Reconstruction accuracy enhancement of fiber shape sensing by Kabsch-algorithm-based pose correction

Fiber-optic shape sensing is being actively developed for navigation in minimally invasive procedures, but reconstruction accuracy remains limited by both physical error sources and the reconstruction procedure itself. The four commonly used algorithms can achieve shape reconstruction including the Frenet-Serret frame (FS), the rotation minimizing frame (RMF), the helical extension method (HEM), and the transformation matrix method (TM). However, all four algorithms are based on the centerline by integrating local curvature and orientation along the fiber, in which small errors near the proximal end can accumulate and lead to larger deviations at the distal tip. In order to achieve high accuracy of the distal tip, we have theoretically compared the reconstruction accuracy and analyzed the noise robustness of the four reconstruction algorithms. In noise-free studies, TM algorithm can produce the smallest reconstruction errors compared with the FS, RMF, and HEM algorithms, showing great potential in the reliability of tip localization in clinical procedures. But when the strain noise and angular noise exist, the reconstruction accuracy of TM degrades, especially at high spatial resolution. To enhance the reconstruction accuracy, we have proposed Kabsch-algorithm-based pose correction that the principal axis direction of the shape reconstruction is corrected based on the minimum deviation of the proximal coordinate points. As a result, the relative accuracy enhancement of TM exceeds 35.7% under strain-spatial-resolution coupling noise and exceeds 37.8% and 42.7% under angular noises with 0.24° and 0.45° standard deviation, respectively. We have further investigated the reconstruction accuracy of complex path in minimally invasive procedures, e.g. brachial-artery-to-heart path. By utilization of TM algorithm with pose correction, the mathematical expectation of the mean shape reconstruction error in the presence of noise can be reduced from 1.25 mm to 0.90 mm, indicating the accuracy can be enhanced by 28%. Our obtained results provide a general guidance for selecting noise-robust reconstruction methods and show that Kabsch-algorithm-based pose correction offers a simple way to improve reconstruction accuracy for clinically relevant catheter paths.