Image processing apparatus and color separation processing method by interpolation processing using a multi-dimensional lookup table

An image processing apparatus comprising:

• a one or more processors;
• a memory coupled with the one or more processors and including instructions stored thereon that, when executed by the one or more processors, cause the image processing apparatus to:
• obtain an input value of an input image;
• select information indicating a change characteristics expression corresponding to the input value out of a plurality of pieces of information, each indicating change characteristics expressions corresponding to the input value;
• and
• perform, by interpolation processing using a lookup table having a plurality of dimensions in accordance with signal components of the input image based on the selected information indicating the change characteristics expression, color separation of the input value that is each pixel value of the input image into an output value corresponding to each of signal components handled by an output device, wherein
• each piece of information represents a change characteristics expression at each portion between adjacent grid points for each dimension of the plurality of dimensions, and
• at least a part of grid points of the lookup table are associated with any one of the pieces of information.