1. A biometric authentication apparatus comprising: one or more processors configured to: control a light source that emit a light having a predetermined wavelength to a finger portion; extract a vein image showing positions of veins from an image including veins in the finger portion; divide the extracted vein image into a plurality of partial regions; count a number of pixels corresponding to the veins in each of the partial regions; arrange, in a predetermined order, count results of the respective partial regions; generate a vein distribution vector, which is a numerical sequence representing a degree of distribution of the veins in the vein image; authenticate the generated vein distribution vector based on a registered vein distribution vector, which is a vein distribution vector registered in advance; calculate a degree of similarity between the generated vein distribution vector and the registered vein distribution vector, while one of the generated vein distribution vector and the registered vein distribution vector is repeatedly shifted by a predetermined number of elements; correct the vein image by performing at least one of a parallel moving processing and a rotation processing on the extracted vein image; perform a principal component analysis on a not-yet-corrected vein image, and rotate the not-yet-corrected vein image such that a direction of a first principal component is in parallel with a side in a longitudinal direction of the vein image; and calculate a barycenter of a distribution of pixels corresponding to the positions of the veins in the not-yet-corrected vein image, and move the not-yet-corrected vein image in parallel such that the barycenter matches a central position of the vein image.