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> Audio samples are point samples (usually). This is nice, because there's a whole theory on how to upsample point samples without loss of information.

This signal processing applies to images as well. Resampling is used very often for upscaling, for example. Here's an example: https://en.wikipedia.org/wiki/Lanczos_resampling

> It was already wrong in 1995 when monitors where CRTs, and it's way wrong in 2025 in the LCD/OLED era where pixels are truly discrete.

I don't think it has anything to do with display technologies though. Imagine this: there is a computer that is dedicated to image processing. It has no display, no CRT, no LCD, nothing. The computer is running a service that is resizing images from 100x100 pixels to 200x200 pixels. Would the programmer of this server be better off thinking in terms of samples or rectangular subdivisions of a display?

Alvy Ray Smith, the author of this paper, was coming from the background of developing Renderman for Pixar. In that case, there were render farms doing all sorts of graphics processing before the final image was displayed anywhere.

> I don't think it has anything to do with display technologies though.

I think your two examples nicely illustrate that it's all about the display technology.

> The computer is running a service that is resizing images from 100x100 pixels to 200x200 pixels. Would the programmer of this server be better off thinking in terms of samples or rectangular subdivisions of a display?

That entirely depends on how the resizing is done. Usually people choose nearest neighbor in scenarios like that to be faithful to the original 100x100 display, and to keep the images sharp. This treats the pixels as squares, which means the programmer should do so as well.

> Alvy Ray Smith, the author of this paper, was coming from the background of developing Renderman for Pixar.

That's meaningful context. I'm sure that in 1995, Pixar movies were exposed onto analog film before being shown in theatres. I'm almost certain this process didn't preserve sharp pixels, so "pixels aren't squares" was perhaps literally true for this technology.

> Usually people choose nearest neighbor in scenarios like that to be faithful to the original

Perhaps I should have chosen a higher resolution. AIUI, in many modern systems, such as your OS, it’s usually bilinear or Lanczos resampling.

You say that the resize should be faithful to the “100x100 display”, but we don’t know whether it was used from such a display, or coming from a camera, or generated by software.

> I'm almost certain this process didn't preserve sharp pixels

Sure, but modern image processing pipelines work the same way. They are working to capture the original signal, with a hopeful representation of the continuous signal, not just a grid of squares.

I suppose this is different for a “pixel art” situation, where resampling has to be explicitly set to nearest neighbor. Even so, images like that have problems in modern video codecs, which model samples of a continuous signal.

And yes, I am aware that the “pixel” in “pixel art” means a little square :). The terminology being overloaded is what makes these discussions so confusing.

> I don't think it has anything to do with display technologies though. Imagine this: there is a computer that is dedicated to image processing. It has no display, no CRT, no LCD, nothing. The computer is running a service that is resizing images from 100x100 pixels to 200x200 pixels. Would the programmer of this server be better off thinking in terms of samples or rectangular subdivisions of a display?

How about a counter example: As part of a vectorization engine you need to trace the outline of all pixels of the same color in a bitmap. What other choice to you have than to think of pixels as squares with four sides?

> As part of a vectorization engine you need to trace the outline of all pixels of the same color in a bitmap. What other choice to you have than to think of pixels as squares with four sides?

I think that’s a bad example. For vector tracing, you want the ability to trace using lines and curves at any angle, not alongside the pixel boundaries, so you want to see the image as a function from ℝ² to RGB space for which you have samples at grid positions. Target then is to find a shape that covers the part of ℝ² that satisfies a discriminator function (e.g. “red component at least 0.8, green and blue components at most 0.1) decently well, balancing the simplicity of the shape (in terms of number of control points or something like that) with the quality of the cover.

I really think it would be defined by the set of pixels not of that color that border that color, but maybe I'm thinking about this wrong.

If your model of the pixels is that they're point samples, they have no edges and there's no way to know what they do or don't border. They're near other pixels, but there could be anything in between.

A pixel is a box that changes color to match the point sample it represents. What's the issue?

To quote my post that you reply to, it's

> a bad approximation that can only result in unnecessarily blurry images

I think you're wrong. According to my knowledge the pixels on CRT were rectangular and were throwing their color on neighbouring pixels. Graphics created for CRT were shown nicely on those screens, had much better visuals than displayed on LCD/LED and were antialiases by default (i.e. by the display technology)

Pixels displayed on CRT displays are not squares, but they are not infinitely small dots either. They are much less well-defined blobs, that even overlap with each other.

There is also the complication of composite video signals, where you can't treat pixels as linearly independent components.

Good PC monitors (especially in 1995) displayed pixels as almost perfect discrete squares. It was home consoles on televisions where people get the idea from that all CRTs were blurry.

Let me guess: when game creators were thinking about result visuals were they considering that everyone would have this good pc monitor with exact square pixel, or were they taking into account possible distortions that would occur on average CRT?

Also: people playing retro nowadays use shaders to emulate CRT https://youtube.com/shorts/W_ZI3w9CYnI

As I said,

>> It was home consoles on televisions where people get the idea from that all CRTs were blurry.

The video you linked shows a PS1 game, which proves my point. It's possible you're too young to remember the big difference between a CRT TV and a CRT monitor. Monitors really did show discrete pixels (which was important for tiny text in applications to be readable), while TVs were blurry messes.