Globally Optimal Registration for Describing Joint Kinematics

Investigation of joint kinematics contributes to a better understanding of musculoskeletal condition pathologies. However, the most commonly used optoelectronic motion analysis systems cannot determine the movements of underlying bone landmarks with high accuracy because of soft tissue artifact. We are developing a computer-aided tracking and motion analysis with ultrasound (CAT & MAUS) system to track the underlying bone anatomy in a 3D global coordinate frame for describing joint kinematics. To quantify the rotation and translation of joints, registration is an essential component in our computer-aided tracking pipeline. In this paper, we consider a globally optimal Iterative Closest Point (ICP) registration algorithm to quantify joint kinematics. We use a global branch-and-bound (BnB) scheme to speed up the search in the entire 3D motion space. A globally optimal result is guaranteed by iterating the BnB scheme and ICP registration. We collected phantom data for validation and in-vivo data from ten healthy volunteers. The globally optimal ICP registration results have been compared to the results from traditional ICP registration. The overall average rotation angle error is less than 1̊. The registration result is then converted into local joint coordinate systems defined by the International Society of Biomechanics for joint kinematics description. The results from globally optimal registration defined a general hip joint kinematics model of healthy subjects during gait which can be compared as a reference to the results from subjects with hip joint conditions.