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

It is well-known that the Hilbert transfonn (HLT) is useful for generating the analytic signal, and saving the bandwidth required in communication. However, it is known by less people that the HLT is also a useful tool for edge detection. In this paper, 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 techniques (such as section dividing and shorter impulse response modification), we can use the GRHLT to detect the edges of images exactly. Using the GRHLT for edge detection has higher ability of noise immunity than other edge detection algorithms. Besides, we can also use the GRHLT for directional edge detection, i.e., detect the edges with certain directions.