1. An image processing apparatus comprising: a memory for storing an executable program; and a processor configured to execute the program to perform the following processes: a projection conversion coefficient acquisition process that acquires projection conversion coefficients that are coefficients for doing projection conversion on an image, the number of such coefficients being the same as the number of a plurality of reference points at differing positions in the image; a post-projection-conversion image acquisition process that does projection conversion on the image through the respective projection conversion coefficients of the same number as the number of the plurality of reference points, acquired by the projection conversion coefficient acquisition process, and acquires the same number of post-projection-conversion images from the image as the number of the reference points; a setting process that sets, for coordinates of pixels comprising the image, a plurality of weightings that differ in accordance with distances from the coordinates to the plurality of reference points; a weighted average process that makes a weighted average of coordinates of corresponding pixels corresponding among the plurality of post-projection-conversion images, using a plurality of weightings set by the setting process for coordinates of original pixels of the corresponding pixels in the image; and a weighted average image acquisition process that acquires a weighted average image comprising pixels with coordinates after weighted averaging by the weighted average process.