How it works

One observation carries the whole method: to make a small change visible, you do not have to find what moved. Amplify how each part of the picture changes over time, and the movement follows.

That is what "Eulerian" means here. The alternative — tracking each feature from frame to frame and exaggerating its path — is harder, slower, and fails when the movement is smaller than a pixel. Watching a fixed point and amplifying how it changes needs no tracking at all.

The four stages

Every pipeline in this library does the same four things.

1. Separate brightness from colour. Frames are converted so one channel carries brightness and two carry colour. The two kinds of change want different treatment — a pulse is mostly colour, a movement is mostly brightness at edges — and amplifying them by different amounts is what keeps the result usable.

2. Split by scale. The image is reduced, repeatedly. What is kept depends on the job:

• For colour, only the reduced image is kept. Shrinking averages over a region, and a heartbeat changes a whole region of skin together while sensor noise does not — so shrinking keeps the signal and drops much of the noise.
• For motion, the difference between each size and the next is kept: a stack of images, each holding the detail at one scale. Movement shows up as change in these detail layers.

3. Filter over time. Each pixel is now a series of values through time. Keeping only a band of frequencies discards everything changing too slowly or too quickly to be what you want. A heartbeat is about one cycle a second; a guitar string is eighty.

4. Amplify and add back. What survives the filter is multiplied and added to the original. The output is the original video with the selected change made large.

Why amplifying detail moves things

For motion this seems to prove too much: multiplying image detail should make the picture brighter and darker, not make things move.

It works because of what a small shift does to an image. Shift a picture by far less than its detail, and the difference is very nearly the image's spatial slope times the shift. Adding a multiple of that difference back is therefore nearly the same as shifting further. The approximation holds while the movement is small compared with the detail — which is why lambda_c exists: fine detail is where it breaks first, so fine detail is amplified less.

This also explains the failure everyone meets. Push alpha high enough and edges tear into ripples and haloes — the approximation falling apart, not a bug.

The amplification schedule

The motion pipelines do not amplify every scale by the same amount. They follow a schedule from the original paper: full amplification at coarse scales, tapering to none at the finest, with the crossover set by lambda_c, and the coarsest and finest layers zeroed outright. This is the single largest reason the published results look clean rather than shimmering.