I understand intuitively that supersampling approximates the pre-filtering, but is there a mathematical proof or logic that can show this more formerly?

willyj2k

If you consider box filtering with k*k sub-pixel granularity and supersampling a grid with the same k*k sub-pixel granularity, a potential mathematical argument comes from expressing the output pixel values in terms of the sub-pixel values. In both cases, I believe you would essentially be taking an average over the same k*k sub-pixel values; hence the two methods would give equivalent outputs.

I understand intuitively that supersampling approximates the pre-filtering, but is there a mathematical proof or logic that can show this more formerly?

If you consider box filtering with k*k sub-pixel granularity and supersampling a grid with the same k*k sub-pixel granularity, a potential mathematical argument comes from expressing the output pixel values in terms of the sub-pixel values. In both cases, I believe you would essentially be taking an average over the same k*k sub-pixel values; hence the two methods would give equivalent outputs.