Biomechanical Angle Estimation
A pose-to-kinematics framework that transforms 3D joint positions from markerless pose estimation into clinically relevant, ISB-standard biomechanical joint angles using a transformer-based mapping architecture.
3D Pose to Biomechanical Angle Representation
Wang J.
Skeleton to joint angle conversion
Overview
Current markerless 3D pose estimation models predict joint positions optimized for spatial metrics like MPJPE, but these do not guarantee biomechanical validity — two poses with similar position errors may imply very different joint-angle configurations. This work develops a pose-to-biomechanical angle conversion algorithm that transforms estimated 3D joint positions into clinically relevant joint angles following ISB standards. Using a transformer-based architecture, the framework supports both elementary angles (elbow and knee flexion) and multi-planar joint angles at the hip and shoulder, bridging the gap between computer vision and biomechanics for applications in sports performance, ergonomics, rehabilitation, and clinical monitoring.
Abstract
Background
Joint angles provide a standardized and interpretable description of human movement that is invariant to body size, anthropometric variability, and camera perspective. Traditional biomechanics relies on joint angle trajectories to evaluate performance, injury mechanisms, and rehabilitation progress. However, current markerless 3D pose estimation models predict joint positions — not joint rotations — and are optimized using spatial metrics that do not guarantee biomechanical validity.
Problem
Two poses with similar Mean Per Joint Position Error (MPJPE) may imply very different joint-angle configurations, some of which may be anatomically implausible. The difficulty varies across joints: simple hinge joints like the elbow have one rotational degree of freedom, while multi-axial joints like the hip and shoulder exhibit three degrees of freedom where small positional errors propagate nonlinearly during angle estimation.
Methods
We develop a transformer-based pose-to-kinematics mapping model that learns the nonlinear relationship between 3D joint positions and anatomical joint angles. Ground-truth angles are derived from motion capture markers following ISB standards using Cardan XYZ rotation sequences. All poses are standardized via root-joint alignment and limb-scale normalization. The framework is validated on Human3.6M (~3.6M frames) and AthletePose3D (~1.2M frames) datasets.
Outputs
The model produces four continuous joint-angle variables: shoulder flexion/extension, hip flexion/extension, elbow flexion, and knee flexion. These angles capture the primary degrees of freedom contributing to gross limb motion and functional biomechanics, enabling standardized comparison across individuals and integration with clinical analysis workflows.
Impact
By enabling joint-angle computation from markerless pose data, this framework bridges the gap between human pose estimation and biomechanics. A proposed extension incorporates joint-angle consistency loss directly into 2D-to-3D lifting model training, producing 3D poses that are both spatially accurate and biomechanically plausible — laying the groundwork for real-time movement assessment in sports, ergonomics, and rehabilitation.
Challenges
- 1Position-based metrics (MPJPE) do not guarantee biomechanically valid joint configurations
- 2Multi-axial joints (hip, shoulder) have three rotational degrees of freedom with nonlinear error propagation
- 3Pose estimation skeletons differ structurally from biomechanical models
- 4Limited documentation of rotation conventions in existing datasets like Human3.6M
Methodology
The framework transforms estimated 3D joint positions into clinically relevant biomechanical angles through a multi-stage pipeline encompassing dataset preparation, ground-truth computation, model training, and biomechanical benchmarking.
Dataset Description
Two datasets are utilized. Human3.6M provides ~3.6 million frames of synchronized RGB video and 3D pose data from four calibrated cameras, with ground-truth via marker-based motion capture. AthletePose3D contains ~1.2 million frames with millimeter-level marker trajectories and includes both marker-based and Human3.6M-style skeleton representations, enabling direct comparison between spatial accuracy and kinematic validity.
Ground Truth Joint Kinematic Computation
Ground-truth joint angles are derived from motion capture marker trajectories following International Society of Biomechanics (ISB) standards. Segment coordinate systems are defined for the pelvis, thigh, shank, upper arm, and forearm. Rotation matrices between adjacent segments are resolved using a Cardan XYZ rotation sequence corresponding to flexion/extension, abduction/adduction, and internal/external rotation.
Pose-Kinematics Mapping Model
A transformer-based architecture maps standardized 3D joint coordinates to anatomical joint angles, leveraging its capacity to model long-range spatial dependencies and inter-joint correlations across the full skeleton. The input is normalized by root joint position and limb-scale factors to remove translational and anthropometric variability. The output consists of four continuous joint-angle variables: shoulder flexion/extension, hip flexion/extension, elbow flexion, and knee flexion.
Data Standardization and Preprocessing
All poses are translated by aligning the root joint to the origin and scaled to unit limb length. Frames with less than 95% marker visibility are removed. 3D joint coordinates are temporally smoothed using a 4th-order low-pass Butterworth filter with a 6 Hz cutoff frequency to suppress high-frequency noise while maintaining biomechanical fidelity.
Evaluation Metrics
Model performance is assessed using Root Mean Square Error (RMSE) between predicted and ground-truth ISB-derived joint angles, computed independently for each joint. Supplementary analyses evaluate robustness across pose distributions and identify bias related to joint visibility, occlusions, and camera viewpoint.
Benchmarking State-of-the-Art Models
State-of-the-art 3D pose estimation algorithms are benchmarked by converting their predicted joint coordinates into anatomical angles via the inverse kinematics procedure. Estimated angles are compared against ISB-derived ground truth using RMSE and Pearson correlation, extending evaluation beyond MPJPE to directly assess biomechanical validity.
Biomechanically-Constrained 2D-to-3D Lifting
A planned extension incorporates biomechanical constraints directly into 2D-to-3D lifting model training. A joint-angle consistency loss regularizes estimated 3D poses toward anatomically valid configurations. The total loss combines standard positional loss with a weighted kinematic term, guiding the model toward poses that respect natural joint coupling and physiological range-of-motion limits.
Approach
- 1Developed transformer-based pose-to-kinematics mapping from 3D joint positions to ISB-standard joint angles
- 2Computed ground-truth angles from motion capture markers using ISB anatomical coordinate systems and Cardan XYZ decomposition
- 3Standardized poses via root-joint alignment and limb-scale normalization to remove anthropometric variability
- 4Benchmarked state-of-the-art pose estimators on biomechanical fidelity, not just spatial accuracy
Results & Demos
Joint angle visualization
Comparison with ground truth
Findings
The evaluation framework reveals critical gaps between spatial accuracy and biomechanical validity in current pose estimation systems, and establishes the foundation for anatomy-aware model training.
Position vs. Angle Accuracy Gap
Analysis demonstrates that models achieving competitive MPJPE scores can produce substantially different joint-angle configurations. This gap is most pronounced at multi-axial joints (shoulder, hip), where three rotational degrees of freedom amplify small positional errors into large angular discrepancies. The finding confirms that MPJPE alone is insufficient for biomechanical applications.
Joint-Specific Error Patterns
Error analysis across joints reveals systematic patterns: hinge joints (elbow, knee) with a single primary degree of freedom show consistently lower RMSE, while ball-and-socket joints (shoulder, hip) exhibit higher and more variable errors. Shoulder flexion/extension is particularly challenging due to the complex interplay between glenohumeral and scapulothoracic motion.
Biomechanical Benchmarking
Benchmarking state-of-the-art pose estimators on kinematic accuracy — rather than just spatial metrics — provides a more rigorous assessment of model suitability for clinical and sports applications. Models that rank similarly on MPJPE can diverge substantially when evaluated on joint-angle fidelity, highlighting the need for biomechanics-aware evaluation protocols.
Constrained Loss Function
The proposed biomechanically-constrained training objective combines standard positional loss with a joint-angle consistency loss: L_total = L_pos + λ_ang · L_ang. By incorporating anatomical constraints into the lifting model's training objective, the framework guides 3D reconstruction toward physiologically plausible configurations, reducing anatomically implausible predictions even when spatial alignment remains strong.
Key Outcomes
- Enabled computation of shoulder and hip flexion/extension, elbow flexion, and knee flexion from markerless pose data
- Demonstrated that MPJPE alone is insufficient for evaluating biomechanical validity
- Established a benchmarking framework for assessing kinematic accuracy of pose estimation models
- Proposed biomechanically-constrained loss function for training anatomy-aware 3D lifting models
Discussion
This work addresses a fundamental gap between computer vision and biomechanics, with implications for both research methodology and practical applications.
Beyond Spatial Metrics
The dominance of MPJPE as the primary evaluation metric in pose estimation has created a blind spot: models are optimized for spatial accuracy without regard for biomechanical plausibility. By introducing joint-angle evaluation as a complementary metric, this work advocates for a paradigm shift in how pose estimation models are assessed — particularly for applications where the clinical interpretation of motion depends on angular, not positional, accuracy.
Two-Stage Training Framework
The proposed two-stage pipeline — a pretrained pose-to-kinematics mapping module followed by a constrained lifting model — offers a practical path toward biomechanics-aware pose estimation. The pretrained mapping module (f_φ) converts 3D poses to ISB-compliant angles, while the lifting model (g_ψ) is trained with both positional and kinematic losses. This modular design allows the kinematic constraint to be applied to any existing lifting architecture without modifying its core structure.
Clinical and Applied Implications
Accurate markerless joint-angle estimation opens pathways for real-time movement assessment outside of laboratory settings. In sports performance, it enables automated technique analysis from standard video. In rehabilitation, it allows remote monitoring of recovery trajectories through joint range-of-motion tracking. In ergonomics, it supports continuous workplace posture assessment without instrumentation. The ISB-standard output ensures compatibility with existing clinical workflows and normative databases.