EETimes published a nice story saying that when interpolating an image data, one needs to care not only about the interpolated data continuity, but also about the continuity of its first derivative. A discontinuity in the first derivative may create visible artifacts. The second derivative can be discontinuous, though.
This is well known. Draw a sharp object (black disk on a white background for instance) and use a blur tool like Photoshop lens blur (uniform circular kernel) to create a large blur and you'll see some "ringing" at the derivative discontinuity, while blurring with a Gaussian filter does not produce this effect.
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