1. A feature extraction device comprising: a feature extraction unit that extracts M types of features from each of a plurality of original images and each of a plurality of altered images obtained by applying an alteration; and a feature selection unit that selects a collection of N types of features from the M types of features extracted from each of the plurality of the original images and each of the plurality of the altered images, the N types being smaller in number than that of the M types, based on a value of an evaluation formula represented by a sum of discrimination capability and robustness, the discrimination capability being a degree of distinguishing respectively two different original images, an original image and an altered image obtained by applying an alteration process to an original image different from the original image, and two altered images obtained by respectively applying an alteration process to two original images that are different from each other, the robustness being a degree that a value of a feature of the original image does not vary due to an alteration process applied to the original image, wherein the feature selection unit calculates, with use of the features extracted from the respective images, discrimination capability of the N types of features as a value of a sum of information entropies of the N types of features, a joint entropy of a collection including the N types of features, or a value of a sum of mutual information amounts between the N types of features.