1. A face image synthesis apparatus comprising: a storage device configured to store a plurality of face images and a plurality of feature points including an origin and being set to each of the plurality of face images; and an arithmetic processing unit configured to generate a plurality of deformed face images, origins thereof are located in a same position, and the plurality of feature points thereof are located in same positions, by deforming the plurality of face images, and to generate a synthesized face image from the plurality of deformed face images, wherein the plurality of feature points includes a basing point and a reference point, and the arithmetic processing unit includes: an image scaling section configured to generate a plurality of scaled face images by scaling the plurality of face images based on the plurality of face images and the plurality of feature points to a distance between preset feature points of each of the plurality of scaled face images being same; an image normalizing section configured to calculate a location of the reference point from the origin in each of the plurality of scaled face images based on the plurality of scaled face images and the plurality of feature points, to set a location of the reference point after face image synthesis, and to generate the plurality of deformed face images which are normalized to the reference point of each of the plurality of scaled face images being located in a position of the reference point after face image synthesis; and an image synthesizing section configured to generate the synthesized face image by matching the reference point of each of the plurality of deformed face images and calculating a weighted average of at least one of a color and a luminance by a synthesis ratio for each pixel based on the plurality of deformed face images and the plurality of feature points, and the plurality of feature points includes a first feature point located in first quadrant, a second feature point located in second quadrant, a third feature point located in third quadrant and a fourth feature point located in fourth quadrant from the origin.