# American Institute of Mathematical Sciences

September  2007, 6(3): 829-852. doi: 10.3934/cpaa.2007.6.829

## Parity symmetry in multi-dimensional signals

 1 Institute of Computer Science, Christian-Albrechts-University, 24118, Kiel, Germany, Germany

Received  February 2006 Revised  June 2006 Published  June 2007

Parity symmetry is an important local feature for qualitative signal analysis. It is strongly related to the local phase of the signal. In image processing parity symmetry is a cue for the line-like or edge-like quality of a local image structure. The analytic signal is a well-known representation for 1D signals, which enables the extraction of local spectral representations as amplitude and phase. Its representation domain is that of the complex numbers. We will give an overview how the analytic signal can be generalized to the monogenic signal in the $n$D case within a Clifford valued domain. The approach is based on the Riesz transform as a generalization of the Hilbert transform with respect to the embedding dimension of the structure. So far we realized the extension to 2D and 3D signals. We learned to take advantage of interesting effects of the proposed generalization as the simultaneous estimation of the local amplitude, phase and orientation, and of image analysis in the monogenic scale-space.
Citation: Gerald Sommer, Di Zang. Parity symmetry in multi-dimensional signals. Communications on Pure & Applied Analysis, 2007, 6 (3) : 829-852. doi: 10.3934/cpaa.2007.6.829
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