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, wherein each of the detection image parts includes a plurality of regions having respective luminance values different from each other, and the detection image generation section changes a luminance distribution of each of the detection image parts of the detection image to be generated so that maximum luminance values of the detection image parts included in a taken detection image obtained by taking the detection image projected on the projection surface fall within an allowable range.