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A note on perimeter and diameter in digital pictures

Authors
Journal
Information and Control
0019-9958
Publisher
Elsevier
Publication Date
Volume
24
Issue
4
Identifiers
DOI: 10.1016/s0019-9958(74)80061-6

Abstract

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).

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