Source-linked AI summary
Automatic Joint Parameter Estimation from Magnetic Motion Capture Data
James F. O'Brien, Robert E. Bodenheimer, Gabriel J. Brostow, Jessica K. Hodgins
TL;DR
The paper tackles the need to calibrate articulated motion-capture models without tedious external measurements. It fits rotary-joint parameters to magnetic motion data and recovers hierarchy structure when topology is unknown, achieving sensor-resolution accuracy on a mechanical linkage and biomechanics-consistent accuracy on human data.
Problem
Manual calibration requires measuring limb lengths and sensor offsets, which is tedious, error-prone, and impractical in some capture applications.
Method
The method fits a rotary-joint model to magnetic motion data, estimates joint and sensor parameters, and constructs a spanning-tree hierarchy from pairwise joint-fit residuals.
Results
The method achieves sensor-resolution accuracy on a mechanical rotary-joint device, while human-data accuracy is consistent with biomechanics-based error estimates.
Takeaways & Limitations
The technique provides rapid automatic calibration for magnetic motion-capture systems and can identify marker slippage through large changes in joint residuals.
Takeaways & Limitations
When a joint rotates about only one axis, its center is not uniquely determined; unknown hierarchies are also assumed to be strict trees without loop joints.
Abstract
from arXiv · showhide
This paper describes a technique for using magnetic motion capture data to determine the joint parameters of an articulated hierarchy. This technique makes it possible to determine limb lengths, joint locations, and sensor placement for a human subject without external measurements. Instead, the joint parameters are inferred with high accuracy from the motion data acquired during the capture session. The parameters are computed by performing a linear least squares fit of a rotary joint model to the input data. A hierarchical structure for the articulated model can also be determined in situations where the topology of the model is not known. Once the system topology and joint parameters have been recovered, the resulting model can be used to perform forward and inverse kinematic procedures. We present the results of using the algorithm on human motion capture data, as well as validation results obtained with data from a simulation and a wooden linkage of known dimensions.
1 Introduction
The paper addresses tedious, error-prone calibration in magnetic motion capture by inferring joint locations and sensor relationships directly from captured motion. Its rotary-joint fitting approach can also recover an articulated hierarchy when topology is unknown.
- Motion capture preserves performers’ characteristic style and supports rapid generation of human-like animation for training and entertainment applications.
- Manual measurements of limb lengths and sensor-to-joint offsets are tedious, error-prone, and impractical when calibration must avoid technician contact.
- The algorithm computes articulated joint locations from global transformation matrices of individual bodies using magnetic motion data.
- It determines relative sensor locations without external measurement, without constraining sensor positions or requiring particular subject configurations.
- The data must exercise all joint degrees of freedom for the technique to return an unambiguous answer.
- For sensor pairs spanning a rotary joint, the method fits collocated points across transformation sequences and computes residual error under noise and non-ideal joint motion.
- When topology is unknown, joint residuals serve as edge weights for constructing a spanning tree over body parts.
- The paper evaluates the method on human motion capture data and validates it with simulation and a wooden linkage of known dimensions.
2 Background
The background distinguishes this method from related optical, biomechanical, and robotic calibration approaches. The paper targets animation models that need joint centers approximating motion over an entire sequence rather than instantaneous biomechanical centers.
- Related graphics work includes identifying anatomic skeletons from optical motion capture data.
- Inverse kinematics extracts joint angles from global position data, whereas this paper estimates the skeleton dimensions and joint parameters needed by such procedures.
- Biomechanics studies instantaneous centers of rotation, defined as points of zero velocity during infinitesimally small rigid-body motions.
- Biomechanicists estimate rotation centers from markers placed on limbs across multiple configurations, often using redundant markers and least-squares fitting.
- For animation, the required joint center is a reasonable approximation over an entire motion sequence because the target skeleton uses simple rotary joints.
- Human-joint and skin-motion variability limits accuracy: knee-center movement during walking averaged 7 mm compression, 14.3 mm front-to-back, and 5.6 mm side-to-side, while tibial skin movement reached 3 cm during running.
- Robotic calibration methods may require isolated joint actions or particular configurations, making them difficult to adapt to human performers.
3 Methods
The method models articulated bodies with time-varying transformations and rotary-joint constraints, then estimates joint locations by fitting those constraints across motion frames. It can also detect single-axis ambiguities and infer an unknown body hierarchy from joint-fit errors.
- Transformation model: Each body transformation comprises a translation vector and a 3 × 3 rotational matrix, with transformations sampled across discrete motion frames.The global transformation T i→ω maps a body coordinate system to world coordinates.
- Hierarchy representation: An articulated hierarchy is a rooted tree whose geometry specifies each joint in both its outboard and inboard body coordinate frames.The joint locations are represented by ci for body i and li for its parent P(i).
- Rotary-joint constraint: For connected rotary-joint bodies, the corresponding joint points must transform to the same world location at every frame, enforcing that the joint stays together.This replaces an unconstrained translational term with a rotation-dependent expression involving the joint locations.
- Parameter estimation: Joint parameters are solved from an assembled linear system across frames; because measurement errors prevent exact fits, the method uses a best-fit solution.The system solves for ci and li and is generally over-constrained except with only two motion frames.
- Single-axis joints: Single-axis motion leaves the joint center non-unique, while near-zero singular values of bQ identify this rank-deficient case and expose the joint axis in both frames.Any point along a single rotation axis fits equally well, so the SVD solution is essentially arbitrary on that axis.
- Hierarchy inference: When topology is unknown, the algorithm selects the parent function by minimizing joint-fit errors, equivalent to constructing a minimal spanning tree over bodies.Bodies are nodes, joints are edges, and each joint-fit error εi is an edge weight.
4 Results
The algorithm was validated on simulated data, a wooden linkage, and human motion-capture data, recovering hierarchies and limb parameters with varying accuracy. Mechanical-linkage errors were near sensor resolution, while human results were less precise because biological joints depart from the rotary-joint model.
- Simulation: Errors were less than 10^-6 m in simulated limb lengths, and the algorithm determined the correct hierarchy.The simulation contained 48 degrees of freedom, all exercised during movement.
- Mechanical linkage: The wooden linkage produced a maximum error of 1.1 cm across six trials, with the hierarchy computed correctly for every trial.Set 6 changed marker positions to test robustness.
- Mechanical linkage: Residual errors for the mechanical linkage were on the order of sensor resolution, indicating very good fits for the best and worst shoulder trials.Figures 6 and 7 show residual-vector norms for Set 1 right shoulder and Set 6 left shoulder data.
- Human subjects: 4.1 cm was the maximum difference between measured and calculated human limb lengths for the male subject, occurring at the left upper arm.Mean differences were below one centimeter for every limb except the upper arms, which measured 1.4 cm and 2.2 cm on the right and left, respectively.
- Human subjects: 2.4 cm was the largest calculated-versus-measured difference for the female subject, again at the left upper arm.Mean differences exceeded one centimeter for the right lower leg, left upper leg, and left upper arm.
- Hierarchy recovery: The hierarchy was correct for all exercise trials, but three of five walk trials incorrectly assigned one upper leg as a child of the other rather than the pelvis.The walk data produced less satisfactory hierarchy results than the exercise data.
5 Discussion and Conclusions
The method estimates motion-capture model parameters automatically and supports calibration, performer-specific modeling, hierarchy recovery, and motion-data processing. Its main scope boundary is the strict-tree assumption, while more sophisticated nonlinear models remain a future extension.
- Results: The method achieves accuracy consistent with sensor resolution on a mechanical rotary-joint device and with biomechanics estimates for human data.The human-data estimate assumes rotational joints and no skin movement relative to bone.
- Applications: Rapid calibration can identify marker slippage through large changes in joint residual, enabling problematic segments to be repeated during capture.This is intended to reduce the burden of production-environment calibration.
- Evaluation: The reported limb-length comparisons cover isolated-degree-of-freedom, simultaneous-motion, and female-subject datasets.Tables 2–4 compare measured and calculated limb lengths, with Table 4 reporting centimeter differences.
- Applications: Recovered parameters support performer-specific digital characters and fitting motion to graphical models with different dimensions.The method can provide best-fit limb lengths before constant-limb-length modification and constraint-based adaptation.
- Applications: Joint-center discontinuities can expose optical-marker swaps caused by occlusion, even when marker trajectories remain relatively smooth.This provides a way to disambiguate markers during processing.
- Hierarchy recovery: Automatic hierarchy identification could help when object connections are dynamic, including dancing pairs or subjects manipulating instrumented objects.For relatively clean data, the algorithm can extract the hierarchy automatically.
- Limitations: The method assumes a strict tree without cycles, so unknown loop joints are omitted from the recovered hierarchy unless the loop is known beforehand.A low-error unused joint fit could signal this issue to the user.
- Future extensions: More complex nonlinear models could represent non-rotational joints, skin slippage, and magnetic-system noise more explicitly.Motion reconstruction is described as a first step toward separating subject motion from error-related components.