  Continuum robots have emerged as a promising technology in the medical field
due to their potential of accessing deep sited locations of the human body with
low surgical trauma. When deriving physics-based models for these robots,
evaluating the models poses a significant challenge due to the difficulty in
accurately measuring their intricate shapes. In this work, we present an
optimization based 3D shape registration algorithm for estimation of the
backbone shape of slender continuum robots as part of a pho togrammetric
measurement. Our approach to estimating the backbones optimally matches a
parametric three-dimensional curve to images of the robot. Since we incorporate
an iterative closest point algorithm into our method, we do not need prior
knowledge of the robots position within the respective images. In our
experiments with artificial and real images of a concentric tube continuum
robot, we found an average maximum deviation of the reconstruction from
simulation data of 0.665 mm and 0.939 mm from manual measurements. These
results show that our algorithm is well capable of producing high accuracy
positional data from images of continuum robots.
