A strong chord property for 4-connected convex digital sets

Abstract

The chord property was introduced by Rosenfeld in the study of digital straight line segments. It is known that a digital set has that property if and only if it is 8-connected and convex. We define a stronger property, which we call the strong chord property , and show that a digital set satisfies it if and only if it is 4-connected and convex. We give also another expression for the chord and strong chord properties, and some consequences of our results.