1. A local feature descriptor extracting apparatus comprising: a feature point detecting unit configured to detect feature points in an image; a first local region acquiring unit configured to acquire a local region for each of the feature points; a first subregion dividing unit configured to divide each local region into a plurality of subregions; a first subregion feature vector generating unit configured to generate a feature vector with a plurality of dimensions for each of the subregions in each local region; and a dimension selecting unit configured to select dimensions from the feature vector in each subregion so as to reduce a correlation between proximate subregions based on positional relations among the subregions in each local region and output elements of the selected dimensions as a feature descriptor of the local region.