1. A projector that is equipped with a projection lens movable in a direction substantially perpendicular to an optical axis and uses the projection lens to project and display an image on a projection object, the projector comprising: an imaging structure that photographs an area including at least the projected image on the projection object to take a photographed image; a shift level detection unit that detects a shift level of the projection lens; a control module that specifies a reference line to be processed in the photographed image; and a storage unit that stores a map of positional information to each shift level, where the positional information represents an expected relative line position to the projected image included in the photographed image, wherein the control module specifies a display position of the projected image included in the photographed image, the control module controlling the shift level detection unit to detect the shift level, reading the positional information corresponding to the detected shift level from the map stored in the storage unit, and specifying the reference line, based on the expected relative line position represented by the read positional information and the specified display position of the projected image.