  We show how an image can, in principle, be described by the tangles of the
graph of its pixels.
  The tangle-tree theorem provides a nested set of separations that efficiently
distinguish all the distinguishable tangles in a graph. This translates to a
small data set from which the image can be reconstructed.
  The tangle duality theorem says that a graph either has a certain-order
tangle or a tree-structure witnessing that this cannot exist. This tells us the
maximum resolution at which the image contains meaningful information.
