Shift And Rotation Invariant Object Reconstruction Using The Bispectrum

Triple correlations and their Fourier transforms, called bispectra, have properties desirable for image sequence analysis. Specifically, the triple correlation of a 2-d sequence is shift -invariant, it vanishes for a zero-mean colored Gaussian random field, and can be used to uniquely recover the original sequence to within a linear phase shift. An FFTbased algorithm for reconstructing a 2-d sequence from its bispectrum is reviewed and tested. The bispectrum is also applied to estimate a randomly translating and rotating object from a sequence of noisy images. The technique does not require solution of the correspondence problem, and is insensitive to additive colored Gaussian noise of unknown spectral density. Some simulation results for the random translation case are presented.