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Comment by IshKebab | Hacker News Reader

This is wrong. Pixels may not be perfect little squares but they are not perfect point samples either. They're normally somewhere in-between.

Cameras do not sample points, and even though with sufficient filtering they can be equivalent to point samples of a low passed image, plenty of cameras don't have any filtering.

Similarly displays basically never have filtering to make pixels point samples. If they did then anti-aliasing wouldn't be a thing!

Hell, most projectors literally project little squares! (Even in 1995 IIRC.)

This must have been written by someone that just learnt about sampling theory and thought "aha! Pixels are samples!" without actually thinking about real life.

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I think Alvy Ray Smith understands both the fundamentals of sampling theory and the practicalities of real-world image synthesis and display, given his role in the creation of computer graphics.

Re "If they [displays] did [filtering] then anti-aliasing wouldn't be a thing" - that doesn't match my understanding of sampling theory. If the computer graphics process of image synthesis has folded down high frequencies in the hypothetical source signal, well above (half) the image sampling resolution, so that they now overlap with lower frequencies of the image -- i.e. the image generation suffers aliasing -- then no "filtering" downstream (at least in the traditional signal processing sense) can undo that, and the shape the display elements certainly won't save you either. The job of anti-aliasing is to prevent high-frequency energy from landing in the band-pass in the first place.

Re "plenty of cameras don't have any filtering": the physical act of counting photons that fall onto the areal extent of a CCD element (with an the associated directional distribution created by the prior optics) is absolutely a filtering of the incoming optical signal. That is independent of any subsequent digital filtering of the pixel data.

It was written by this guy:

https://en.wikipedia.org/wiki/Alvy_Ray_Smith

Ok I stand corrected! Still he should know better.

This may be one of the most incorrect and arrogant things I've ever read.

This must have been written by someone that just learnt about sampling theory and thought "aha! Pixels are samples!" without actually thinking about real life.

This was written by one of the fathers of computer graphics.

chriswarbo was completely right, but was downvoted anyway. You are conflating displays of pixels with calculating the color of each pixel that goes into an image.

Each pixel in a rendered image is weighted average using a specific filter over an area around a pixel. If you treat that as a square, you get a 1x1 box filter which is terrible for anti-aliasing. You can try this by playing with renderer settings so you understand what he's talking about in the context he was talking about.

> If they did then anti-aliasing wouldn't be a thing!

Anti-aliasing makes perfect sense, even if you assume that individual pixels are points.

You're conflating many different things, all under the name "pixel". I think that's where your confusion is coming from:

> Cameras do not sample points

Cameras use sensor-elements (silver-iodide grains, CCD arrays, etc.). If you want to use the p-word, we could call them "sensor pixels", or suchlike.

> displays basically never have filtering to make pixels point samples

I don't understand what this means; displays are physical devices, which must have 3D extent.

In any case, we can call the display-elements of such devices "display pixels", to avoid confusion.

> most projectors literally project little squares

Again, these are display-elements (or "display pixels", if you must).

> This must have been written by someone that just learnt about sampling theory and thought "aha! Pixels are samples!" without actually thinking about real life.

The author is using the term "pixel" to refer to image data. That is not the same thing as display-elements, or sensor components, etc.

If you read it carefully, you'll see those examples are actually mentioned explicitly; along with e.g. the tone patterns used by printers.

Image data is recorded from sensor pixels (or rendered pixels) and displayed on screen pixels or pinted using ink pixels, without additional filtering unless the image is scaled or rotated. None of these are perfect pixels due to physical limitations but they all try to be mostly that: little squares.

It is convenient to think of image data as point samples because that lets you use sampling theory but that does not mean image pixels are actually point samples.

Or ro put it another way, if it's captured like a little square and displayed like a little square, it is a little square.

You are making the exact same mistake even though this person explained it to you.

This isn't about what a pixel in a display looks like, it is about what a pixel in an image buffer represents and how to render it without aliasing.

To anti-alias a pixel you have to realize that it is the weighted average of multiple samples over an area.

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