Conference Paper

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

Dept. of Electr. Eng., Nat. Taiwan Univ., Taipei, Taiwan
DOI: 10.1109/ICASSP.2003.1199484 Conference: Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on, Volume: 3
Source: IEEE Xplore

ABSTRACT 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.

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Available from: Jian-Jiun Ding, Sep 26, 2015
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    • "It can quantitatively obtain the phase distribution, even if there are small errors in the interferogram [17]. The third advantage is that the Hilbert transform has higher ability of noise immunity [18]. Most of the other methods may recognize the locations of the noise as the edges. "
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    ABSTRACT: The Hilbert Transform (HT) and the analytic signal (AS) are widely used in their one-dimensional version for various applications. However, in the bi-dimensional (2D) case as occur for images, the definition of the 2D-HT is not unique and several approaches to it have been developed, having as one of the main goals to obtain a meaningful 2D-AS or analytic image, which can be used for various practical applications. In this work, one particular approach to the 2D-HT is introduced that allowed the calculation of analytic images which satisfy the basic properties that these functions have in the 1D case, and that produces a 2D spectrum equal to zero in one quadrant. The methods for calculation of the discrete version of the 2D-HT and the associated AS are presented and analyzed, as well as two applications, for edge detection and for envelope detection in a 2D AM modulated radial chirp.
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    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.
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