Angle-Retaining Color Space for Color Data Visualization and Analysis

The Angle-Retaining Chromaticity diagram (ARC) is used to map tristimulus values in a two-dimensional representation, so that angular distances in the original three-dimensional space are preserved as Euclidean distances in ARC. This property makes the ARC diagram particularly useful for computational color constancy, where the illuminant intensity is purposely discarded and illuminant chromaticities are compared in terms of angular distances, through either the recovery error or the reproduction error. We expand the ARC diagram by designing a full-fledged color space that adopts a cylindricalcoordinate color model. The resulting ARC space incorporates a third dimension encoding the intensity information of the initial color, while maintaining the angle-retaining properties of the ARC diagram for the first two dimensions. We formalize the equations that describe the mutual conversion between RGB and ARC space. We illustrate the emerging geometric properties of the ARC space, and its relationship with angular distances. We present a number of potential applications of the ARC space related to color constancy, texture analysis, and image enhancement.