Color lookup table generation which minimizes interpolation errors over the entire color space of a color gamut

A system for generating a color lookup table that minimizes interpolation errors over the entire color space, said system comprising:

• a memory;
• a storage medium for storing data;
• and
• a processor in communication with said storage medium and said memory, said processor executing machine readable instructions for performing the method of:
• defining a plurality of grid points of a color space of an output color device and vectors f, and g, where the component of vector f, given by:
• f(q,x,y,z), is a mapping function which maps the color at (x,y,z) to the amount of output device colorant q, and where the component of vector g, given by:
• g(q,i,j,k), is the amount of colorant q at grid location (i,j,k) where (i,j,k) are grid indices;
• determining values for vector f based upon any of:
• a printer model at densely sampled locations in said device color space, or by printing and measuring color patches using said output color device;
• formulating a total interpolation error energy based upon said values for vector f, wherein, in response to said interpolation having been performed in a color space which is the same as the color space of said output color device, said total interpolation error energy comprising:
• e=∥f−Cg∥,
• otherwise comprising:
• e=∥J(f−Cg)∥,
• where J is a matrix containing Jacobians which specifies a color transformation or is a matrix which transforms from a device color space to another color space where a Euclidian distance is a more appropriate measure of the perceived color error, and where C is a matrix of interpolation coefficients defined by said interpolation;
• and
• generating a LUT by determining g, the LUT entries that minimize said total interpolation error energy.

A computer implemented method for generating a color lookup table that minimizes interpolation errors over the entire color space, the method comprising:

• defining a plurality of grid points of a color space of an output color device and vectors f, and g, where the component of vector f, given by:
• f(q,x,y,z), is a mapping function which maps the color at (x,y,z) to the amount of output device colorant q, and where the component of vector g, given by:
• g(q,i,j,k), is the amount of colorant q at grid location (i,j,k) where (i,j,k) are grid indices;
• formulating values for vector f based upon any of:
• a printer model at densely sampled locations in said device color space, and by printing and measuring color patches using said output color device;
• calculating a total interpolation error energy based upon said values for vector f, wherein, in response to said interpolation having been performed in a color space which is a same as the color space of said output color device, said total interpolation error energy comprising:
• e=∥f−Cg∥,
• otherwise comprising:
• e=∥J(f−Cg)∥,
• where J is a matrix containing Jacobians which specifies a color transformation or which transforms from a device color space to a space where a Euclidian distance is a more appropriate measure of the perceived color error, and where C is a matrix of interpolation coefficients defined by said interpolation;
• and
• generating a LUT by determining g, the LUT entries that minimize said total interpolation error energy.