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We present the radial gradient transform (RGT) and a fast approximation, the approximate RGT (ARGT). We analyze the effects of the approximation on gradient quantization and histogramming. The ARGT is incorporated into the rotation-invariant fast feature (RIFF) algorithm. We demonstrate that, using the ARGT, RIFF extracts features 16× faster than SURF while achieving a similar performance for image matching and retrieval.