Bayesian Comparison of Models for Images
A H Barnett and David J C MacKay
Probabilistic models for images are analysed quantitatively
using Bayesian hypothesis comparison on a set of image
data sets. One motivation for this study is to produce models which can be used as
better {\em priors} in image reconstruction problems.
The types of model vary from the simplest, where spatial
correlations in the image are irrelevant, to more complicated
ones based on a radial power law for the standard deviations
of the coefficients produced by Fourier or Wavelet
Transforms. In our experiments the Fourier
model is the most successful, as its {\em evidence} is
conclusively the highest. This ties in with the statistical scaling self-similarity (fractal property)
of many images. We discuss the invariances of the models,
and make suggestions for further investigations.
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