  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 degrees. Considering that the torsional
buildup of these catheters can be more than 180 degrees, we believe that this
method can be used for catheter control with improved safety due to the
reduction of this uncertainty.
