Context. Filaments host star formation and are fundamental structures of galaxies. Their diversity, as observed in the interstellar medium, from very low-density structures to very dense hubs, and their complex life cycles make their complete detection challenging over this large diversity range.Aims. Using 2D H2 column density images obtained as part of the Herschel Hi-GAL survey of the Galactic plane (Gp), we want to detect, simultaneously and using a single model, filaments over a large range of column density and contrast over the whole Gp. In particular, we target low-contrast and low-density structures that are particularly difficult to detect with classical algorithms.Methods. The whole H2 column density image of the Gp was subdivided into individual patches of 32 × 32 pixels. Following our proof of concept study aimed at exploring the potential of supervised learning for the detection of filaments, we propose an innovative supervised learning method based on adding information by encoding the position of these patches in the Gp. To allow the segmentation of the whole Gp, we introduced a random procedure that preserves the balance within the model training and testing datasets over the Gp plane. Four architectures and six models were tested and compared using different metrics.Results. For the first time, a segmentation of the whole Gp has been obtained using supervised deep learning. A comparison of the models based on metrics and astrophysical results shows that one of the architectures (PE-UNet-Latent), where the position encoding was done in the latent space gives the best performance to detect filaments over the whole range of density and contrast observed in the Gp. A normalized map of the whole Gp was also produced and reveals the highly filamentary structure of the Gp in all density regimes. We successfully tested the generalization of our best model by applying it to the 2D 12CO COHRS molecular data obtained on a 58.°8 portion (in longitude) of the plane.Conclusions. We demonstrate the interest of position encoding to allow the detection of filaments over the wide range of density and contrast observed in the Gp. The produced maps (both normalized and segmented) offer a unique opportunity for follow-up studies of the life cycle of Galactic filaments. The promising generalization possibility tested on a molecular dataset of the Gp opens new opportunities for systematic detection of filamentary structures in the big data context available for the Gp.