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: a projecting unit configured to project a pattern image on the projection surface, by controlling an image projecting device; a capturing unit configured to obtain a captured image of the projection surface on which the pattern image is projected, by controlling an image capturing device; a feature point extracting unit configured to extract feature points in the captured image corresponding to feature points in the pattern image; a three-dimensional coordinates measuring unit configured to 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; a reliability calculating unit configured to calculate reliabilities of the measuring points; a reliability area defining unit configured to convert the three dimensional coordinates of the measuring points into two-dimensional coordinates as defined in a view from an arbitral viewpoint and define a reliability area including the converted measuring points that respectively have the reliabilities exceeding a certain threshold; a reference table creating unit configured to create a reference table in which a distortion of a projection image viewed from the arbitral viewpoint is expressed by association of the two-dimensional coordinates on the reliability area with two-dimensional coordinates on an image projecting coordinate system; and an image correcting unit configured to correct the original image so that a distortion for offsetting the distortion expressed in the reference table is given to the original image, wherein the reliabilities are defined based on at least one of lens aberration and detection errors of the feature points.