We propose a method for semantic image segmentation, combining a deep neural network and spatial relationships between image regions, encoded in a graph representation of the scene. Our proposal is based on inexact graph matching, formulated as a quadratic assignment problem applied to the output of the neural network. The proposed method is evaluated on a public dataset used for segmentation of images of faces and compared to the U-Net deep neural network that is widely used for semantic segmentation. Preliminary results show that our approach is promising. In terms of Intersection-over-Union of region bounding boxes, the improvement is of 2.4% in average, compared to U-Net, and up to 24.4% for some regions. Further improvements are observed when reducing the size of the training dataset (up to 8.5% in average).