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 regarding each feature point; a feature point selecting unit configured to select a prescribed number of feature points in an order of importance from the plurality of detected feature points, based on the feature point information; a local region acquiring unit configured to acquire a local region corresponding to each selected feature point; a subregion dividing unit configured to divide each local region into a plurality of subregions; a subregion feature vector generating unit configured to generate a feature vector of a plurality of dimensions for each subregion in each local region; and a dimension selecting unit configured to select a dimension from the feature vector for each subregion so that a correlation between neighboring subregions is lowered, based on a positional relationship between subregions in each local region and output an element of the selected dimension as a feature descriptor of the local region.