This paper introduces a new 1-D model to encodecoloured images for an efficient subsequent processing. Thisrepresentation is equivalent to, but more compact than, the 3-DHCL conical representation. It consists in gathering all the hue,chroma and luminance information in one component, namely,the cumulative spiral angle, where the spirals in question aredefined as a sampling of the solid HCL cone. We use theproposed model for joint bilateral upsampling of low-resolutiondepth maps. The results show that, in addition to preserving theperceptual properties of the HCL colour representation, usingthe proposed model leads to a solution that is more accuratethan when using grayscale images.