Improving ultrasound-based bone registration using the iterative closest point algorithm paired with a complex optimization solver

The Iterative Close Point (ICP) algorithm is used for bone registrations based on ultrasound measurements. However, the ICP has been shown to suffer from local minima. The Complex optimization, as a more robust routine compared to the commonly used gradient-based algorithms, could be an alternative for solving the ICP problem. In this study, we investigated the effect of the initial estimate and the number of registration points on bone registrations achieved using the ICP and a Complex optimization routine and we compared it against using Quadratic Sequential Programming (SQP). Ultrasound measurements were performed with an A-mode probe on a bovine humerus and an ovine femur embedded into ballistic gel. Simultaneously, the bones and the probe were tracked in 3D space using retroreflective markers. Kinematic, ultrasound and geometrical data obtained from scans of the specimens and the probe served as input to a bone registrations routine. Registrations were performed using two ICP solvers for different initial estimates and number of registration points. On average, 68 % of the Complex optimization registrations had less than 1 mm translation error and less than 1° rotational error for perturbations of the initial estimate from the reference measurements compared to the 35 % of the SQP ones. Similar medians of registration errors were observed between the two methods for variations of the number of the employed registration points. Although the Complex optimization provided accurate bone registrations for all cases, the objective function could not always determine the registrations with the smallest registration error. Future research should explore methodologies to overcome this challenge.