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Compact Figures in Digital Pictures

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1 Author(s)
Rosenfeld, Azriel ; Computer Science Center, University of Maryland, College Park, Md. 20742.

The square of the perimeter of a figure divided by its area P2/A is a classical measure of the noncompactness of the figure. In Euclidean geometry, P2/A is always at least 4¿, and takes on this minimum value only if the figure is a circle; larger values correspond to figures that are less compact than circles. In digital pictures, however, certain squares or octagons¿depending on how P is measured¿yield smaller values than do digitized circles. Thus for digital pictures, though P2/A may be useful as a practical measure of noncompactness, it possesses certain pathological features of which users should be aware.

Published in:

Systems, Man and Cybernetics, IEEE Transactions on  (Volume:SMC-4 ,  Issue: 2 )

Date of Publication:

March 1974

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