2-D Cauchy wavelets and symmetries in images

We recall the definition and basic properties of 2-D directional wavelets. We then focus on a particular class of wavelets, namely the Cauchy wavelets introduced by Antoine et al. (1996), and give several examples of its use in detecting and handling symmetries in images. We also compare these results with those obtained using the well-known 2-D Morlet wavelet. These directional wavelets can be used to evaluate the global symmetry of an object or to measure its intrinsic orientation