Digitization of Non-Regular Shapes

Only the very restricted class of r-regular shapes is proven not to change topology during digitization. Such shapes have a limited boundary curvature and cannot have corners. In this paper it is shown, how a much wider class of shapes, for which the morphological open-close and the close-open-operator with an r-disc lead to the same result, can be digitized correctly in a topological sense by using an additional repairing step. It is also shown that this class is very general and includes several commonly used shape descriptions. The repairing step is easy to compute and does not change as much pixels as a preprocessing regularization step. The results are applicable for arbitrary, even irregular, sampling grids.