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 In proceeding of: Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on, Volume: 3 Source: IEEE Xplore

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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.01/2008; - [Show abstract] [Hide abstract]

**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.Image Analysis and Recognition, 4th International Conference, ICIAR 2007, Montreal, Canada, August 22-24, 2007, Proceedings; 01/2007 - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, the performance of image filtering using the Hilbert Matrix and its inverse is studied first and according to its results, a new edge enhancement and embossing algorithm is proposed. Most of the Laplacian and Sobel-based edge detection methods use small masks. The algorithm suggested here not only enhances and sharpens the edges of the image, but also makes it possible to use customized masks in Hilbert matrix and its inverse. Practical results show that this algorithm can be exploited in different fields such as angiography. The proposed method has been compared with sharpening method using Laplacin and Sobel operators.01/2010;

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