A Reversible Jump MCMC Sampler for Object Detection in Image Processing

Abstract

To detect an unknown number of objects from high resolution images,we use spatial point processes models. The method is adapted to ourimage processingapplications since it describes images as realizations of a pointprocess whosepoints represent geometrical objects. We consider models made of twoparts: a dataterm which quantifies the relevance of a set of objects with respectto the image anda prior term, containing strong geometrical interactions between objects.We usethe Maximum A Posteriori estimator, which is obtained by combininga reversibleMarkov chain monte carlo (RJMCMC) point process sampler with a simulatedannealingprocedure. The quality of the results and the speed of the algorithmstronglydepend on the used sampler.We present here an adaptation of Geyer-M�llersamplerfor point processes and show that the resulting Markov Chain keepsthe requiredconvergence properties. In particular, we design an updating schemewhich allowsthe generation of points in the neighborhood of some others, and checkthe relevanceof such moves on a toy example. We present experimental results onthe difficultproblem of the detection of buildings in a Digital Elevation Modelof a dense urbanarea.