An Application of Fourier Analyses on the Shapes of Letters and Numbers

Abstract

To find basic factors for the recognition and lettering of alpha-numerical characters (alphabet and numbers), Fourier analyses were applied on the orthogonal components (X and Y components) involved in the drawing motion to reproduce some samples of lettering as line figures. Relative contributions of harmonics in the X and Y components were examined by the following ways: 1) Harmonics in each of the X and Y Fourier series were eliminated one by one in the order of their frequencies, and 2) the compositions of thus reduced functions were reproduced as typed lines composed of 1 with the aid of Computer HIPAC 103, and 3) these reproductions of characters were visually evaluated. The results of these analyses showed that the reproductions of characters become gradually worse as the number of harmonics used for reproduction decreases, but the basic feature of the character is always kept as far as the first three harmonics, which have usually large amplitudes, are remained, except that H, K and R need four to six harmonics. In this sense, the invariant feature of an alpha-numerical character depends upon these small number of harmonic combinations. From the founding that some alpha-numerical characters, such as S, Z and 8, have almost the same harmonic combinations as the essential factor to keep their basic features, the phase differences between the X and Y component series were considered as the second important factor for the discrimination among such characters. It is also found that the part, where the drawing line of an alpha-numerical character is discontinued, will be the third important factor for discrimination among the characters.