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). Similar to analytic signal, the 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 competing methods on real-world images consistently show the superiority of the proposed methods.