Edge detection methods based on modified differential phase congruency of monogenic signal

Abstract

Monogenic signal is regarded as a generalization of analytic signal from one dimensional to higher dimensional space, which has been received considerable attention in the literature. It is defined by an original signal with its isotropic Hilbert transform (the combination of Riesz transform). Like the analytic signal, monogenic signal can be written in the polar form. Then it provides the signal features representation, such as the local attenuation and the local phase vector. The aim of the paper is twofold: first, to analyze the relationship between the local phase vector and the local attenuation in the higher dimensional spaces. Secondly, a study on image edge detection using modified differential phase congruency is presented. Comparisons with Preprint submitted to Multidimensional Systems and Signal Processing arXiv:1607.00097v2 [math.CA] 16 Dec 2016 competing methods on real-world images consistently show the superiority of the proposed methods.1. We give the solution of the problem: if the higher dimensional signal is not intrinsically 1D signal, we derive the relationship between the local phase-vector and and local attenuation.2. We proposed the local attenuation (LA) method for edge detection operator. We establish the theoretical and experiment results on the newly methods.3. We proposed the modified differential phase congruency (MDPC) method for the edge detection operator. We establish the theoretical and experiment results on the newly methods.4. We show that in higher dimensional space, the instantaneous frequency

Phase‐based edge detection algorithms

“…The second algorithm is called the QDPC method, which is motivated by the study of Felsberg et al Felsberg et al applied the scale derivative of the local phase angle of the 1D intrinsically monogenic scale function (Hardy function in the upper half complex plane) to obtain the DPC method for the edge detection problem, while Yang et al applied the scale derivative of the local phase vector (non 1D intrinsically monogenic scale function) …”

“…By calculating the scales partial derivatives of local phase angle θ (quaternion Hardy function), we propose the QDPC method, which is under the QFT and different from the DPC and MDPC algorithms …”

“…Due to its importance, the higher dimensional extensions of analytic signals are widely studied over the last century . For higher dimensional (>2D) case, the Clifford analysis is applied to generalize the analytic signal, which is called the monogenic signal. The 1D analytic signal is generalized to the 2D monogenic signal in previous studies .…”

“…For higher dimensional (>2D) case, the Clifford analysis is applied to generalize the analytic signal, which is called the monogenic signal. The 1D analytic signal is generalized to the 2D monogenic signal in previous studies . The monogenic scale space is the extension of (upper half or lower half) Hardy space in the higher dimension .…”

“…The 1D analytic signal is generalized to the 2D monogenic signal in previous studies . The monogenic scale space is the extension of (upper half or lower half) Hardy space in the higher dimension . The monogenic scale function provides the local features such as local phase vector and local attenuation in scale space, applications in edge detection are also developed …”