1. A local feature descriptor extracting apparatus comprising: a feature point detecting unit configured to detect a plurality of feature points in an image and output feature point information that is information on each of the feature points; a feature point selecting unit configured to select the predetermined number of feature points from the detected plurality of feature points in order of decreasing importance based on the feature point information; and a local feature descriptor generating unit configured to generate a local feature descriptor that is a feature descriptor in a local region for each of the selected feature points.