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 two-dimensional (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.