Forest point processes for the automatic extraction of networks in raster data

In this paper, we propose a new stochastic approach for the automatic detection of network structures in raster data. We represent a network as a set of trees with acyclic planar graphs. We embed this model in the probabilistic framework of spatial point processes and determine the most probable configuration of trees by stochastic sampling. That is, different configurations are constructed randomly by modifying the graph parameters and by adding or removing nodes and edges to/ from the current trees. Each configuration is evaluated based on the probabilities for these changes and an energy function describing the conformity with a predefined model. By using the Reversible jump Markov chain Monte Carlo sampler, an approximation of the global optimum of the energy function is iteratively reached. Although our main target application is the extraction of rivers and tidal channels in digital terrain models, experiments with other types of networks in images show the transferability to further applications. Qualitative and quantitative evaluations demonstrate the competitiveness of our approach with respect to existing algorithms.