On the ratios and the logarithms of dark colors in image processing

In image processing and color science, colors are often specified by their luminance and chromaticity (such as Y x y). Chromaticities are color ratios, which can be difficult to compute reliably due to noise, when the tristimulus values are small, e.g., for dark colors. A detailed statistical analysis of ratio distributions shows that below a certain signal/noise ratio, the computed color ratios are very noisy and often wrong. This contrasts with human vision, where a given chromaticity viewed at high luminance will appear to the viewer as having a distinct color, but when that same chromaticity is viewed at low luminance, it will be seen as dark and almost hue-less. Therefore, dark color processing can take advantage of the perceptual characteristics to avoid producing excessive color noise and unnatural colors. In this study, we perform a detailed analysis of ratio distributions and propose a method to handle dark colors in image processing, using a logarithmic-like transformation (called plog) that maps dark colors to reduced excitation purity. A color ratio 0/0 is mapped to 1 (as the neutral). The plog transformation removes the singularity of the logarithmic transformation and allows us to estimate and process the ratios of dark colors in a manner consistent with human color perception without increasing color noise. It also offers the additional benefit of reducing the dynamic range of dark colors for tone reproduction.