1. An image sorting apparatus comprising: an image inputting unit that inputs an image; a distribution function preparing unit that prepares a distribution function of pixel values of the image; a describing unit that performs series expansion on the distribution function by using base functions that form a complete set and are orthogonal to each other due to different weights in a distribution area and describing the distribution function by expansion coefficients, an evaluating unit that evaluates features of the shape of the distribution function based on the expansion coefficients, and a sorting unit that sorts the image to images of at least two categories based on results of the evaluation, wherein the describing unit uses base functions that are orthogonal to each other due to different weights between a center portion and two end portions of the distribution area spreading in a positive region.