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-noticable-differences between color
which are measured with the help of color-matching experiments. The constructed
mappings are 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 to 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 analyse 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 (SD) tests.Comment: Full resolution color pictures are available from the author