1. A method for generating a multi-dimensional printer profile look-up table for color correction, the method comprising the steps of: receiving color signals defining a plurality of nodes in a device independent color space; and for each of the nodes: generating, by a processor without user interaction and using the received color signals in the device independent color space and a K-function, an initial estimate for a black (K) component in a four-color color space for the received color signals in the device independent color space, the K-function being defined as: K = 1 U η ⁢ ⅇ - α ⁡ ( a * 2 + b * 2 ) / L * 2 + 1 - 1 2 ⁢ U η where U = 2 ⁢ ( 1 ⅇ - β ⁡ ( L * L 0 - L * ) 2 + 1 - 1 2 ) and L o , η, β, and α are predetermined values; generating initial estimates for the non-black components in the four-color color space from the generated initial estimate for the black (K) component and the received color signals in the device independent color space, and generating a printer profile comprising a map that maps the device independent color space to the four-color color space using the generated initial estimates for the black (K) and the non-black components in the four-color color space.