1. An automatic projection image correction system comprising: a projection image frame detection unit that detects straight lines forming a frame of a screen-projected image which is projected onto a screen by a projector from a captured image obtained by capturing the screen-projected image using a camera; and a projector plane parameter estimation unit that sets coordinate axes to a projector image, which is an original image of the screen-projected image, and the captured image and estimates at least one of a distance between the screen and the projector, an inclination of the screen with reference to an optical axis of the projector, and a zoom ratio of the projector, using an inclination of the optical axes of the projector and the camera, a distance between the optical centers of the projector and the camera, an intrinsic parameter of the camera, coordinate data of the detected straight lines at coordinates of the captured image, and coordinate data of straight lines corresponding to the frame at coordinates of the projector image.