Pattern width at a given angle

Abstract

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 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.