Elastic reflection symmetry based shape descriptors

Reflection symmetry is an important feature of an object. Main goals in symmetry analysis include quantifying the amount of asymmetry in an object and finding the nearest symmetric object to a given asymmetric one. Samir et al. [19] achieved these goals using a shape distance between representations of curves termed square-root velocity functions. We extend their work by defining shape descriptors based on this representation. The descriptors are based on asymmetry measures computed for a set of reflections of a curve and are invariant to all shape preserving transformations (translation, scale, rotation and re-parameterization). We utilize these descriptors for retrieval of shapes in the Flavia leaf database and a subset of a handwritten digit dataset. We show that we outperform the commonly used angle function and other state of the art descriptors.