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chaos5 In reply to lyc [2008-01-07 23:50:54 +0000 UTC]

What would be the correct name for such a thing? Basically it makes the colors closer to the center have more weight in the average. That’s why I called it a bias.

R is the distance from the center to the test point, and rmax is the distance from the center to the corner of the test area.

Lets call that e^(-k*(r/rmax)^2) B

The color values are multiplied by it, colorR*B and colorG*B etc..
And then B is added to the N value N+=B

Finally I divide the colors by N like this (colorR)/N for each component.

I know it’s not the same as the f(x)/p(x) sampling we worked on last week, so I see why it may be wrongly called a “bias”.

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lyc In reply to chaos5 [2008-01-07 23:59:37 +0000 UTC]

basically you're now integrating f(x)w(x)/p(x), where you're distributing x samples according to p. so it's not really bias, it's just an extra function -- and if you think about it, it's not really "extra", it was just a constant 1 before!

what you're doing with this pixel filter is to filter out excessively high frequency information, which cannot be stored at the current resolution's sampling rate. that high frequency is what causes aliasing, which is "jaggies" to you and me this is why so many people (even some "experts" - i kid you not) have difficulty distinguishing a blur from an antialiasing filter; it's true that both remove high frequency information, but antialiasing aims to do so in exactly the right amount so as to produce the ideally reconstructed signal. this is necessary because the function you're sampling, the one that's defined over the whole cartesian plane and not just integer pixel locations, is being represented at only a few sample locations, so it should be representative of the whole function near the sample, minus all the high frequency information it can't possibly represent.

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