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This paper presents a novel and domain-independent approach for graph-based structure learning. The approach is based on solving the maximum common subgraph-isomorphism problem to generalise a model graph over a set of training examples. Then a full probabilistic model is assigned to the learnt graph. We call this approach probabilistic structure graphs (PSGs). This article explains how PSG models are learnt and how probabilities for model instances are derived. It shows how to use PSG models to perform MAP classification, and presents evaluation of learnt models in the context of image understanding. Here, we classify observable object structures in the domain of building facade images (average classification rate Â¿ 80%). Additionally, we present encouraging results from interpreting facade images, where we detect instances of learnt models in a set of cluttered objects. We show that bottom-up scene interpretation based solely on learnt models seems achievable, without any hand-crafted domain knowledge.