In this paper we present an algorithm for creating region-adjacency-graph (RAG) pyramids on TurboNet, an experimental parallel computer system. Each level of these hierarchies of irregular tessellations is generated by independent stochastic processes that adapt the structure of the pyramid to the content of the image. RAGs can be used in multiresolution image analysis to extract connected components from labeled images. The implementation of the algorithm is discussed and performance results are presented for three different communication techniques which are supported by the TurboNet's hybrid architecture. The results indicate that efficient communications are vital to good performance of the algorithm.