This paper presents a method intended for the estimation of external force and moment applied at the tip of thin continuum robots using vision-based shape measurements. A versatile vision process that does not require any additional markers nor sensors provides an accurate 3D reconstruction of the deformable rod shape. Then, the tip loads are directly deduced from the curvature along this curve formed by deformed rod thanks to the resolution of a linear system without requiring any iterative optimization. The curvature is determined with a robust method that allows filtering out measurement noise and artefacts. Simulations show that this approach gives fast and precise results in both 2D (planar forces estimation without torsion) and 3D (spatial forces estimation). Experimental results on cantilever rods show an accuracy of 2.2% and 2.7% of the applied forces and moments, respectively.