There's school of thought that pixels are point samples of a waveform (separately along horizontal and vertical axis, and that separation is useful for performance). In such interpretation resizing is downsampling that removes higher frequencies. You can then reason about this mathematically and show that you have an optimal filter, which preserves as many frequencies as possible, without bias or aliasing.
In practice, it's a bit more complicated, because pixels can form a square wave without Gibb's phenomenon. Physically they're not points. And there are all kinds of biological factors in perception.
As for reference to neural networks, I'm not sure. They're used for superresolution (upscaling), but I haven't seen them used for downscaling. They could be in theory.
Damn you seem to know quite a bit about this. That's an interesting way to map the problem domain. You hit it on the nail from my perspective because the author of the linked library is known for his audio plugins (voxengo). So he's definitely coming at it from the perspective of bandwidth and frequencies. Interesting.
Just curious if this makes you think of similar things that might be equally interesting to think about (share?)
The earliest pre 2000 JPG specification included compression based on FFT and Fourier theory - using long (infinite) additive waveforms to match image features and then knocking off least terms to compress with some sense of "least" loss.
Using traditional FFT long waveforms introduced particular kinds of artifacts.
The 2000 JPG spec included the use of localised cosine wavelets .. just like trad. FFT (kind of) but scaled from one at origin to zero at a local radius to suppress the echoing artifacts.
The notion first (IIRC) appeared in the "infinitely scrollable" and "instantly loading" (at top level .. with infill as time passed) not-JPEG earth scale mapping images used by both LizardTech (DejaVu(?)) and ERMapper (ECW images) in the early 1990s.
The "google map style" applications kind of died on the vine for a bit after a series of dragged out patent arguments then came back in modified form.
In practice, it's a bit more complicated, because pixels can form a square wave without Gibb's phenomenon. Physically they're not points. And there are all kinds of biological factors in perception.
As for reference to neural networks, I'm not sure. They're used for superresolution (upscaling), but I haven't seen them used for downscaling. They could be in theory.