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Bayesian inference for vector-based images. (English) Zbl 0836.62024

Titterington, D. M. (ed.), Complex stochastic systems and engineering. Based on the proceedings of the IMA conference held at Leeds. UK, September 1993. Oxford: Clarendon Press, Inst. Math. Appl. Conf. Ser., New Ser. 54, 121-139 (1995).
Summary: Polygonal models form a new and promising family of distributions for image modeling, since objects of natural interest in images, such as \(I,V,T,Y\) and \(X\) vertices, edges and regions are random variables in the model, varying both in number and in type. Realizations of Polygonal models form mosaic patterns in a window of \({\mathfrak R}^2\), with regions bounded by straight lines and vertices. These patterns have a Markov property in the continuum.
We give an introduction to Polygonal models and then show how Bayesian image analysis can be carried out with such intermediate-level image variables. The Arak process is a particular instance of a Polygonal model: we explain how to move through the space of its allowed colourings via a triangulation of vertices, using Markov-chain Monte Carlo. In particular we give a set of moves which we believe to give irreducibility. We finish with an example, in which we extract the most probable legal edge and region structure in a noisy synthetic image.
For the entire collection see [Zbl 0827.00045].

MSC:

62F15 Bayesian inference
68U10 Computing methodologies for image processing
62P99 Applications of statistics
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