We use methods from Riemann geometry to investigate transformations between the color spaces of color-normal and color-weak observers. The two main applications are the simulation of the perception of a color weak observer for a color-normal observer, and the compensation of color images in a way that a color-weak observer has approximately the same perception as a color-normal observer. The metrics in the color spaces of interest are characterized with the help of ellipsoids defined by the just-noticeable-differences between the colors which are measured with the help of color-matching experiments. The constructed mappings are the isometries of Riemann spaces that preserve the perceived color differences for both observers. Among the two approaches to build such an isometry, we introduce normal coordinates in Riemann spaces as a tool to construct a global color-weak compensation map. Compared with the previously used methods, this method is free from approximation errors due to local linearizations, and it avoids the problem of shifting locations of the origin of the local coordinate system. We analyze the variations of the Riemann metrics for different observers obtained from new color-matching experiments and describe three variations of the basic method. The performance of the methods is evaluated with the help of semantic differential tests.

We introduce normal coordinates in Riemann spaces as a tool to construct color-weak compensation methods. We use them to compute color stimuli for a color weak observers that result in the same color perception as the original image presented to a color normal observer in the sense that perceived color-differences are identical for both. The compensation is obtained through a color-difference-preserving map, i.e. an isometry between the 3D color spaces of a color-normal and any given color-weak observer. This approach uses discrimination threshold data and is free from approximation errors due to local linearization. The performance is evaluated with the help of semantic differential (SD) tests.