1. A display device comprising: a display unit that displays an image; a touch detection unit that detects an instruction input provided by a pointing device to a display surface of the display unit; an acquisition unit that acquires information indicating a display color at an instruction input position, the display color being detected by a color sensor included in the pointing device; and a determination unit that performs determination processing to determine the instruction input position based on a color of the image and the color indicated by the information acquired by the acquisition unit.