An advantage of the invention is to provide an image processing apparatus and a medium therefor, which enable shortening of processing time necessary for performing the whole color conversion in the case where only one of LUTs used for the color conversion can be stored in a storage means having a high access rate. In the image processing apparatus, for image data including a plurality of pixels and being a target for a color conversion, when performing the color conversion of the image data, a value of a counter for pictures, which indicates a predicted total number of references to an LUT for pictures, and a value of a counter for texts, which indicates a predicted total number of references to an LUT for texts, are derived.