Elliptical Monogenic Wavelets for the Analysis and Processing of Color Images

This paper studies and gives new algorithms for image processing based on monogenic wavelets. Existing greyscale monogenic filter banks are reviewed and we reveal a lack of discussion about the synthesis part. The monogenic synthesis is therefore defined from the idea of wavelet modulation, and an innovative filterbank is constructed by using the Radon transform. The color extension is then investigated. First, the elliptical Fourier atom model is proposed to generalize the analytic signal representation for vector-valued signals. Then, a color Riesz-transform is defined so as to construct color elliptical monogenic wavelets. Our Radon-based monogenic filterbank can be easily extended to color according to this definition. The proposed wavelet representation provides efficient analysis of local features in terms of shape and color, thanks to the concepts of amplitude, phase, orientation, and ellipse parameters. The synthesis from local features is deeply studied. We conclude the paper by defining the color local frequency, proposing an estimation algorithm.