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We describe a technique for computing scale-invariant features on range maps produced by a range sensor, such as a time-of-flight camera. Scale invariance is achieved by computing the features on the reconstructed three-dimensional surface of the object. The technique is general and can be applied to a wide range of operators. Features are computed in the frequency domain; the transform from the irregularly sampled mesh to the frequency domain uses the Nonequispaced Fast Fourier Transform. We demonstrate the technique on a facial feature detection task. On a dataset containing faces at various distances from the camera, the equal error rate (EER) for the case of scale-invariant features is halved compared to features computed on the range map in the conventional way. When the scale-invariant range features are combined with intensity features, the error rate on the test set reduces to zero.