How does filter bank work in image processing?
Sorry, I couldn't access the paper behing the paywall, so here is an educated guess about the figure that you linked in the question.


$H_0$ is a low-pass filter, while $H_1$ is a high-pass filter. You can note that the union of both domains correctly yield the full bandwidth of the input signal.
These filters are directional, i.e., they operate on different subbands that correspond to a set of orientations. This is shown in the figure by the 1,2,3,4 triangles: each triangle corresponds to a set of low/high-frequency of a given set of orientations. For example, 1 corrresponds to lower frequencies, and the slope of the lines in 1 is positive.
Finally, the directional filter bank consists in two operations: separatig low/high frequencies (the filter bank part) and applying a transfer function that also depends on the orientation of the current frequency (the directional part).


I'm note sure that you can implement the figure from this explanation though. A good starting point now would be for you to look for an example code that does similar things.