In this work, we present an original technique for unsupervised segmentation of color images which is based on an extension, for an use in the u' v' chromaticity diagram, of the well-known k-means algorithm, widely adopted in cluster analysis. We suggest exploiting the separability of color information which, represented in a suitable 3D space, may be "projected" onto a 2D chromatic subspace and onto a 1D luminance subspace. One can first compute the chromaticity coordinates (u',v') of colors and find representative clusters in such a 2D space, by using 1 1D k-means algorithm, a simple dimensionally reduced version of the previous one. Experimental evidence of the effectiveness of our technique is reported.