Title :
A new class of shift-invariant operators
Author_Institution :
Machine Vision Group, Univ. of Oulu, Finland
fDate :
6/1/2004 12:00:00 AM
Abstract :
This letter proposes a class of operators with a shift invariance property. These operators are derived from two-dimensional (2-D) complex moment invariants based on the observation that there is a duality between rotation invariance and shift invariance. A general form of the shift invariants belonging to this class is presented, which shows that polyspectral invariants such as the power spectrum and the bispectrum are members of the class. Methods for computing shift invariants for one-dimensional (1-D) and 2-D signals are also presented. The examples given in the paper suggest that the higher order operators can preserve the original signal waveform better than autocorrelation.
Keywords :
discrete Fourier transforms; invariance; mathematical operators; multidimensional signal processing; spectral analysis; bispectrum; discrete Fourier transform; higher order operator; pattern recognition; polyspectral invariants; power spectrum; rotation invariance; shift invariance property; translation invariance; two-dimensional complex moment invariant; Autocorrelation; Delay; Discrete Fourier transforms; Equations; Fourier transforms; Higher order statistics; Prototypes; Signal analysis; Signal processing; Two dimensional displays; Bispectrum; discrete Fourier transform; moment invariants; power spectrum; translation invariance;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2004.827915