SKEL Model: Biomechanics-Based 3D Body

• SKEL Model is a 3D human body representation that integrates a biomechanics-informed skeleton within the SMPL mesh to achieve anatomically valid joint positions.
• It uses bilevel optimization and regressor learning to accurately determine bone scales and joint orientations, reducing errors seen in conventional graphics models.
• The model upgrades existing pose datasets for applications in vision, biomechanics, and animation, supporting realistic motion analysis and simulation.

The SKEL model is a parametric 3D human body model that re-rigs the SMPL mesh with a biomechanics-informed internal skeleton. It is designed to yield biomechanically accurate joint locations, bone rotations, and movement degrees of freedom, establishing a more realistic substitute for commonly used graphics-oriented human models. SKEL enables anatomically valid posing “in the wild” and can upgrade existing pose and shape datasets for use in vision, graphics, and biomechanics applications (Keller et al., 8 Sep 2025).

1. Motivation and Definition

Body models like SMPL are widely adopted in vision and graphics but employ simplified kinematic trees and over-parametrized joints (72 degrees of freedom), which do not correspond to actual human joint mechanics. This misalignment limits their utility for scientific biomechanics, where exact joint locations and articulation ranges are crucial. SKEL resolves this by embedding a “biomechanics skeleton” (BSM) inside SMPL meshes, producing a parametric model matching real anatomical structure with physically correct joint limits and rotational axes. SKEL comprises:

• 24 bones with scaling parameters $s \in \mathbb{R}^{24 \times 3}$,
• 46 pose parameters $q$ representing movement (corresponding to real human degrees of freedom, e.g., 1 DoF for the knee),
• a full skin mesh (SMPL topology),
• a biomechanically correct kinematic tree for skeletal articulation.

2. Model Construction and Optimization

SKEL is built on a bilevel optimization combining the SMPL mesh and the BSM skeleton. The process includes:

• Virtual Markers: Synthetic “bony” and “soft” markers are attached to the SMPL mesh.
• Marker Fitting: Marker locations are transferred from OSSO skeleton predictions to the BSM template.
• Optimization: For each mesh and motion sequence (from AMASS), the bone scales $s$ and frame-wise poses $q_f$ are optimized to minimize a weighted sum of marker placement errors, plus biomechanical priors:

$$\min_{s, q_f} \sum_{f=1}^{N_F} \sum_{k=1}^{N_M} \lambda_k \| \mathrm{BSM}^{m}(s, q_f, m_0)_k - m_k \| + \lambda_p P(s,\ldots)$$

where $N_F$ is the number of frames, $N_M$ the number of markers, and $P(\cdot)$ is a prior over bone scale or pose.

• Bone Rotation Decomposition: Per-bone orientation is split into a shape-dependent corrective rotation and a learned base rotation:

$$R_i(q) = R_i^{\text{shape-dependent}}(q) \cdot R_i^{\text{base}}$$

where $R_i^{\text{base}}$ is averaged from training data, and the corrective term aligns the bone segment vector with anatomical directions.

This produces paired SMPL and BSM skeleton fits for over 9 hours of motion data across 113 subjects, yielding a training set of biomechanically accurate pose-shape pairs.

3. Regressor Learning and Reparametrization

To re-rig generic SMPL meshes with BSM skeletons, SKEL trains regressors that infer anatomical joint locations and bone orientations directly from mesh vertices:

• Joint Regressor: Learned via nonnegative least squares to predict anatomical joint positions from SMPL mesh points, reducing errors in critical joint localization (e.g., femur head).
• Bone Orientation Estimation: For each bone, a shape-dependent rotation aligns the anatomical segment (parent-child vector) and is combined with the learned base rotation.
• Skin Deformation: The mesh is posed via new skinning equations:

$$v(\beta, q) = \sum_{i=1}^{N_j} W_i^{\text{skin}} \cdot G_i^{\text{skin}}(\beta, q) \cdot (T + B_S[\beta] + B_P[q])$$

where $G_i^{\text{skin}}$ are chains of rigid bone transformations for skinning.

After reparametrization, SKEL preserves SMPL's shape space but uses a kinematic tree and joint positions derived from biomechanics for anatomically realistic posing.

4. Anatomical Validation and Comparison

Quantitative analysis shows that SKEL achieves superior biomechanical accuracy compared to standard SMPL:

• Joint Localization: The regressed joint locations (e.g., shoulders, femurs, knees) are closer to anatomical centers, reducing localization errors.
• Bone Fitting: The BSM skeleton fits entirely within the skin mesh across diverse shapes and poses, correcting issues with bone extrusion and misalignment.
• Reduced Degrees of Freedom: SKEL uses 46 pose parameters, reflecting actual human joint articulation, as opposed to the 72 unconstrained DoF in SMPL.
• Animation Validity: Advanced articulation is supported, such as scapula sliding along an ellipsoid model of the thorax and realistic pronation/supination of the forearm.

5. Data Augmentation and Upgrading Existing Datasets

Fitting SKEL to SMPL meshes in large datasets allows direct augmentation of vision benchmarks and motion capture collections:

• The paired BioAMASS dataset provides SMPL meshes with fitted biomechanical skeletons and motion parameters.
• Existing datasets using SMPL (e.g., 3DPW, BEDLAM) can be “upgraded” to include SKEL parameters, providing biomechanically valid pose and shape labels for training downstream models.

6. Practical Applications

SKEL extends the scope of human body modeling in several research and applied domains:

• Biomechanics: Enables in-the-wild pose estimation and kinematic analysis with anatomically valid joint positions for gait studies, injury prediction, and motion analysis.
• Computer Vision: Improves the accuracy of joint detectors by providing more realistic ground truth and enables training of models that penalize non-anatomical articulations.
• Graphics and Animation: Supports physically constrained rigging and character animation, producing plausible movements (e.g., correct flexion at the knee, proper rotation for the forearm).
• Simulation: Facilitates integration with musculoskeletal modeling platforms (e.g., OpenSim), supporting clinical and sports science research.

7. Availability

SKEL, along with the complete BioAMASS paired dataset, re-rigging code, and training scripts, is available for research purposes at https://skel.is.tue.mpg.de (Keller et al., 8 Sep 2025). These resources enable further development and evaluation of pose estimation, biomechanics, and digital human animation using anatomically sound models.