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I think the story is a lot more complicated. Talking about "the best possible output quality" is a big claim, and I have no reason to believe it can be achieved

I think the story is a lot more complicated. Talking about "the best possible output quality" is a big claim, and I have no reason to believe it can be achieved by mathematically simple techniques (ie linear convolution with a kernel). Quality is ultimately a function of human perception, which is complex and poorly understood, and optimizing for that is similarly not going to be easy. The Mitchell-Netravali paper[1] correctly describes sampling as a tradeoff space. If you optimize for frequency response (brick wall rejection of aliasing) the impulse response is sinc and you get a lot of ringing. If you optimize for total rejection of aliasing while maintaining positive support, you get something that looks like a Gaussian impulse response, which is very smooth but blurry. And if you optimize for small spatial support and lack of ringing, you get a box filter, which lets some aliasing through. Which is best, I think, depends on what you're filtering. For natural scenes, you can make an argument that the oblique projection approach of Rocha et al[2] is the optimal point in the tradeoff space. I tried it on text, though, and there were noticeable ringing artifacts; box filtering is definitely better quality to my eyes. I like to think about antialiasing specific test images. The Siemens star is very sensitive in showing aliasing, but it also makes sense to look at a half-plane and a thin line, as they're more accurate models of real 2D scenes that people care about. It's hard to imagine doing better than a box filter for a half-plane; either you get ringing (which has the additional negative impact of clipping when the half-planes are at the gamut boundary of the display; not something you have to worry about with natural images) or blurriness. In particular, a tent filter is going to be softer but your eye won't pick up the reduction in aliasing, though it is certainly present in the frequency domain. A thin line is a different story. With a box filter, you get basically a non antialiased line of single pixel thickness, just less alpha, and it's clearly possible to do better; a tent filter is going to look better. But a thin line is just a linear combination of two half-planes. So if you accept that a box filter is better visual quality than a tent filter for a half-plane, and the other way around for a thin line, then the conclusion is that linear filtering is not the correct path to truly highest quality. With the exception of thin lines, for most 2D scenes a box filter with antialiasing done in the correct color space is very close to the best quality - maybe the midwit meme applies, and it does make sense to model a pixel as a little square in that case. But I am interested in the question of how to truly achieve the best quality, and I don't think we really know the answer yet. [1] https://www.cs.utexas.edu/~fussell/courses/cs384g-fall2013/lectures/mitchell/Mitchell.pdf https://www.cs.utexas.edu/~fussell/courses/cs384g-fall2013/l... [2] https://www.inf.ufrgs.br/~eslgastal/SBS3/Rocha_Oliveira_Gastal_EG2020_Sharp_Filter_SBS3.pdf https://www.inf.ufrgs.br/~eslgastal/SBS3/Rocha_Oliveira_Gast...

dahart 2y ago
Oh I agree with all of that. And nice to see you on HN Raph - was nice to meet you at HPG the other day. It’s subjective, so box filter being ‘close’ is a somewhat accurate statement. I’m coming from the film world, and so I have a pretty hard time agreeing that it’s “very” close. Box filter breaks often and easily, especially under animation, but it’s certainly better than nearest neighbor sampling, if that’s our baseline. Box filter is pretty bad for nearly any scenario where there are frequencies higher than the pixel spacing, which includes textures, patterns, thin lines, and all kinds of things, and the real world is full of these box-filter-confounding features. One interesting question to ask is whether you the viewer can reliably identify the size of a pixel anywhere in the image. If you can see any stepping of any kind, the pixel size is visible, and that means the filter is inadequate and cannot achieve “best possible output quality”. Most people are not sensitive to this at all, but I’ve sat through many filter evaluation sessions with film directors and lighting/vfx supervisors who are insanely sensitive to the differences between well tuned and closely matching Mitchell and Gaussian filters, for example. Personally, for various reasons based on past experience, I think it’s better to err slightly on the side of too blurry than too sharp. I’d rather use a Gaussian than bicubic, but the film people don’t necessarily agree and they think Gaussian is too blurry once you eliminate aliasing. Once you find the sharpest Gaussian you can that doesn’t alias, you will not be able to identify the size of a pixel - image features transition from sharp to blurry as you consider smaller scales, but pixel boundaries are not visible. I’ve never personally seen another filter that does this always, even under contrived scenarios. That said, I still think it’s tautologically true that box filter is simply not the “best” quality, even if we’re talking about very minor differences. Bilinear and Bicubic are always as good or better, even when the lay person can’t see the differences (or when they don’t know what to look for). My opinion is that there is no such thing as “best” output quality. We are in a tradeoff space, and the optimal result depends on goals that need to be stated explicitly and elaborated carefully. It depends heavily on the specific display, who/what is looking at the display, what the viewer cares about, what the surrounding environment is like, etc., etc.. * edit just to add that even though I don’t think “best” visual quality exists, I do think box filter can never get there, the contention for top spot is between the higher order filters, and box filter isn’t even in the running. I had meant to mention that even a single 2d plane that black on one side and white on the other, when rendered with box filter, yields an edge in which you can identify visible stepping. If you handle gamma & color properly, you can minimize it, but you can still see the pixels, even in this simplest of all cases. For me, that’s one reason box filter is disqualified from any discussion of high quality rendering.

dahart 2y ago

Oh I agree with all of that. And nice to see you on HN Raph - was nice to meet you at HPG the other day. It’s subjective, so box filter being ‘close’ is a somewhat accurate statement. I’m coming from the film world, and so I have a pretty hard time agreeing that it’s “very” close. Box filter breaks often and easily, especially under animation, but it’s certainly better than nearest neighbor sampling, if that’s our baseline. Box filter is pretty bad for nearly any scenario where there are frequencies higher than the pixel spacing, which includes textures, patterns, thin lines, and all kinds of things, and the real world is full of these box-filter-confounding features. One interesting question to ask is whether you the viewer can reliably identify the size of a pixel anywhere in the image. If you can see any stepping of any kind, the pixel size is visible, and that means the filter is inadequate and cannot achieve “best possible output quality”. Most people are not sensitive to this at all, but I’ve sat through many filter evaluation sessions with film directors and lighting/vfx supervisors who are insanely sensitive to the differences between well tuned and closely matching Mitchell and Gaussian filters, for example. Personally, for various reasons based on past experience, I think it’s better to err slightly on the side of too blurry than too sharp. I’d rather use a Gaussian than bicubic, but the film people don’t necessarily agree and they think Gaussian is too blurry once you eliminate aliasing. Once you find the sharpest Gaussian you can that doesn’t alias, you will not be able to identify the size of a pixel - image features transition from sharp to blurry as you consider smaller scales, but pixel boundaries are not visible. I’ve never personally seen another filter that does this always, even under contrived scenarios. That said, I still think it’s tautologically true that box filter is simply not the “best” quality, even if we’re talking about very minor differences. Bilinear and Bicubic are always as good or better, even when the lay person can’t see the differences (or when they don’t know what to look for). My opinion is that there is no such thing as “best” output quality. We are in a tradeoff space, and the optimal result depends on goals that need to be stated explicitly and elaborated carefully. It depends heavily on the specific display, who/what is looking at the display, what the viewer cares about, what the surrounding environment is like, etc., etc.. * edit just to add that even though I don’t think “best” visual quality exists, I do think box filter can never get there, the contention for top spot is between the higher order filters, and box filter isn’t even in the running. I had meant to mention that even a single 2d plane that black on one side and white on the other, when rendered with box filter, yields an edge in which you can identify visible stepping. If you handle gamma & color properly, you can minimize it, but you can still see the pixels, even in this simplest of all cases. For me, that’s one reason box filter is disqualified from any discussion of high quality rendering.