A Shape Representation for Planar Curves by Shape Signature Harmonic Embedding

This paper introduces a new representation for planar curves. From the well-known Dirichlet problem for a disk, the harmonic function embedded in a circular disk is solely dependent on specified boundary values and can be obtained from Poisson’s integral formula. We derive a discrete version of Poisson’s formula and assess its harmonic properties. Various shape signatures can be used as boundary values, whereas only the corresponding Fourier descriptors are needed for the framework. The proposed approach is similar to a scale space representation but exhibits greater generality by accommodating using any type of shape signature. In addition, it is robust to noise and computationally efficient, and it is guaranteed to have a unique solution. In this paper, we demonstrate that the approach has strong potential for shape representation and matching applications.