Modeling, Measuring, and Compensating Color Weak Vision.

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.

Color-weak compensation using local affine isometry based on discrimination threshold matching.

We develop algorithms for color-weak compensation and color-weak simulation based on Riemannian geometry models of color spaces. The objective function introduced measures the match of color discrimination thresholds of average normal observers and a color-weak observer. The developed matching process makes use of local affine maps between color spaces of color-normal and color-weak observers. The method can be used to generate displays of images that provide color-normal and color-weak observers with a similar color difference experience. It can also be used to simulate the perception of a color-weak observer for color-normal observers. We also introduce a new database of measurements of color discrimination threshold data for color-normal and color-weak observers obtained at different lightness levels in CIELUV space. The compensation methods include compensations of chromaticity using local affine maps between chromaticity planes of color-normal and color-weak observers, and one-dimensional (1D) compensation on lightness. We describe how to determine correspondences between the origins of local coordinates in color spaces of color-normal and color-weak observers using a neighborhood expansion method. After matching the origins of the two coordinate systems, a local affine map is estimated by solving a nonlinear equation, or singular-value-decomposition (SVD). We apply the methods to natural images and evaluate their performance using the semantic differential (SD) method.