In this project we studied the basics of Higher Order Spectra (HOS) and its application to texture modeling. Moments and Cumulants of higher order were defined. The Fourier transform of the 3rd order cumulant is denoted as the bispectrum. The main properties of HOS are
1. Detecting deviations from Gaussianity.
2. Extracting non-minimum phase information
3. Detecting and characterizing non-linearity

We defined and implemented the non-redundant region of the bispectrum and cumulant for 2-D signals  to reduce memory and computational requirements.

We modeled textures as linear, non-Gaussian random processes and verified the model properties using the properties of the bispectrum.
Most of the natural textures turned out to be linear, non-Gaussian and spatially irreversible. We implemented a method for the synthesis of textures using causal and non-causal AR filters in an efficient manner. The generated texutures had very good visual feel! Finally, we discussed a parameter estimation procedure for 2-D AR models and  evaluated its performance.

There was a very high cost in terms of memory and computation inspite of calculating only the non-redundant region of the bispectrum and cumulant. Although using HOS gives very good performance in many situations, we strongly feel that they are not suitable for real-time applications yet!

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last updated on 7th May 2000