The correction of the effects of color-weakness is difficult if not impossible. One of the reasons is that are no objective criterions available to evaluate corrections since it is difficult to quantify the color perception of an individual. Also the degree and the character of color-weakness vary widely among individuals and different color stimuli. In this paper, we use Riemann geometry to construct a new method for color-weakness correction. The basic mechanism is the matching between the discrimination thresholds of color-weak and of color-normal observers. The goal is to provide the same color perception of color-normal observers to the color-weak observer: it takes into account the individual differences between observers and since it defines a global deformation of the whole color space it is applicable for correction of complex visual inputs such as natural images.