Projection of magnetic flux tubes on a horizontal plane cutting the northern hemisphere of the Sun at z = 0.34 R_⋆ (with z being the height in cylindrical coordinates). Each point represents the projected position of the maximum entropy inside the flux tube in a given meridional plane. These points are supposed to map the center line of the magnetic flux tube. The radii of the dashed circles are a proxy for the curvature radii ℛ of the flux tubes at the apex. Panels a–d show suitable estimates of ℛ. Panels e and f show cases where the estimation fails.