We introduce normal coordinates in Riemannspaces as a tool to construct color-weak compensation methods.We use them to compute color stimuli for a color weakobservers that result in the same color perception as theoriginal image presented to a color normal observer in the sensethat perceived color-differences are identical for both. Thecompensation is obtained through a color-difference-preservingmap, i.e. an isometry between the 3D color spaces of a colornormaland any given color-weak observer. This approach usesdiscrimination threshold data and is free from approximationerrors due to local linearization. The performance is evaluatedwith the help of semantic differential (SD) tests.Virtual Photo Set (VPS)European Community’s Seventh Framework Programme FP7/2007-2013 - Challenge 2 Cognitive Systems, Interaction, Robotics - under grant agreement No 247947 - GARNICS