1. An image processing apparatus having a color conversion unit configured to perform color conversion using a look-up table (LUT) for defining conversion from an input color to an output color, the apparatus comprising: an input unit configured to input an image that is to be a target of color conversion; an accepting unit configured to accept designation of a specific color; and a generation unit configured to register an output value corresponding to the specific color at an unused grid point in the LUT, and generate a specific color-associated LUT, wherein, if the specific color is used in an image input by the input unit, the color conversion unit performs color conversion using the specific color-associated LUT generated by the generation unit.