A Note on Perimeter and Diameter in Digital Pictures

It is shown that the “intrinsic diameter” of a connected digital object C—i.e., the maximum distance in C between any two points of C—never exceeds half of C's total perimeter (counting all of C's borders, including hole borders). As a preliminary result, it is shown that a simply connected digital object is a simple arc if and only if it has at most two “end” or “corner” points (and, in fact, it can then only have two “end” points).