Short response Hilbert transform for edge detection

Abstract

In this paper, we define the short-response Hilbert transform (SRHLT) and use it for edge detection. The SRHLT has a parameter b. When b = 0, it becomes the Hilbert transform (HLT). When b is infinite, it becomes differentiation. Many edge detection algorithms are based on differentiation. However, they are sensitive to noise. By contrast, when using the HLT for edge detection, the noise is reduced but the resolution is poor. The proposed SRHLT in this paper can compromise the advantages of differentiation and HLTs. It is robust to noise and can simultaneously distinguish edges from non-edge regions very successfully.