On properties of discretized convex curves

The connection between a continuous convex curve and its discrete image is investigated using an appropriate definition of discrete convexity. It is shown that the discrete image of continuous convex curve may not be convex; however, its deviation from convexity (in the discrete definition) is bounded by a small constant. The actual pixel patterns that are obtained by discretizing convex curves are studied. Certain constraints on the context of discrete images of continuous convex curves were discovered.<>