1. A computer-implemented method for generating a set of color-toning curves, the method comprising: using a computer to perform: receiving an input image; receiving a first set of color-toning parameters for shadow regions, a second set of color-toning parameters for highlight regions, and an invariance property to be maintained during color toning, wherein the invariance property is represented by an equation that specifies a relationship between input values and output color channel values; computing a set of color-toning-curve values and a set of color-toning-curve slopes using the first set of color-toning parameters, the second set of color-toning parameters, and the invariance property, wherein computing the set of color-toning-curve values and the set of color-toning-curve slopes comprises: generating a set of linear equations on the set of color-toning-curve values and the set of color-toning-curve slopes using the first set of color-toning parameters, the second set of color-toning parameters, and the invariance property, wherein generating the set of linear equations comprises taking the limit of a hue function; and solving the set of linear equations to determine the set of color-toning-curve values and the set of color-toning-curve slopes; generating the set of color-toning curves using the set of color-toning-curve values and the set of color-toning-curve slopes; and generating a color-toned image based on the input image and the set of color-toning curves.