Biomechanical Reconstruction with Confidence Intervals from Multiview Markerless Motion Capture

TL;DR

The paper tackles the lack of per-trial, camera-specific confidence intervals in multiview markerless motion capture by introducing a probabilistic, end-to-end framework that learns a posterior $q_\phi(\boldsymbol \theta_t)$ over biomechanical pose trajectories. It combines an implicit trajectory representation with a differentiable biomechanical forward model and a learnable keypoint likelihood, optimized via a variational ELBO, to produce tight, well-calibrated confidence intervals for joint angles and body positions. Extensive experiments on synthetic data and a large, heterogeneous human dataset demonstrate good calibration (low ECE) and realistic uncertainty patterns, including correlation structures between joints and sensitivity to camera geometry and occlusions. The approach enables identifying time segments with high uncertainty, supports clinical use and big-data movement analysis, and provides a principled framework for evaluating MMMC reliability across novel participants and camera configurations.

Abstract

Advances in multiview markerless motion capture (MMMC) promise high-quality movement analysis for clinical practice and research. While prior validation studies show MMMC performs well on average, they do not provide what is needed in clinical practice or for large-scale utilization of MMMC -- confidence intervals over specific kinematic estimates from a specific individual analyzed using a possibly unique camera configuration. We extend our previous work using an implicit representation of trajectories optimized end-to-end through a differentiable biomechanical model to learn the posterior probability distribution over pose given all the detected keypoints. This posterior probability is learned through a variational approximation and estimates confidence intervals for individual joints at each moment in a trial, showing confidence intervals generally within 10-15 mm of spatial error for virtual marker locations, consistent with our prior validation studies. Confidence intervals over joint angles are typically only a few degrees and widen for more distal joints. The posterior also models the correlation structure over joint angles, such as correlations between hip and pelvis angles. The confidence intervals estimated through this method allow us to identify times and trials where kinematic uncertainty is high.

Figures (8)

• Figure 1: Overview of our approach. Samples from the variational posterior distribution, $q_\phi(\boldsymbol \theta)$ is transformed by the biomechanical forward kinematic model, $\mathcal{M}_\beta$ and then projected through the camera model $\Pi_c$ to produce a predicted probability distribution over the keypoints, $p_\phi^{\mathbf Y^c}(\mathbf y^c|\boldsymbol \theta)$. The detected keypoints are evaluated by this likelihood function to optimize the ELBO.
• Figure 2: Influence of distribution rank. The left panel shows the distribution entropy relative to the 0-rank distribution. The middle shows the median value for the joint angle uncertainty, taken over time and joints. The right panel shows the $\mathrm{ECE}_0$ for the different ranks.
• Figure 3: Influence of artificially injected keypoint noise. The left panel shows the distribution entropy relative to the no-noise condition. The middle shows the median value for the joint angle uncertainty. The right panel shows $\psi_0$ for the different noise levels.
• Figure 4: The influence of removing cameras. The left panel shows the distribution entropy relative to the full camera complement. The middle shows the median value for the joint angle uncertainty. The right panel shows the median spatial error.
• Figure 5: The top row shows the 50th percentile spatial confidence interval for the body parts. The second row shows the 95th percentile confidence interval.