We describe an empirical study on the feature space of interest points for natural images. Although local features have been widely used in image analysis as building blocks of various algorithms, there is still a lack of study on the space of local features, in particular the distributions of local features extracted from the locations of interest points. Based on an approximate neighborhood probing scheme, we devise an efficient representation that is not only helpful in visualizing the distributions of local features, but also effective in modeling the neighborhood structures of local features for fast matching. We present various experimental results that provide useful insights into feature description and fast image matching.