We propose Compact And Real-time Descriptors (CARD) which can be computed very rapidly and be expressed by short binary codes. An efficient algorithm based on lookup tables is presented for extracting histograms of oriented gradients, which results in approximately 16 times faster computation time per descriptor than that of SIFT. Our lookup-table-based approach can handle arbitrary layouts of bins, such as the grid binning of SIFT and the logpolar binning of GLOH, thus yielding sufficient discrimination power. In addition, we introduce learning-based sparse hashing to convert the extracted descriptors to short binary codes. This conversion is achieved very rapidly by multiplying a very sparse integer weight matrix by the descriptors and aggregating signs of their multiplications. The weight matrix is optimized in a training phase so as to make Hamming distances between encoded training pairs reflect visual dissimilarities between them. Experimental results demonstrate that CARD ou...