Nowadays, large collections of photos are tagged with GPS coordinates. The modelling of such large geo-tagged corpora is an important problem in data mining and information retrieval, and involves the use of geographical information to detect topics with a spatial component. In this paper, we propose a novel geographical topic model which captures dependencies between geographical regions to support the detection of topics with complex, non-Gaussian distributed spatial structures. The model is based on a multi-Dirichlet process (MDP), a novel generalisation of the hierarchical Dirichlet process extended to support multiple base distributions. Our method thus is called the MDP-based geographical topic model (MGTM). We show how to use a MDP to dynamically smooth topic distributions between groups of spatially adjacent documents. In systematic quantitative and qualitative evaluations using independent datasets from prior related work, we show that such a model can exploit the adjacency of regions and leads to a significant improvement in the quality of topics compared to the state of the art in geographical topic modelling.