Image segmentation by polygonal Markov Fields

Mathematical Methods for Signal and Image Analysis and Representation

“…These were introduced a decade later in a series of our joint papers with M.N.M. van Lieshout and R. Kluszczynski [256,257,377,380,424] where a polygonal field optimization approach for image segmentation was advocated. Although these methods were quite succesful in global shape recognition, the problem we faced in that work was related to the lack of local parametrization tools designed to deal with intermediate scale image characteristics-even though the applied simulated annealing algorithm would eventually converge to the target polygonal segmentation, we were looking for a more efficient explicit mechanism to drive the local search.…”

“…Next, in Sects. 15.4 and 15.5 we develop a Markovian optimization dynamics for image segmentation, under which both the polygonal configuration and the underlying local activity function are subject to optimization-whereas the polygonal configuration evolves according to a simulated annealing scheme in the spirit of [256,257], the local activity function is initially chosen to reflect the image gradient information, whereupon it undergoes adaptive updates in the spirit of the celebrated Chen algorithm, see [73] and 10.2.4.c. in [333], with the activity profile reinforced along polygonal paths contributing to the improvement of the overall segmentation quality and faded along paths which deteriorate the segmentation quality.…”

An introduction to planar random tessellation models

“…The idea of using polygonal Markov field models for this purpose can be traced back to Clifford and Middleton (1989); see also Clifford and Nicholls (1994). Since the Monte Carlo methods employed at that time turned out to be rather onerous, the theme was not picked up again until the mid-2000s (Paskin and Thrun, 2005) when further theoretical results (Schreiber, 2005) motivated the development of conceptually and computationally easier algorithms (Kluszczyński et al, 2005(Kluszczyński et al, , 2007Schreiber and Lieshout, 2010;Lieshout, 2012). In the meantime, Voronoi (Green, 1995;Heikkinen and Arjas, 1998;Møller and Skare, 2001) and triangulation (Nicholls, 1998) models had also been tried.…”

Discrete Multicolour Random Mosaics with an Application to Network Extraction

“…Papers in this direction include those by Clifford & Middleton (), by Clifford & Nicholls (), by Kluszczyński et al. () and by Paskin & Thrun ().…”