1. An image processing apparatus provided with a processing unit, the processing unit executing: a provisional coefficient acquisition process that acquires provisional coefficients for doing projection conversion on an image, on the basis of feature points indicating features of the image; a conversion process that does projection conversion on a polygon having a plurality of fixed points as vertices, using the provisional coefficients acquired by the provisional coefficient acquisition process; a transformation degree acquisition process that acquires a transformation degree indicating a magnitude of the transformation degree of the polygon from the polygon prior to projection conversion by the conversion process and the polygon after projection conversion by the conversion process; a determination process that determines whether or not the transformation degree acquired by the transformation degree acquisition process exceeds a permitted transformation degree; and a projection conversion process that, when the transformation degree is determined to not exceed the permitted transformation degree by the determination process, does projection conversion on the image using as actual coefficients the provisional coefficients acquired by the provisional coefficient acquisition process.