While the world of computer vision is constantly facing new challenges and moves towards more complex learning architectures, new research directions are investigating how to extend existing deep learning methods to new types of data. Geometric Deep Learning tackles the challenge to extend the most successful image-based deep learning methods, such as convolutional neural networks, to 3D shapes and graphs. Starting from the great potential of graph convolutional neural networks, the core idea of this thesis project is to tackle image-based tasks via graph-based deep learning methods. It requires to find a bridge that re-combines back the two worlds of images and graphs mapping the former into the latter.