A multi-dimensional printer profile look-up table for color correction is generated. First, an initial estimate for a black (K) component in a four-color color space for received color signals in the device independent color space is generated by using a three-dimensional parametric function. Next, initial estimates for the three non-black color components of the four-color color space are generated from the generated initial estimate for the black (K) component and the received color signals. Then, a printer profile including a map that maps the device independent color space to the four-color color space is generated using the generated initial estimates for the black (K) and the three non-black color components in the four-color color space.