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.