Angle-Retaining Chromaticity and Color Space: Invariants and Properties

The angle-retaining color space (ARC) and the corresponding chromaticity diagram encode information following a cylindrical color model. Their main property is that angular distances in RGB are mapped into Euclidean distances in the ARC chromatic components, making the color space suitable for data representation in the domain of color constancy. In this paper, we present an in-depth analysis of various properties of ARC: we document the variations in the numerical precisions of two alternative formulations of the ARC-to-RGB transformation and characterize how various perturbations in RGB impact the ARC representation. This was done empirically for the ARC diagram in a direct comparison against other commonly used chromaticity diagrams, and analytically for the ARC space with respect to its three components. We conclude by describing the color space in terms of perceptual uniformity, suggesting the need for new perceptual color metrics.