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Carefully crafted, often imperceptible, adversarial perturbations have been shown to cause state-ofthe-art models to yield extremely inaccurate outputs, rendering them unsuitable for safety-critical application domains. In addition, recent work has shown that constraining the attack space to a low frequency regime is particularly effective. Yet, it remains unclear whether this is due to generally constraining the attack search space or specifically removing high frequency components from consideration. By systematically controlling the frequency components of the perturbation, evaluating against the top-placing defense submissions in the NeurIPS 2017 competition, we empirically show that performance improvements in both the whitebox and black-box transfer settings are yielded only when low frequency components are preserved. In fact, the defended models based on adversarial training are roughly as vulnerable to low frequency perturbations as undefended models, suggesting that the purported robustness of state-ofthe-art ImageNet defenses is reliant upon adversarial perturbations being high frequency in nature. We do find that under ∞ = 16/255, the competition distortion bound, low frequency perturbations are indeed perceptible. This questions the use of the ∞ -norm, in particular, as a distortion metric, and, in turn, suggests that explicitly considering the frequency space is promising for learning robust models which better align with human perception.

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Automatic identification of landmarks in cephalometry is very important and useful for orthognathic surgery. A computerised automatic cephalometric analysis system (CACAS), based on image processing, is presented. For an original X-ray image, median filtering and histogram equalisation are used to improve image quality. The edge of an X-ray image is detected by a wavelet transform and Canny filter. Seventeen landmarks in cephalometry are successfully identified by knowledge-based edge tracing and changeable templates. Seventy-three measurements based on distances, angles and ratios between landmarks are computed automatically. The reliability of the landmarks and the validity of the measurements are compared for automatic and manual operation. The values of measurements obtained by CACAS are more precise and reliable: the mean error for linear measurements is less than 0.9mm; the mean error for angular measurements is less than 1.2 degrees. The rate of validity is over 80%, even if the image quality is poor. For an image with a high signal-to-noise ratio, the rate of validity of landmarking and measurements using the CACAS system is over 90%.