Edge feature enhancement approach using hilbert transform of Cauchy distribution and its applications

Abstract

Building on past work showing that the Hilbert transform can be used for edge feature enhancement, a new edge feature enhancement method is developed using a twodimensional (2D) isotropic Hilbert transform of the Cauchy distribution. First, both the shape of the Hilbert kernel and the Hilbert transform of edge feature models (step and delta) and various simulated signals result in edge feature enhancement, the properties of which are derived and confirmed. Second, Cauchy distribution as low-pass filter is introduced in Hilbert transform to get new edge feature enhancement operator, and its efficiency under various criteria is comprehensively discussed. Third, a 2D isotropic extension is presented using a circularly symmetric window function. Finally, two experiments, including edge detection and image segmentation, are performed to validate the proposed edge feature enhancement method. The experimental results of the method applied to the Berkeley Segmentation Dataset and remote sensing images demonstrate that the new method is effective for edge detection and image segmentation. INTRODUCTIONEdges are important features in images and provide prominent information about objects in the natural scenes, while edge strength is essential to computer vision, image processing, and pattern recognition, especially directly edge detection, contour detection, and image segmentation. Its applications benefit many fields, including image segmentation [1-3], object recognition[4], remote sensing [5,6], medical imaging [7-9], 3D reconstruction [10], face recognition [11,12], and image retrieval [11,13]. In the past several decades, various edge feature enhancement approaches have been proposed, including gradient-based methods [14][15][16], morphology gradient methods [17,18], logicbased methods [19], machine learning methods [2,20,21], local energy [22,23], and phase congruency [24,25]. Though considerable progress has been made regarding the efficiency of edge feature enhancement, there is still a challenge, particularly obtaining more efficient edge strength for further application.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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