Active cable/tendon-driven catheters are becoming an established part of the minimally invasive surgical procedures. Therefore, there has been growing interest in literature in estimating the shape of their distal end especially using clinical ultrasound (US) imaging systems. The purpose of this thesis is to use a B-mode US imaging system to design time-efficient, accurate and robust algorithm for 3D shape estimation of tendon-driven catheters. Kalman filter (KF), Adaptive Kalman filter
(AKF) and Particle filter (PF) algorithms were developed for this purpose. First, they were applied to a series of simulated US B-mode images where AKF provided the best estimate (error: 0.2 ± 0.1 mm). Second, they were applied to a series of experimentally obtained US B-mode images. Calibration procedures were carried out to calibrate these US images in the experiment’s workspace. The PF was shown to provide the best 3D shape estimate (error: 8.6 ± 0.1 mm). However, since
almost the same accuracy could be achieved with AKF in ten times less computational time, AKF was concluded to be the best method, in terms of accuracy and efficiency, to estimate the 3D shape of tendon-driven catheters.
Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach