Color correction describes the transformation process between device RGB values and CIEXYZ or CIELAB values. This mapping is in general not unique, because the spectral sensitivities of most of the devices do not satisfy the Luther condition and the acquisition and viewing light sources have a different power spectrum. Therefore, there exists a set of colors with different reflectance spectra which result in the same device RGB response (device metamerism), but leads to different tristimuli for an observer under the viewing light source. To determine an optimal mapping between a given device RGB and a CIELAB color, the distribution of metamers in a metamer mismatch gamut has to be characterized in the viewing CIELAB space. We present a novel method by estimating the distribution of metamers within the mismatch gamut using a Monte Carlo method. The main idea is the construction of a basic collection of metameric blacks (used by the Monte Carlo method) that is calculated by using a representative set of reflectance spectra and performing principle component analysis (PCA) within the black space of the device. The transformation of the sum of a fundamental metamer for the sensor response and the basic collection in the CIELAB color space leads to a point cloud with a centroid approximating the center of gravity of the mismatch gamut. This point is the optimal color correction in the sense of the smallest mean error.