In this paper, we study the application of models from stochastic geometry to the problem of image segmentation. The input is a grey-scale image and the desired output is a collection of geometric objects. Here, those objects are equilateral triangles. The considered priors are paire-wise interaction point processes used in stochastic geometry. They are chosen so that their realisations are close to partitions of the input image. We define an algorithm for their simulation which includes birth or death and geometric transformations of an object in the current configuration. Posterior mode solutions are studied by coupling this algorithm with a simulated annealing. This approach includes post-processing to merge objects of similar radiometry.