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By analytically integrating the function f over each pixel in the image (explanation), the following "true" image is obtained:
The following grid shows difference images between the ones above and the "true" image. Below each image in the L2 error in the image, compared to the "true" image. Note that in all cases the error decreases as the sampling rate increases. Surprisingly, random sampling performs better than jittered. This may be because jittered sampling is still too "regular" for the extremely high frequencies in the target function; in this case, throwing caution to the wind and using a completely aimless sampling method may work better simply because it gives the function fewer chances to "trick" such a method into presenting aliased results.
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