These invariants are standard practice in computer vision. In fact, you won't go anywhere without translation and brightness invariance, more often you need also scale (uniform) and rotation invariance, and limited projective transform tolerance.

There are various ways to deal with this in ML (not really an expert in ML), but AFAIU in most cases you get candidate transforms via model-based methods, and then make the decision using ML-based methods trained to allow for limited transformations (convolution nets are good at that).