  Monogenic signal is regarded as a generalization of analytic signal from the
one dimensional space to the high dimensional space. It is defined by an
original signal with the combination of Riesz transform. Then it provides the
signal features representation, such as the local attenuation and the local
phase vector. The main objective of this study is to analyze the local phase
vector and the local attenuation in the high dimensional spaces. The
differential phase congruency is applied for the edge detection problems.
