Comment by pornel

We commonly use hardware like LCDs and printers that render a sharp transition between pixels without the Gibbs' phenomenon. CRT scanlines were close to an actual 1D signal (but not directly controlled by the pixels, which the video cards still tried to make square-ish), but AFAIK we've never had a display that is a 2D signal that we assume in image processing.

In signal processing you have a finite number of samples of an infinitely precise contiguous signal, but in image processing you have a discrete representation mapped to a discrete output. It's contiguous only when you choose to model it that way. Discrete → contiguous → discrete conversion is a useful tool in some cases, but it's not the whole story.

There are images designed for very specific hardware, like sprites for CRT monitors, or font glyphs rendered for LCD subpixels. More generally, nearly all bitmap graphics assumes that pixel alignment is meaningful (and that has been true even in the CRT era before the pixel grid could be aligned with the display's subpixels). Boxes and line widths, especially in GUIs, tend to be designed for integer multiples of pixels. Fonts have/had hinting for aligning to the pixel grid.

Lack of grid alignment, an equivalent of a phase shift that wouldn't matter in pure signal processing, is visually quite noticeable at resolutions where the hardware pixels are little squares to the naked eye.