The generalized radial Hilbert transform and its applications to 2D edge detection (any direction or specified directions)

It is well-known that the Hilbert transform (HLT) is useful for generating analytic signals, and saving the bandwidth required, in communication. However, it is less known that the HLT is also a useful tool for edge detection. We introduce the generalized radiant Hilbert transform (GRHLT), and illustrate how to use it for edge detection. The GRHLT is the general form of the two-dimensional HLT. Together with some other techniques (such as section dividing and shorter impulse response modification), we can use the GRHLT to detect the edges of images exactly. The GRHLT used for edge detection has a higher capability for noise immunity than other edge detection algorithms. Besides, we can also use the GRHLT for directional edge detection, i.e., detecting edges with certain directions.