On the Completeness of Coding with Image Features

We present a scheme for measuring completeness of local feature extraction in terms of image coding. Completeness is here considered as good coverage of relevant image information by the features. As each feature requires a certain number of bits which are representative for a certain subregion of the image, we interpret the coverage as a sparse coding scheme. The measure is therefore based on a comparison of two densities over the image domain: An entropy density pH(x) based on local image statistics, and a feature coding density pc(x) which is directly computed from each particular set of local features. Motivated by the coding scheme in JPEG, the entropy distribution is derived from the power spectrum of local patches around each pixel position in a statistically sound manner. As the total number of bits for coding the image and for representing it with local features may be different, we measure incompleteness by the Hellinger distance between pH(x) and pc(x). We will derive a procedure for measuring incompleteness of possibly mixed sets of local features and show results on standard datasets using some of the most popular region and keypoint detectors, including Lowe, MSER and the recently published SFOP detectors. Furthermore, we will draw some interesting conclusions about the complementarity of detectors.