Color monogenic wavelets for image analysis

We define a color monogenic wavelet transform. This is based on the recent grayscale monogenic wavelet transform and a non-marginal extension to color signals. To our knowledge, wavelet based color image processing schemes have always been made by using a grayscale tool separately on color channels. This may have some unexpected effect on colors because those marginal schemes are not necessarily justified. Here we propose a definition that considers a color (vector) image right at the beginning of the mathematical definition and so brings an actual color wavelet transform - which has not been done so far to our knowledge. This so provides a promising multiresolution color geometric analysis of images.