Locally Specified Polygonal Markov Fields for Image Segmentation

Abstract

We introduce a class of polygonal Markov fields driven by local activity functions. Whereas the local rather than global nature of the field specification ensures substantial additional flexibility for statistical applications in comparison to classical polygonal fields, we show that a number of simulation algorithms and graphical constructions, as developed in our previous joint work with M.N.M. van Lieshout and R. Kluszczynski, carry over to this more general framework. Moreover, we provide explicit formulae for the partition function of the model, which directly implies the availability of closed form expressions for the corresponding likelihood functions. Within the framework of this theory we develop an image segmentation algorithm based on Markovian optimization dynamics combining the simulated annealing ideas with those of Chen-style stochastic optimization, in which successive segmentation updates are carried out simultaneously with adaptive optimization of the local activity functions.