1. A local feature descriptor extracting apparatus comprising: a computer configured to perform determining a detection range of feature points in an image, detecting a plurality of feature points in the image within the determined detection range and output feature point information that is information on each of the feature points, the feature point information including scale information indicative of a scale of each feature point; selecting a plurality of feature points from the detected plurality of feature points in an order based on the scale information included in the feature point information; repeating said determining, detecting, and selecting until a number of the feature points selected from the detected plurality of feature points becomes equal to or larger than a predetermined number, and generating a local feature descriptor that is a feature descriptor in a local region for each of the selected feature points; and a memory storing the local feature descriptor for each of the selected features points.