I try to wrap my mind around causility and complex analytic filters, created by the Hilbert transform.
So far, I understand that there are no negative frequencies in an analytic filter and thus even though the filter is complex, the real and imaginary parts cancel out nicely s.t. you can have a meaningful complex valued representation of an analytical signal.
If I understand correctly, that also means that the signal is causal, thus there is a direct dependence of past values (one direction of the signal x-axis).
But now I cant figure out how that process would work in 2d images. What direction of what axis is now the causal one? And are the 2 image axis related to the real and imaginary axis? Or should I interpret the complex image in 4d space?