1. An image processing device comprising: a plane conversion unit which receives a subject image in which a subject having a particular shape has been captured and shape information about three-dimensional shape of the subject and converts the subject image into a plane image in which the subject is viewed from a prescribed direction based on the shape information; and an in-plane position detection unit which recognizes a subject area in the plane image as an area representing the subject and determines a position of the subject in the plane image.