This chapter addresses the fundamental task of semantic image analysis by exploiting structural information (spatial relationships between image regions). We propose to combine a deep neural network (DNN) with graph matching (formulated as a quadratic assignment problem (QAP)) where graphs encode efficiently structural information related to regions segmented by the DNN. Our novel approach solves the QAP sequentially for matching graphs, in the context of image semantic segmentation, where the optimal sequence for graph matching is conveniently defined using reinforcement learning (RL) based on the region membership probabilities produced by the DNN and their structural relationships. Our RL-based strategy for solving QAP sequentially allows us to significantly reduce the combinatorial complexity for graph matching. Two experiments are performed on two public datasets dedicated respectively to the semantic segmentation of face images and sub-cortical region of the brain. Results show that the proposed RL-based ordering performs better than using a random ordering, especially when using DNNs that have been trained on a limited number of samples. The open-source code and data are shared with the community.