Fourier descriptors for broken shapes

Fourier descriptors are powerful features for the recognition of two-dimensional connected shapes. In this article, we propose a method to define Fourier descriptors even for broken shapes, i.e. shapes that can have more than one contour. The method is based on the convex hull of the shape and the distance to the closest actual contour point along the convex hull. We define different invariant Fourier descriptors for this three-dimensional representation of a two-dimensional shape and compare them on different data sets. The recognition rates are comparable to normal Fourier descriptors while the new scheme at the same time offers the option to also deal with broken contours. We also discuss and evaluate different normalisation schemes that make the descriptors invariant under scale and rotation.