Deep learning based pipelines for semantic segmentation often ignore structural information available on annotated images used for training. We propose a novel post-processing module enforcing structural knowledge about the objects of interest to improve segmentation results provided by deep neural networks (DNNs). This module corresponds to a “many-to-one-or-none” inexact graph matching approach, and is formulated as a quadratic assignment problem. Our approach is compared to a DNN-based segmentation on two public datasets, one for face segmentation from 2D RGB images (FASSEG), and the other for brain segmentation from 3D MRIs (IBSR). Evaluations are performed using two types of structural information: distances and directional relations that are user defined, this choice being a hyper-parameter of our proposed generic framework. On FASSEG data, results show that our module improves accuracy of the DNN by about 6.3% i.e. the Hausdorff distance (HD) decreases from 22.11 to 20.71 on average. With IBSR data, the improvement is of 51% better accuracy with HD decreasing from 11.01 to 5.4. Finally, our approach is shown to be resilient to small training datasets that often limit the performance of deep learning methods: the improvement increases as the size of the training dataset decreases.