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That's the definition used in the paper. The other definition is that a pixel is in fact, a square window containing many samples that fall within that region a

That's the definition used in the paper. The other definition is that a pixel is in fact, a square window containing many samples that fall within that region and rendered as their average. This is known as antialiasing.

rspeer 12y ago
The article illustrates antialiasing, but chooses to use sinc-based circular windows, not square windows. Am I right to think that you'd only use square windows in the 3D-rendered graphics case, where you've already assumed the sub-pixels are square for efficiency?
- robert_tweed 12y ago
  The main point is that there are two conflicting views of what a "pixel" is. One is the representation of the samples and the other is what is actually displayed on-screen. Take for instance a ray tracer. Each ray is a sample and these are cast from the focal point, through the view frustum, and the colour is calculated where it intersects an object in the scene. In the naive case, this is done through the precise centre of each pixel, so there is a one-to-one mapping between display pixels and rendered pixels. However, that leads to very bad sampling error (aliasing), so typically you instead take lots of samples (which throws up more problems of sampling bias which I'll ignore for now). Now you have to decide how to map those samples to screen pixels. This is where the phrase "a pixel is a window" comes from. If the point sample falls within the current pixel boundaries, it's a contributor to its value. Pixels are generally considered to be rectangular windows, because that maps nicely to the way they are laid out in a grid. In particular, when displayed on-screen, each pixel represents a rectangular area of the screen. However, that's independent of how the image data was quantised originally. The point the paper seems to be making is that this rectangular mapping isn't very good, and overlapping circular windows are better. That's debatable and it depends what you're doing. With this model some point samples are contributors to more than one screen pixel, but on the upside, contributors to each pixel are all within an equal distance from the midpoint. A square allows samples that are further away on the diagonals, which is not right. It's correct for display, but not for manipulation. Either way, a pixel is still a window. You can choose different shapes for that window, with different trade-offs, but a pixel still describes the average of samples within the region it covers, rather than any single sample. That unfortunately is then quantised into a single sample for the pixel, ostensibly at its midpoint. Of course, the bigger problem is that quantisation step. If each point sample were stored as a vector, you could have lots of randomly positioned samples and re-quantize them into any shape pixels you like, which might be useful for something like the barrel-distorted projection used in the Oculus Rift, where it would be advantageous for every pixel to have a unique size and shape depending on how close it is to the centre (or think of a spherical projection where it also makes sense for pixels to be non-square). Unfortunately, that's not the way pixels are represented in any image formats we have, which is the particular view of pixels the paper is concerned with.
gaze 12y ago
That's definitely not anti aliasing and definitely the idea that the paper was railing against.

rspeer 12y ago

The article illustrates antialiasing, but chooses to use sinc-based circular windows, not square windows. Am I right to think that you'd only use square windows in the 3D-rendered graphics case, where you've already assumed the sub-pixels are square for efficiency?

robert_tweed 12y ago
The main point is that there are two conflicting views of what a "pixel" is. One is the representation of the samples and the other is what is actually displayed on-screen. Take for instance a ray tracer. Each ray is a sample and these are cast from the focal point, through the view frustum, and the colour is calculated where it intersects an object in the scene. In the naive case, this is done through the precise centre of each pixel, so there is a one-to-one mapping between display pixels and rendered pixels. However, that leads to very bad sampling error (aliasing), so typically you instead take lots of samples (which throws up more problems of sampling bias which I'll ignore for now). Now you have to decide how to map those samples to screen pixels. This is where the phrase "a pixel is a window" comes from. If the point sample falls within the current pixel boundaries, it's a contributor to its value. Pixels are generally considered to be rectangular windows, because that maps nicely to the way they are laid out in a grid. In particular, when displayed on-screen, each pixel represents a rectangular area of the screen. However, that's independent of how the image data was quantised originally. The point the paper seems to be making is that this rectangular mapping isn't very good, and overlapping circular windows are better. That's debatable and it depends what you're doing. With this model some point samples are contributors to more than one screen pixel, but on the upside, contributors to each pixel are all within an equal distance from the midpoint. A square allows samples that are further away on the diagonals, which is not right. It's correct for display, but not for manipulation. Either way, a pixel is still a window. You can choose different shapes for that window, with different trade-offs, but a pixel still describes the average of samples within the region it covers, rather than any single sample. That unfortunately is then quantised into a single sample for the pixel, ostensibly at its midpoint. Of course, the bigger problem is that quantisation step. If each point sample were stored as a vector, you could have lots of randomly positioned samples and re-quantize them into any shape pixels you like, which might be useful for something like the barrel-distorted projection used in the Oculus Rift, where it would be advantageous for every pixel to have a unique size and shape depending on how close it is to the centre (or think of a spherical projection where it also makes sense for pixels to be non-square). Unfortunately, that's not the way pixels are represented in any image formats we have, which is the particular view of pixels the paper is concerned with.

gaze 12y ago

That's definitely not anti aliasing and definitely the idea that the paper was railing against.