Phase‐based edge detection algorithms

Abstract

Quaternion analytic signal is regarded as a generalization of analytic signal from 1D to 4D space. It is defined by an original signal with its quaternion partial and total Hilbert transforms. The quaternion analytic signal provides the signal features representation, such as the local amplitude and local phase angle, the latter includes the structural information of the original signal. The aim of the present study is twofold. Firstly, it attempts to analyze the Plemelj‐Sokhotzkis formula associated with quaternion Fourier transform and quaternion linear canonical transform. With these formulae, we show that the quaternion analytic signals are the boundary values of quaternion Hardy functions in the upper half space of 2 complex variables space. Secondly, the quaternion analytic signal can be extended to the quaternion Hardy function in the upper half space of 2 complex variables space. Two novel types of phase‐based edge detectors are proposed, namely, quaternion differential phase angle and quaternion differential phase congruency methods. In terms of peak signal‐to‐noise ratio and structural similarity index measure, comparisons with competing methods on real‐world images consistently show the superiority of the proposed methods.

A Robust Lane Detection Associated with Quaternion Hardy Filter

“…In order to mention the proposed method, some basic knowledge about quaternion algebra, 11 quaternion Fourier transform, 16,19 quaternion Hardy space, 8 Jin's gradient operator 21 and Hough transform 23 are reviewed as follows.…”

“…type of noises are necessary. Quaternion Hardy function 8 and Quaternion analytic signal 8 consist of Poisson and conjugate Poisson kernels. In 2016, Hu et al analyzed the Quaternion Hardy function 8 and Quaternion analytic signal 8 for edge detection problem.…”

“…Quaternion Hardy function 8 and Quaternion analytic signal 8 consist of Poisson and conjugate Poisson kernels. In 2016, Hu et al analyzed the Quaternion Hardy function 8 and Quaternion analytic signal 8 for edge detection problem. It was proved that these edge detectors has significant properties associated with Quaternion Fourier transform.…”

“…Quaternion analysis recently draws wide attention in color image processing. [8][9][10][11][12] The recently developed concepts of quaternion Fourier transform, [13][14][15][16][17] quaternion representation 10 and quaternion analytic signal, 8,9,18 which are based on quaternion algebra, have been found to be an indispensable tool in the representation of the multidimensional signal. In earlier 1992, Ell 19 studied the two-sided quaternion Fourier transform and apply it to the color image analysis.…”

“…In 2017, the quaternion analytic signal are studied and applied to edge detection. 8 The goal of this study is introducing a novel lane-mark extraction algorithm which can handle complex scenarios. Firstly, edge enhancement based on Quaternion Hardy filter 18 was used to enhance the pre-processing lane image's edges.…”