Synchronization involves the task of inferring unknown vertex values (belonging to a group) in a graph, from edges labeled with vertex relations. While many matrix groups (e.g., rotations or permutations) have received extensive attention in Computer Vision, a complete solution for projectivities is lacking. Only the \(3 \times 3\) case has been addressed so far, by mapping the problem onto the Special Linear Group, but the \(4 \times 4\) projective case has remained unexplored and is the focus here. We propose novel strategies to address this task, and demonstrate their effectiveness in synthetic experiments, as well as on an application to projective Structure from Motion.