Stochastic Geometry for Image Analysis

Chapter 8

Structure Extraction 1

In this chapter, we consider more structured object configurations. We look at cartographic applications, such as the extraction of a road network. A road is not represented by a single object but by a set of interacting segments. Likewise, we examine macro-textures, which are object textures consisting of a set of simpler geometrical objects. Consequently, the prior models that are defined are more complex and severely constrain the layout of the objects. In particular, we will see not only alignment constraints but also contact constraints between close objects. The defined energy landscape thus has very marked local minima. Also, optimization proves to be more complex than for the examples described in the preceding chapter. In this context, the selection of adapted transitions, within the framework of a reversible jump Monte Carlo Markov chain (MCMC) algorithm, is crucial. For example, we will find transitions involving birth of an object in the vicinity of an object of the current configuration, or transitions that involve the change of shape of an object. In addition, in population counting applications, the model trusts the data, while the prior primarily avoids overdetections. On the other hand, in this chapter, we are reunited with the Bayesian idea of a prior that compensates for the imperfections in the data, for example, by ensuring the connectivity of a road network, and forcing connections, even in the face of loss of local contrast ...