1. An image processing apparatus comprising: a controller being configured to: acquire provisional coefficients for doing projection conversion on an image, on the basis of feature points indicating features of the image; perform projection conversion on a polygon having a plurality of fixed points as vertices, using the acquired provisional coefficients; acquire a transformation degree indicating a magnitude of the transformation degree of the polygon from the polygon prior to projection conversion and the polygon after projection conversion; determine whether or not the transformation degree acquired by the transformation degree acquisition process exceeds a permitted transformation degree; and when the transformation degree is determined to not exceed the permitted transformation degree perform projection conversion on the image using as actual coefficients the acquired provisional coefficients.