Small catheters undergo significant torsional deflections during endovascular interventions. A key challenge in enabling robot control of these catheters is the estimation of their bending planes. This paper considers approaches for estimating these bending planes based on bi-plane image feedback. The proposed approaches attempt to minimize error between either the direct (position-based) or instantaneous (velocity-based) kinematics with the reconstructed kinematics from bi-plane image feedback. A comparison between these methods is carried out on a setup using two cameras in lieu of a bi-plane fluoroscopy setup. The results show that the position-based approach is less susceptible to segmentation noise and works best when the segment is in a non-straight configuration. These results suggest that estimation of the bending planes can be accompanied with errors under 30°. Considering that the torsional buildup of these catheters can be more than 180°, we believe that this method can be used for catheter control with improved safety due to the reduction of this uncertainty.