Geodesic Fourier Descriptor for 2D Shape Matching

Fourier descriptor is widely used for shape analysis and shape matching. Generally, the Euclid distance from boundary point to shape centroid is used in constructing Fourier descriptor. This kind of shape descriptor, however, is sensitive for rigid-transform. In this paper, we proposed a new kind of shape descriptor, namely geodesic Fourier descriptor. It remains robust under rigid transform. We first define a reference point by Poisson equation, which remains almost invariant under rigid transform. Then, the geodesic distance from shape boundary to reference point is used to construct GFD. Geodesic distance shows distinct advantage over the Euclid distance due to its robustness under rigid transformation. An algorithm based on two-scan dilating operation is presented to compute the geodesic distance efficiently in discrete image fields. Finally, experiments are carried out to show that geodesic Fourier descriptor can achieve better matching precision than Euclid distance based Fourier descriptor.