This is an interactive demo that lets you explore how to remove certain wavelength-related (frequency) content from an image. By wavelength, I mean intensities that vary by some rate-of-change of pixels either across horizontally or up-and-down vertically in the image. The low-cut slider sets up a threshold below which content is removed, and the high-cut slider sets up an equivalent threshold above which content is removed.

I think it is interesting because it reveals a couple things. First, that most of the content we find essential to the image is in the low-frequencies (the high-cut slider can be moved very far left before the image appears altered). Second, it demonstrates that a sharp cutoff of frequencies results in ringing (oscillations) in the image (the opposite is also true -- a sharp edge in the image will produce oscillating wavelength magnitudes in the frequency plot).

This method of removing wavelength-related content (called Fourier Filtering) is very precise in terms of cutting out specific frequencies, but the effect can be undesirable in terms of producing images that appear smooth and artifact-free (no blemishes). If you want to produce a smoother image which has certain periodic content removed, you would have to filter it out gradually in the Fourier representation (called filter "roll-off") instead of a sharp cut-off.

A Fourier transform maps a signal from a time domain into an equivalent [0] signal in the frequency domain.

This demo:

1. Performs a Fourier transform on some image pixels, taking the pixel data from the "time" domain into the frequency domain. (Think of time as "how far through the image we are", and the pixel's intensity as the signal's magnitude; frequency in this case becomes a slightly abstract concept.)

2. Visualises that frequency domain in various ways - by default you're seeing the magnitude of the transformed signal

3. applies a band-pass filter to that frequency domain - i.e. only allowing signals above a certain frequency (low-cut) and below another certain frequency (high-cut), and removing the rest. Playing with this might give you an intuitive notion of what "frequency" means here.

4. applies the inverse transform, giving you a signal back in the time domain (i.e. a normally viewable image).

You can see what the effect of bandpassing the frequency-domain signal is on the end result. Thinking about it in terms of Information, if we band-pass half of the given frequency spectrum out, we're essentially throwing away half of the Information... but yet the image is still useful to a human (this is the principle of how lossy compression algorithms work, as others have noted).

[0] In the case of a "perfect" transform, in reality most algorithms are lossy

I won't ELI5, but maybe someone here remembers the name for chimeric pictures which contain one image in the low frequencies, and a different one in the high, so one gets different impressions (smile vs frown, etc.) depending upon one is seated at one's monitor or viewing from across the room?

Edit: https://en.wikipedia.org/wiki/Hybrid_image

Are those worth a thousand words?