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

Abstract

In image processing and color science, colors are often specified by their luminance and chromaticity (such as Yxy). 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.