We define a method for incorporating strong prior shape information into a recently extended Markov point process model for the extraction of arbitrarily-shaped objects from images. To estimate the optimal configuration of objects, the process is sampled using a Markov chain based on a stochastic birth-and-death process defined in a space of multiple objects. The single objects considered are defined by both the image data and the prior information in a way that controls the computational complexity of the estimation problem. The method is tested via experiments on a very high resolution aerial image of a scene composed of tree crowns.