Dynamic trees for image modelling

Abstract

This paper introduces a new class of image model which we call dynamic trees or DTs. A dynamic tree model specifies a prior over structures of trees, each of which is a forest of one or more tree-structured belief networks (TSBN). In the literature standard tree-structured belief network models have been found to produce "blocky" segmentations when naturally occurring boundaries within an image did not coincide with those of the subtrees in the rigid fixed structure of the network. Dynamic trees have a flexible architecture which allows the structure to vary to create configurations where the subtree and image boundaries align, and experimentation with the model has shown significant improvements.For large models the number of tree configurations quickly becomes intractable to enumerate over, presenting a problem for exact inference. Techniques such as Gibbs sampling over trees and search using simulated annealing have been considered, but a variational approximation based upon mean field was found to work faster while still producing a good approximation to the true model probability distribution. We look briefly at this mean field approximation before deriving an EM-style update based upon mean field inference for learning the parameters of the dynamic tree model. 0 To whom correspondence should be addressed.

Describing Visual Scenes Using Transformed Objects and Parts

“…Grammars, and related rule-based systems, provide one flexible family of hierarchical representations (Tenenbaum and Barrow 1977;Bienenstock et al 1997). For example, several different models impose distributions on hierarchical tree-structured segmentations of the pixels composing simple scenes (Adams and Williams 2003;Storkey and Williams 2003;Siskind et al 2004;Hinton et al 2000;Jin and Geman 2006). In addition, an image parsing (Tu et al 2005) framework has been proposed which explains an image using a set of regions generated by generic or object-specific processes.…”

Soft Mixer Assignment in a Hierarchical Generative Model of Natural Scene Statistics

“…Although the proposed model is more complex than the original GSM, in fact we show that inference is straightforward using standard tools of expectation maximization (Dempster, Laird, & Rubin, 1977) and Markov chain Monte Carlo sampling. Closely related assignment problems have been posed and solved using similar techniques, in a different class of image model known as dynamical tree modeling (Williams & Adams, 1999;Adams & Williams, 2003) and in credibility networks (Hinton, Ghahramani, & Teh, 1999).…”

“…Williams and Adams (1999) suggested using Gibbs sampling to solve a similar assignment problem in the context of dynamic tree models. Variational approximations have also been considered in this context (Adams & Williams, 2003;Hinton et al, 1999).…”

Wavelet-based decomposition and analysis of structural patterns in astronomical images

“…Djamdji et al 1993;Zheng & Chellappa 1993;Adams & Williams 2003;Zitová & Flusser 2003;Paulson et al 2010). Structural patterns observed in astronomical images often do not have a defined or even preferred shape, which is an aspect relied upon in a number of the existing object recognition algorithms (e.g., Agarwal et al 2003).…”