Joint Center Estimation Using Single-Frame Optimization: Part 1: Numerical Simulation

The biomechanical models used to refine and stabilize motion capture processes are almost invariably driven by joint center estimates, and any errors in joint center calculation carry over and can be compounded when calculating joint kinematics. Unfortunately, accurate determination of joint centers is a complex task, primarily due to measurements being contaminated by soft-tissue artifact (STA). This paper proposes a novel approach to joint center estimation implemented via sequential application of single-frame optimization (SFO). First, the method minimizes the variance of individual time frames’ joint center estimations via the developed variance minimization method to obtain accurate overall initial conditions. These initial conditions are used to stabilize an optimization-based linearization of human motion that determines a time-varying joint center estimation. In this manner, the complex and nonlinear behavior of human motion contaminated by STA can be captured as a continuous series of unique rigid-body realizations without requiring a complex analytical model to describe the behavior of STA. This article intends to offer proof of concept, and the presented method must be further developed before it can be reasonably applied to human motion. Numerical simulations were introduced to verify and substantiate the efficacy of the proposed methodology. When directly compared with a state-of-the-art inertial method, SFO reduced the error due to soft-tissue artifact in all cases by more than 45%. Instead of producing a single vector value to describe the joint center location during a motion capture trial as existing methods often do, the proposed method produced time-varying solutions that were highly correlated (r > 0.82) with the true, time-varying joint center solution.