Constrained stochastic state estimation of deformable 1D objects: Application to single-view 3D reconstruction of catheters with radio-opaque markers.

Minimally invasive fluoroscopy-based procedures are the gold standard for diagnosis and treatment of various pathologies of the cardiovascular system. This kind of procedures imply for the clinicians to infer the 3D shape of the device from 2D images, which is known to be an ill-posed problem. In this paper we present a method to reconstruct the 3D shape of the interventional device, with the aim of improving the navigation. The method combines a physics-based simulation with non-linear Bayesian filter. Whereas the physics-based model provides a prediction of the shape of the device navigating within the blood vessels (taking into account non-linear interactions between the catheter and the surrounding anatomy), an Unscented Kalman Filter is used to correct the navigation model using 2D image features as external observations. The proposed framework has been evaluated on both synthetic and real data, under different model parameterizations, filter parameters tuning and external observations data-sets. Comparing the reconstructed 3D shape with a known ground truth, for the synthetic data-set, we obtained average values for 3D Hausdorff Distance of 0.81±0.53mm, for the 3D mean distance at the segment of 0.37±0.17mm and an average 3D tip error of 0.24±0.13mm. For the real data-set,we obtained an average 3D Hausdorff distance of 1.74±0.77mm, a average 3D mean distance at the distal segment of 0.91±0.14mm, an average 3D error on the tip of 0.53±0.09mm. These results show the ability of our method to retrieve the 3D shape of the device, under a variety of filter parameterizations and challenging conditions: uncertainties on model parameterization, ambiguous views and non-linear complex phenomena such as stick and slip motions.