1. A projection image correcting apparatus for correcting, according to a three-dimensional shape of a projection surface, an original image to be projected, comprising: memory storing computer-executable instructions; and one or more processors configured to execute the computer-executable instructions such that the one or more processors are configured to, project a pattern image on the projection surface, by controlling an image projecting device, obtain a captured image of the projection surface on which the pattern image is projected, by controlling an image capturing device, extract feature points in the captured image corresponding to feature points in the pattern image, measure, by triangulation using the extracted feature points, three-dimensional coordinates of a plurality of measuring points on the projection surface corresponding to the feature points, calculate reliabilities of the measuring points, convert the three dimensional coordinates of the measuring points into two-dimensional coordinates as defined in a view from a first viewpoint and define a reliability area including the converted measuring points that respectively have the reliabilities exceeding a certain threshold, create a reference table in which a distortion of a projection image viewed from the first viewpoint is expressed by association of the two-dimensional coordinates on the reliability area with two-dimensional coordinates on an image projecting coordinate system, correct the original image so that a distortion for offsetting the distortion expressed in the reference table is given to the original image, and find a projection area that is a rectangular area, having the same aspect ratio as that of the original image, included in the reliability area, and reduce the original image to be disposed within the projection area, before correcting the original image based on the reference table, wherein the reliabilities are defined based on at least one of lens aberration and detection errors of the feature points.