A method for determining coefficients of one or more color correction approximation functions prior to use by one or more target display management systems, the method comprising: receiving an image represented by first image data in a first color space; applying a first color space transformation function on the first image data to convert the first image data into second image data in a second color space; receiving one or more user inputs that define color correction data to be applied in a third color space that is preferred for making color corrections; applying at least one of a tone mapping function or a color volume mapping function on the second image data in the second color space to produce mapped image data in the second color space; applying a second color space transformation on the mapped image data in the second color space to convert the mapped image data into third image data in the third color space; applying the color correction data on the third image data in the third color space to produce first color corrected image data in the third color space; projecting back the first color corrected image data in the third color space to the second color space to produce second color corrected image data in the second color space, wherein projecting back involves using reverse transformations to reverse the sequence of transformations between the mapped image data in the second color space and the second color corrected image data in the second color space; determining coefficients of the one or more color correction approximation functions by an approximation function solver, wherein the one or more color correction approximation functions are configured to fit the mapped image data in the second color space and the back-projected second color corrected image data in the second color space to a mode that represents the non-linear relationship between the mapped image data in the second color space and the back-projected second color corrected image data in the second color space, and wherein the approximation function solver is configured to determine the coefficients of the one or more color correction approximation functions such that the one or more color correction approximation functions, when configured with the generated coefficients and applied to the mapped image data in the second color space, approximate the color correction performed on the third image data in the third color space; storing or transmitting the coefficients of the one or more color correction approximation functions for use by the one or more target display management systems. receiving an image represented by first image data in a first color space; applying a first color space transformation function on the first image data to convert the first image data into second image data in a second color space; receiving one or more user inputs that define color correction data to be applied in a third color space that is preferred for making color corrections; applying at least one of a tone mapping function or a color volume mapping function on the second image data in the second color space to produce mapped image data in the second color space; applying a second color space transformation on the mapped image data in the second color space to convert the mapped image data into third image data in the third color space; applying the color correction data on the third image data in the third color space to produce first color corrected image data in the third color space; projecting back the first color corrected image data in the third color space to the second color space to produce second color corrected image data in the second color space, wherein projecting back involves using reverse transformations to reverse the sequence of transformations between the mapped image data in the second color space and the second color corrected image data in the second color space; determining coefficients of the one or more color correction approximation functions by an approximation function solver, wherein the one or more color correction approximation functions are configured to fit the mapped image data in the second color space and the back-projected second color corrected image data in the second color space to a mode that represents the non-linear relationship between the mapped image data in the second color space and the back-projected second color corrected image data in the second color space, and wherein the approximation function solver is configured to determine the coefficients of the one or more color correction approximation functions such that the one or more color correction approximation functions, when configured with the generated coefficients and applied to the mapped image data in the second color space, approximate the color correction performed on the third image data in the third color space; storing or transmitting the coefficients of the one or more color correction approximation functions for use by the one or more target display management systems.