Algorithmes basés sur les graphes pour la vision par ordinateur, l'apprentissage automatique et le traitement du signal
Jhony Heriberto Giraldo Zuluaga · theses.fr (ABES) · 2022
Graph representation learning and its applications have gained significant attention in recent years. Notably, Graph Neural Networks (GNNs) and Graph Signal Processing (GSP) have been extensively studied. GNNs extend the concepts of convolutional neural networks to non-Euclidean data modeled as graphs. Similarly, GSP extends the concepts of classical digital signal processing to signals supported on graphs. GNNs and GSP have numerous applications such as semi-supervised learning, point cloud semantic segmentation, prediction of individual relations in social networks, modeling proteins for drug discovery, image, and video processing.In this thesis, we propose novel approaches in video and image processing, GNNs, and recovery of time-varying graph signals. Our main motivation is to use the geometrical information that we can capture from the data to avoid data hungry methods, i.e., learning with minimal supervision. All our contributions rely heavily on the developments of GSP and spectral graph theory. In particular, the sampling and reconstruction theory of graph signals play a central role in this thesis. The main contributions of this thesis are summarized as follows: 1) we propose new algorithms for moving object segmentation using concepts of GSP and GNNs, 2) we propose a new algorithm for weakly-supervised semantic segmentation using hypergraph neural networks, 3) we propose and analyze GNNs using concepts from GSP and spectral graph theory, and 4) we introduce a novel algorithm based on the extension of a Sobolev smoothness function for the reconstruction of time-varying graph signals from discrete samples.