorithms

Requirements for the support size and shape are investigated for the class of all adequate fully parallel thinning operators. Eleven pixel supports are shown to be the smallest possible supports, and the possible positions of the support pixels are shown to be well constrained. Constraints on support positions are demonstrated for operators with supports that are larger than optimal, and a sufficient test for connectivity preservation is reviewed. These results allow algorithm designers looking for small support operators to focus on a relatively small set of acceptable supports