1. A projector that projects an image based on image information, the projector comprising: an operation reception unit that receives input operation; a selection unit that allows selection of one of a plurality of controlled objects located in correspondence with vertices of a contour of the image based on the image information and sides of the contour; and a correction unit that allows movement of the controlled object selected by using the selection unit within the image based on the input operation and corrects the contour of the image based on the moved controlled object, wherein the selection unit is a control point selection unit that handles the vertices and predetermined points located on the sides of the contour as control points that are the controlled objects and allows selection of one of the plurality of control points as a selected control point, and the correction unit includes a control point movement unit that allows movement of the selected control point selected by using the control point selection unit within the image based on the input operation, and an image correction unit that forms a contour of the image in such a way that the contour passes through the selected control point moved by using the control point movement unit and corrects the image information to fit in the formed contour.