A new fourier descriptor applicable to open curves

Fourier descriptors are known to be used for describing planner curves in frequency domain. the traditional Fourier descriptors proposed by Zahn and Roskies, and Granlund have the following disadvantages: 1° it is difficult to apply them to open curves; and 2° the end-points of a reproduced curve from the low-frequency part of the descriptors do not necessarily coincide with the end-points of an original curve. the present paper proposes a new Fourier descriptor that does not have these disadvantages and is obtained by expanding in Fourier series the complex-valued exponential function of the total curvature function of a curve. the proposed descriptor is applicable not only to closed curves but also to open curves, and the end-points of its reproduced curve always coincide with those of the original curve. the descriptor is invariant under the translation and dilation of a curve. the descriptor of a rotated or reflected curve has simple relations to that of the original curve. Furthermore, the reproduced curve from the low-frequency part is a good approximation to the original curve in visual sense, and so the information of pattern classes concentrates in its low-frequency part. In this sense, the proposed descriptor may be used to good advantage in pattern recognition. the abovementioned was verified theoretically and/or experimentally.