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Stopped reading at "A pixel is a point sample." No, it's not. We wouldn't have sub-pixel font rendering and hundreds of anti-aliasing filter modes for the graph

Stopped reading at "A pixel is a point sample." No, it's not. We wouldn't have sub-pixel font rendering and hundreds of anti-aliasing filter modes for the graphics cards. The pixel is an /area/ element of your image. And yes, many times, it's a square.

RubyPinch 12y ago
It mentioned colors right after that statement. edit: I do feel we are all smart enough to realize that the circle-vs-square, when considering a single channel, isn't affected much when colors are then considered offsets for each color are not unimaginable
angersock 12y ago
So, you made it to the middle of the second page? Anti-aliasing is a direct result of the fact that pixels are point-samples--the idea is to combine multiple samples and weight them so that the collection of point samples (in the form of a frame buffer) still represents a perceptually-reasonable form of the image.
- davrosthedalek 12y ago
  Sorry, but you got it backwards. Exactly because pixels are /not/ point samples, but have an area, point sampling does not work, and you need anti-aliasing. In the limit of infinite resolution/area of the pixels gets infinitely small, point-sampling would be enough. You say it yourself: Since solving the integration over the pixel area is generally hard, we approximate the integration with multiple point samples.
  - angersock 12y ago
    Hm, I think I see the point you're getting at. It's still a good paper. :)
gumby 12y ago
> Stopped reading at "A pixel is a point sample." > ...yes, many times, it's a square. While "appeal to authority" is generally a bad way to end a discussion, I will start by pointing out that this is Alvy Ray Smith writing, and he was writing in 1995. So while you could end up disagreeing with him (though I hope you wouldn't), you might consider why he was writing. Your comment shows that this paper is just as applicable today. (since you stopped on page two you never saw the several examples of why this matters in the article, including one on scanning and one on pre-rendering geometric computation). Those graphics cards you refer to reflect Smith's influence on their design.You have sub pixel rendering today because pixels aren't squares. This was computationally prohibitive in 1995. The TL;DR of this brief paper is "IO is really really hard, and though accepting shortcuts and defaults only kinda works and here's why." You benefit from a lot of work done in the last 20 years to improve the quality of the libraries and hardware available to you, but still, "photo-realistic" graphics aren't. By the way, rendered pixels weren't squares in those days (they were not-always-circular dots on a screen which itself wasn't flat) and they aren't on today's flat LCDs (you can think of them as rectangular, though the color elements do not present uniformly though the area) and they sure as hell aren't on any device with lenses or mirrors (including projectors and headsets)
- davrosthedalek 12y ago
  I realize that sub-pixel rendering is a misleading term, there are two concepts: a) Making use of fact that a physical pixel is a composite of multiple, disjunct areas of single-colored elements. b) Rendering objects with higher-than-pixel-density resolution, for example lines which appear thinner than a pixel. /Both/ relies on the fact that a pixel has an area, i.e. it is not a point, which is the point I was trying to make. A pixel on LCDs is indeed square most of the time, the subpixel elements are not. CRTs, of course, different story. All the "problems" he describes actually arise from the misconception that a pixel is a /point/ sample. It is an area sample, and if you treat it as such, the rest follows.
- gaze 12y ago
  I think everyone in signal processing writes the same rant against zero-order-hold at some point. The Xiph people did (http://xiph.org/video/ http://xiph.org/video/) and so has this guy.
corysama 12y ago
What is behind the pixel is an area. But, the pixel itself is a pinhole viewport into that area. This article is about resampling and reconstructing images that are already encoded as pixels (texels would be more accurate, but I don't know if that term was around back in 93). So, when zooming in on a pixelated image, how do we fill in the gaps between the pinholes? Declaring pixels to be square areas means that larger views of a given image really should be composed of larger, hard-edged squares for each source pixel. I.e point sampling is truth. The reality is that what's really between the pixel centerpoints is unknown --lost forever or never calculated at all. To fill in the gaps we can only make intelligent guesses. Therefore: sampling theory.
akira2501 12y ago
> And yes, many times, it's a square. Are you sure? In my experience, it depends on the context, but the pixels themselves are _not_ always of equal height:width ratio. http://en.wikipedia.org/wiki/Pixel_aspect_ratio http://en.wikipedia.org/wiki/Pixel_aspect_ratio
- davrosthedalek 12y ago
  not always = many times?
  - akira2501 12y ago
    "And yes, many times, ... " I took it to mean, "yes, many times over." As in, without a doubt, all pixels are square. My error.

RubyPinch 12y ago

It mentioned colors right after that statement. edit: I do feel we are all smart enough to realize that the circle-vs-square, when considering a single channel, isn't affected much when colors are then considered offsets for each color are not unimaginable

angersock 12y ago

So, you made it to the middle of the second page? Anti-aliasing is a direct result of the fact that pixels are point-samples--the idea is to combine multiple samples and weight them so that the collection of point samples (in the form of a frame buffer) still represents a perceptually-reasonable form of the image.

davrosthedalek 12y ago
Sorry, but you got it backwards. Exactly because pixels are /not/ point samples, but have an area, point sampling does not work, and you need anti-aliasing. In the limit of infinite resolution/area of the pixels gets infinitely small, point-sampling would be enough. You say it yourself: Since solving the integration over the pixel area is generally hard, we approximate the integration with multiple point samples.
- angersock 12y ago
  Hm, I think I see the point you're getting at. It's still a good paper. :)

gumby 12y ago

> Stopped reading at "A pixel is a point sample." > ...yes, many times, it's a square. While "appeal to authority" is generally a bad way to end a discussion, I will start by pointing out that this is Alvy Ray Smith writing, and he was writing in 1995. So while you could end up disagreeing with him (though I hope you wouldn't), you might consider why he was writing. Your comment shows that this paper is just as applicable today. (since you stopped on page two you never saw the several examples of why this matters in the article, including one on scanning and one on pre-rendering geometric computation). Those graphics cards you refer to reflect Smith's influence on their design.You have sub pixel rendering today because pixels aren't squares. This was computationally prohibitive in 1995. The TL;DR of this brief paper is "IO is really really hard, and though accepting shortcuts and defaults only kinda works and here's why." You benefit from a lot of work done in the last 20 years to improve the quality of the libraries and hardware available to you, but still, "photo-realistic" graphics aren't. By the way, rendered pixels weren't squares in those days (they were not-always-circular dots on a screen which itself wasn't flat) and they aren't on today's flat LCDs (you can think of them as rectangular, though the color elements do not present uniformly though the area) and they sure as hell aren't on any device with lenses or mirrors (including projectors and headsets)

davrosthedalek 12y ago
I realize that sub-pixel rendering is a misleading term, there are two concepts: a) Making use of fact that a physical pixel is a composite of multiple, disjunct areas of single-colored elements. b) Rendering objects with higher-than-pixel-density resolution, for example lines which appear thinner than a pixel. /Both/ relies on the fact that a pixel has an area, i.e. it is not a point, which is the point I was trying to make. A pixel on LCDs is indeed square most of the time, the subpixel elements are not. CRTs, of course, different story. All the "problems" he describes actually arise from the misconception that a pixel is a /point/ sample. It is an area sample, and if you treat it as such, the rest follows.
gaze 12y ago
I think everyone in signal processing writes the same rant against zero-order-hold at some point. The Xiph people did (http://xiph.org/video/ http://xiph.org/video/) and so has this guy.

corysama 12y ago

What is behind the pixel is an area. But, the pixel itself is a pinhole viewport into that area. This article is about resampling and reconstructing images that are already encoded as pixels (texels would be more accurate, but I don't know if that term was around back in 93). So, when zooming in on a pixelated image, how do we fill in the gaps between the pinholes? Declaring pixels to be square areas means that larger views of a given image really should be composed of larger, hard-edged squares for each source pixel. I.e point sampling is truth. The reality is that what's really between the pixel centerpoints is unknown --lost forever or never calculated at all. To fill in the gaps we can only make intelligent guesses. Therefore: sampling theory.

akira2501 12y ago

> And yes, many times, it's a square. Are you sure? In my experience, it depends on the context, but the pixels themselves are _not_ always of equal height:width ratio. http://en.wikipedia.org/wiki/Pixel_aspect_ratio http://en.wikipedia.org/wiki/Pixel_aspect_ratio

davrosthedalek 12y ago
not always = many times?
- akira2501 12y ago
  "And yes, many times, ... " I took it to mean, "yes, many times over." As in, without a doubt, all pixels are square. My error.