Connectionists: Paper: Varying complexity in image models

[CLAY SPENCE]

The following paper appeared in the Feb. 2006 issue of IEEE Trans. on 
Image Proc., Vol. 15, No. 2, pp. 319-330. It's also available at 
http://liinc.bme.columbia.edu/publications/hip-tip.pdf.

> Varying Complexity in Tree-Structured Image Distribution Models
> Clay Spence, Lucas Parra, and Paul Sajda
>
> Abstract
>
> Probabilistic models of image statistics underlie many approaches in
> image analysis and processing. An important class of such models have
> variables whose dependency graph is a tree. If the hidden variables
> take values on a finite set, most computations with the model can be
> performed exactly, including the likelihood calculation, training with
> the EM algorithm, etc.  Crouse, et al developed one such model, the
> Hidden Markov Tree (HMT). They took particular care to limit the
> complexity of their model.  We argue that it is beneficial to allow
> more complex tree-structured models, describe the use of information
> theoretic penalties to choose the model complexity, and present
> experimental results to support these proposals. For these experiments
> we use what we call the hierarchical image probability (HIP)
> model. The differences between the HIP and the HMT models include the
> use of multi-variate Gaussians to model the distributions of local
> vectors of wavelet coefficients and the use of different numbers of
> hidden states at each resolution. We demonstrate the broad utility of
> image distributions by applying the HIP model to classification,
> synthesis, and compression, across a variety of image types, namely,
> electro-optical (EO), synthetic aperture radar (SAR), and mammograms
> (digitized x-rays).  In all cases we compare with the HMT.
>
> Keywords: image model, hidden Markov tree, Bayesian network, minimum
> description length, hidden variables, classification, synthesis,
> compression, tree-structured belief network
Clay Spence