Recently, binary descriptors have attracted significant attention due to their speed and low memory consumption; however, using intensity differences to calculate the binary descriptive vector is not efficient enough. We propose an approach to binary description called POLAR_MOBIL, in which we perform binary tests between geometrical and statistical information using moments in the patch instead of the classical intensity binary test. In addition, we introduce a learning technique used to select an optimized set of binary tests with low correlation and high variance. This approach offers high distinctiveness against affine transformations and appearance changes. An extensive evaluation on well-known benchmark datasets reveals the robustness and the effectiveness of the proposed descriptor, as well as its good performance in terms of low computation complexity when compared with state-of-the-art real-time local descriptors.