1. An image processing device used for a projector adapted to display an image by projecting the image on a projection surface comprising: a detection image generation section adapted to generate a detection image, which is an image adapted to detect a state of a projection image displayed on the projection surface, and includes a plurality of detection image parts, and a background image adapted to cover respective peripheries of the detection image parts, wherein each of the detection image parts includes a plurality of regions having respective luminance values different from each other, the background image has a luminance value lower than the luminance values of the detection image parts, and the detection image generation section changes at least one of a luminance distribution of each of the detection image parts of the detection image to be generated and a size of the background image so that a luminance distribution of each of the detection image parts included in a taken detection image, which is taken by imaging the detection image projected on the projection surface, is approximated to a luminance distribution of corresponding one of the detection image parts of the detection image.