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We propose a new color extension of the monogenic wavelet transform. Monogenic wavelets give a coherent representation of scalar images through a local phase concept and an underlying orientation analysis. We here define a color extension of the monogenic framework. The underlying local geometric analysis and phase concept are generalized by using the color structure tensor. Resulting transform appears to be a clear improvement of our previous work - that is the only proposition of color monogenic wavelets to our knowledge. This is shift and rotation invariant and efficiently represents multiscale color lines and edges.