We describe the Mediatrix filamentation method, an iterative procedure that decomposes image shapes in filaments over their intensity ridgeline along their main direction using perpendicular bisectors. From this decomposition several morphological features can be derived, such as the length along the main direction and thickness of the object and, for curved objects, estimates of its center of curvature and curvature radius. As an example, we apply this technique to arc-shaped objects: simulated gravitational arcs.