Multiscale image features analysis with circular harmonic wavelets

In this contribution we introduce a new family of wavelets named Circular Harmonic Wavelets (CHW), suited for multiscale feature-based representations, that constitute a basis for general steerable wavelets. The family is based on Circular Harmonic Functions (CHF) derived by the Fourier expansion of local Radial Tomographic Projections. A multiscale general feature analysis can be performed by linearly combining the outputs of CHW operators of different order. After a survey on the general properties of the CHFs, we investigate the relationship between CHF and the wavelet expansion, stating the basic admissibility and stability conditions with reference to the Hankel transform of the radial profiles and describing some fundamental mathematical properties. Finally some applications are illustrated through examples