1. An image processing apparatus comprising: detecting means for detecting a position of a facial feature in a face image; principal component analysis performing means for performing a principal component analysis operation on the position of the facial feature in a registered image that is a pre-registered face image to obtain a principal component; first evaluation value calculating means for calculating a first evaluation value that is used to evaluate the position of the facial feature in a target image, which is a face image to be authenticated, relative to the principal component obtained in the principal component analysis operation; and first determining means for determining whether or not the face in the target image matches the face in the registered image by comparing the calculated first evaluation value with a first threshold set on the basis of the position of the facial feature in the registered image relative to the principal component, wherein the first evaluation value calculated by the first evaluation value calculating means is a square root of a result of subtracting a sum of squares of inner products of a first difference vector and each principal component vector from a magnitude of a first difference vector.