American Institute of Mathematical Sciences

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

Parity symmetry in multi-dimensional signals

Gerald Sommer 1, and  Di Zang 1,

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.
Keywords: monogenic scale-space., Parity symmetry, local phase.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Gerald Sommer, Di Zang. Parity symmetry in multi-dimensional signals. Communications on Pure and Applied Analysis, 2007, 6 (3) : 829-852. doi: 10.3934/cpaa.2007.6.829
[1]

Claudio Meneses. Linear phase space deformations with angular momentum symmetry. Journal of Geometric Mechanics, 2019, 11 (1) : 45-58. doi: 10.3934/jgm.2019003
[2]

Matteo Negri. Crack propagation by a regularization of the principle of local symmetry. Discrete and Continuous Dynamical Systems - S, 2013, 6 (1) : 147-165. doi: 10.3934/dcdss.2013.6.147
[3]

Marcello D'Abbicco, Sandra Lucente. NLWE with a special scale invariant damping in odd space dimension. Conference Publications, 2015, 2015 (special) : 312-319. doi: 10.3934/proc.2015.0312
[4]

Fabrizio Colombo, Irene Sabadini, Frank Sommen. The Fueter primitive of biaxially monogenic functions. Communications on Pure and Applied Analysis, 2014, 13 (2) : 657-672. doi: 10.3934/cpaa.2014.13.657
[5]

Vladimir V. Kisil. Mobius transformations and monogenic functional calculus. Electronic Research Announcements, 1996, 2: 26-33.

[6]

Hebai Chen, Xingwu Chen, Jianhua Xie. Global phase portrait of a degenerate Bogdanov-Takens system with symmetry. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1273-1293. doi: 10.3934/dcdsb.2017062
[7]

Alberto Farina. Some symmetry results for entire solutions of an elliptic system arising in phase separation. Discrete and Continuous Dynamical Systems, 2014, 34 (6) : 2505-2511. doi: 10.3934/dcds.2014.34.2505
[8]

Hebai Chen, Xingwu Chen. Global phase portraits of a degenerate Bogdanov-Takens system with symmetry (Ⅱ). Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4141-4170. doi: 10.3934/dcdsb.2018130
[9]

Pavel Drábek, Stephen Robinson. Continua of local minimizers in a quasilinear model of phase transitions. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 163-172. doi: 10.3934/dcds.2013.33.163
[10]

Antonio Greco, Vincenzino Mascia. Non-local sublinear problems: Existence, comparison, and radial symmetry. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 503-519. doi: 10.3934/dcds.2019021
[11]

Ken Ono. Parity of the partition function. Electronic Research Announcements, 1995, 1: 35-42.

[12]

Thomas Y. Hou, Pengfei Liu. Optimal local multi-scale basis functions for linear elliptic equations with rough coefficients. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4451-4476. doi: 10.3934/dcds.2016.36.4451
[13]

Wen-ming He, Jun-zhi Cui. The estimate of the multi-scale homogenization method for Green's function on Sobolev space $W^{1,q}(\Omega)$. Communications on Pure and Applied Analysis, 2012, 11 (2) : 501-516. doi: 10.3934/cpaa.2012.11.501
[14]

Antonio Garijo, Armengol Gasull, Xavier Jarque. Local and global phase portrait of equation $\dot z=f(z)$. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 309-329. doi: 10.3934/dcds.2007.17.309
[15]

Mohamed Benyahia, Massimiliano D. Rosini. A macroscopic traffic model with phase transitions and local point constraints on the flow. Networks and Heterogeneous Media, 2017, 12 (2) : 297-317. doi: 10.3934/nhm.2017013
[16]

Stig-Olof Londen, Hana Petzeltová. Convergence of solutions of a non-local phase-field system. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 653-670. doi: 10.3934/dcdss.2011.4.653
[17]

Rogério Martins. One-dimensional attractor for a dissipative system with a cylindrical phase space. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 533-547. doi: 10.3934/dcds.2006.14.533
[18]

P. M. Jordan, Louis Fishman. Phase space and path integral approach to wave propagation modeling. Conference Publications, 2001, 2001 (Special) : 199-210. doi: 10.3934/proc.2001.2001.199
[19]

Oskar Weinberger, Peter Ashwin. From coupled networks of systems to networks of states in phase space. Discrete and Continuous Dynamical Systems - B, 2018, 23 (5) : 2021-2041. doi: 10.3934/dcdsb.2018193
[20]

Evgeny L. Korotyaev. Estimates for solutions of KDV on the phase space of periodic distributions in terms of action variables. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 219-225. doi: 10.3934/dcds.2011.30.219

2021 Impact Factor: 1.273

Tools

Metrics

  • PDF downloads (189)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy