[Paper Review] Automatic Joint Parameter Estimation from Magnetic Motion Capture Data

James F. O’Brien, Robert E. Bodenheimer+2 more|arXiv (Cornell University)|Jan 1, 2000

Human Motion and Animation27 references183 citations

TL;DR

This paper presents a method to automatically estimate joint parameters—such as limb lengths, joint locations, and sensor offsets—from magnetic motion capture data without external measurements. By fitting a rotary joint model via linear least squares to sensor transformation data, the algorithm infers a hierarchical skeleton and achieves high accuracy, validated on human subjects, simulations, and a physical linkage with errors under 1.5 cm.

ABSTRACT

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.

Motivation & Objective

• To eliminate the need for manual measurements of limb lengths and joint offsets in motion capture.
• To automatically infer the hierarchical structure of an articulated figure from motion data alone.
• To enable accurate forward and inverse kinematics without prior knowledge of subject anatomy or sensor placement.
• To support real-time or interactive applications where calibration is impractical.
• To provide a robust, automated preprocessing step for mapping motion data to digital characters with different proportions.

Proposed method

• Uses global transformation matrices from magnetic motion capture sensors as input.
• Performs a linear least squares fit of a rotary joint model to pairs of sensors to estimate joint centers.
• Identifies collocated points across sensor pairs that remain fixed relative to each other during motion.
• Computes a residual error metric to assess the quality of fit between sensor pairs.
• Constructs a minimum spanning tree using residuals as edge weights to infer the hierarchical topology.
• Reconstructs the full articulated model by combining joint locations and hierarchy.

Experimental results

Research questions

• RQ1 Can joint centers and limb lengths be accurately estimated from motion data alone, without external measurements?
• RQ2 How well can a hierarchical structure be recovered from motion data when the topology is unknown?
• RQ3 What is the accuracy of the estimated parameters compared to ground truth measurements?
• RQ4 Can the method handle real-world noise and non-ideal joint behavior in human motion?
• RQ5 Can the algorithm detect and handle ambiguous marker assignments due to occlusion or sensor drift?

Key findings

• The method achieved an average error of less than 1.5 cm in limb length estimation across multiple human subjects and motion sequences.
• For a wooden linkage with known dimensions, the algorithm estimated limb lengths within 0.3 cm of ground truth.
• In simulation, the algorithm recovered joint parameters with sub-millimeter accuracy, confirming robustness to noise.
• The hierarchical structure was successfully reconstructed from motion data alone, with the minimum spanning tree approach correctly identifying the correct topology.
• The algorithm detected and isolated low-error joint fits that were not used in the tree, indicating potential cycle detection for closed-loop structures.
• The method demonstrated resilience to sensor noise and non-ideal joint behavior, with errors consistent across diverse motion types including walking and isolated joint exercises.