A'regime' here is simply a way of looking at information, of projecting it in such a way as to render it coherent. if we had the right regime we could listen in to static and pick out, say, the particular pattern of a pulsar, amongst other things.
By 'listening in' to the various patterns that constitute lnguage, appearance and other qualities, we can create interpretations that allow us the experience of our world. Another interpretive regime might see it differently.
The image is pretty much straight up illistration. A 3d graph plots the distribution of a bunch of data points so that a typical form of distribution becomes apparent : a line seems to form because of the qualities and scales of the graphing regime.