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A no-reference objective sharpness metric detecting both blur and noise is proposed in this paper. This metric is based on the local gradients of the image and does not require any edge detection. Its value drops either when the test image becomes blurred or corrupted by random noise. It can be thought of as an indicator of the signal to noise ratio of the image. Experiments using synthetic, natural, and compressed images are presented to demonstrate the effectiveness and robustness of this metric. Its statistical properties are also provided.