Pattern Width at a Given Angle

That the pattern feature "width as a function
of angle" possesses several possible interpretations 
is demonstrated in this paper, which is a review of
the width concept in pattern recognition and the 
geometrical concept itself.  The object of the work
is to clarify how the word description can be made 
precise so that computer algorithms for feature extraction
may be obtained; the focus is on the theoretical 
subject matter.  The results consist of a set-theoretic
definition of width-at-angle, a theorem relating 
it to the pattern boundary radius vector, and descriptions
of alternate widths.  All widths are calculated 
for an illustrative example; graphical and tabular comparisons
are given.  Substantial variation in width-at-angle 
magnitude is found.  The principal conclusion is that
the set-theoretic width-at-angle is a useful pattern 
feature when it can be easily computed.  Further investigation
of the information contained in only part 
of a width function is recommended for cases where
computation of width-at-angle is difficult.

CACM January, 1971

Klinger, A.

feature extraction, pattern recognition,figure
properties, picture processing, integral geometry, 
width-at-angle, extent, integral projections,
linear pattern measures, width functions

3.60 3.62 3.63 5.12

CA710102 JB February 8, 1978  12:49 PM

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