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Circular Symmetry Models in Image Processing

New methods for feature extraction based on the spectral properties of local neighbourhoods is presented. The spectral behaviour of the neighbourhoods is investigated in the spatial domain using the Parseval relation applied to partial derivative pictures. Two types of such properties are considered for circular symmetric and linear symmetric neighbourhoods. These two properties are the existence of point concentration and line concentration in the spectra. For the circular symmetry investigation a new basis function set is introduced. To obtain a spectrum in the terms of these basis function sets, a scalar product is introduced for circular neighbourhoods. The same is carried out for linear symmetry spectra using the well-known basis set and the scalar product consisting of cosines and 𝓛2(Ω) scalar product. Confidence parameters are introduced to measure the significance of the extracted features. These are basically different types of variance measures and they are shown to be specific for the desired information: The existence of point concentration or line concentration in the spectra of the local neighbourhoods.