# Ground reaction forces estimation from markerless motion capture: computation of performance indicators for countermovement jump tests

Alexandre Schortgen, Antoine Muller, Guillaume Saulière, Lionel Réveret

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Alexandre Schortgen, Antoine Muller, Guillaume Saulière, Lionel Réveret. Ground reaction forces estimation from markerless motion capture: computation of performance indicators for countermovement jump tests. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the Société de Biomécanique, 10.46298/mbj.16233. hal-05191788v2

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# Ground reaction forces estimation from markerless motion capture: computation of performance indicators for countermovement jump tests

Alexandre Schortgen<sup>a, b*</sup>, Antoine Muller<sup>c</sup>, Guillaume Saulière<sup>b</sup>, Lionel Revéret<sup>a</sup>

<sup>a</sup> INRIA Grenoble Rhone-Alpes, LJK, UMR 5224, Grenoble, France

<sup>b</sup> Institut de Recherche bio-Médicale et d'Épidémiologie de Sport, EA7329, INSEP, Université de Paris Cité, Paris, France

<sup>c</sup> Univ Lyon, Univ Gustave Eiffel, Univ Claude Bernard Lyon 1, LBMC UMR T9406, Lyon, France

* Corresponding author: alexandre.schortgen@inria.fr

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

**Keywords:** video-based analysis, kinematics, dynamics, sports performance

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Vertical jump tests are often used to assess an athlete's strength and asymmetry at the lower limbs level. Running these tests is of interest both for athlete physical testing and injury rehabilitation. In addition to postural analysis, using force platforms provides further information by monitoring biomechanical indicators. However, these force platforms can prove overly costly and cumbersome for some on-field applications. Video analysis, through the development of markerless (ML) motion capture, could offer a convenient alternative. The scope of this work is to estimate, from both motion and force data, the following 4 key performance indicators of the Counter Movement Jump (CMJ) test that are currently monitored for physical profiling: jump height, velocity, ground reaction forces (GRF), and power output. Both markerbased (MB) and ML motion analysis methods were carried out and compared to the force plates reference currently used on-field.

## 2. Methods

### 2.1 Experimental Data

A total of 32 CMJ, performed by 11 subjects (25.5±3.1 years-old, 1.73±0.08 m, 65±12 kg), were processed. The study was approved by an institutional review board and participants signed an informed consent form. Sequences were recorded by 10 optoelectronic cameras (Miqus M3, Qualisys, Sweden) sampled at 300 Hz, and 10 video cameras (Miqus Video, Qualisys,

Sweden) sampled at 60 Hz (1920x1088 px), along with 2 force plates (Treadmetrix, United States), sampled at 3000 Hz, for ground reaction force measurement. A total of 46 reflective markers were positioned on the whole body (Lahkar et al., 2022). All systems were synchronized and calibrated.

### 2.1 Motion Analysis

For each sequence, the 4 indicators were computed using 3 methods: a force-based approach, and 2 motion-based approaches (MB and ML analyses). From force plates data, these indicators were derived from the equations of motion (Samozino et al. 2008). For ML, 3D positions of 29 keypoints were extract from OpenPose « BODY_135 » model (Cao et al., 2019) and a weighted direct linear transform. MB data from all trials were first processed in QTM (v2021.1.2, Qualysis, Sweden) by labeling and relational interpolation of missing marker trajectories. From both MB & ML motion capture data, the metrics were retrieved through inverse kinematics and subsequent force estimation using a custom software based on Pinocchio (Carpentier et al., 2019). A low-pass filtering step with a 6 Hz cutoff frequency was applied to kinematic results prior to force estimation.

### 2.2 Data analysis

The differences between force-based and motion-based metrics (for both MB and ML) were assessed computing RMSD and relative RMSD (rRMSD) for each trial,
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Average temporal profiles of the metrics, for ML, MB and force-based computation methods.</figcaption></figure>

Credit: Alexandre Schortgen.

and then averaged over all trials. Correlation between methods was expressed with the intraclass correlation coefficient (ICC) for each trial. To enable direct visualization and comparison of the results over time, a mean profile (± standard deviation) of the CMJ was calculated after synchronization of the repetitions on a shared time basis.

### 3. Results and discussion

The average profiles of the metrics for the three computation methods (MB, ML and force-based) are illustrated in Figure 1 and comparison metrics are summarized in Table 1. Very strong correlations (ICC>0.9) were found between force-based and motion-based metrics.

In terms of mean RMSD, similar differences were found for both MB and ML methods, when compared to force-based reference results, for the estimation of jump height (≈ 10 cm, 11%) and vertical velocity (≈ 0.2 m/s, 5%). Conversely, a difference was found between the MB and ML methods in the estimation of vertical forces. The relative differences on force and power estimation range around 5% and 8% for respectively MB and ML results.

Overall, the results of ML vertical GRF estimation are consistent with values found in the literature on ML analysis of CMJ (Colyer et al., 2023).

<table><caption>**Table 1.** Summary of data analysis comparing the metrics computed from both motion-based methods with force-based results.</caption><thead><tr><th>Metric</th><th>Capture</th><th>RMSE (± std)</th><th>rRMSE (± std)</th><th>ICC (± std)</th></tr></thead><tbody><tr><td rowspan="2">Height</td><td>ML</td><td>0.08 ± 0.06 m</td><td>11.2 ± 6.9 %</td><td>0.93 ± 0.07</td></tr><tr><td>MB</td><td>0.09 ± 0.06 m</td><td>11.9 ± 6.7%</td><td>0.92 ± 0.08</td></tr><tr><td rowspan="2">Velocity</td><td>ML</td><td>0.19 ± 0.06 m/s</td><td>4.7 ± 1.7 %</td><td>0.98 ± 0.01</td></tr><tr><td>MB</td><td>0.19 ± 0.08 m/s</td><td>4.6 ± 2.0 %</td><td>0.98 ± 0.01</td></tr><tr><td rowspan="2">Force</td><td>ML</td><td>161 ± 42 N</td><td>8.0 ± 1.8 %</td><td>0.93 ± 0.03</td></tr><tr><td>MB</td><td>112 ± 58 N</td><td>5.1 ± 2.2 %</td><td>0.98 ± 0.01</td></tr><tr><td rowspan="2">Power</td><td>ML</td><td>5.5 ± 1.4 W/kg</td><td>7.2 ± 1.7 %</td><td>0.9 ± 0.04</td></tr><tr><td>MB</td><td>3.5 ± 1.7 W/kg</td><td>4.4 ± 2.1 %</td><td>0.97 ± 0.01</td></tr></tbody></table>

Credit: Alexandre Schortgen.

The greatest differences between motion-based and force-based results are obtained at peak load moments, which are precisely of utmost interest for CMJ testing. Both motion-based methods tend to underestimate kinematic and dynamic metrics. These discrepancies could be explained by the smoothing applied prior to force estimation, which aims to mitigate the noisiness induced by differentiation of joint kinematics (for both MB and ML).
## 4. Conclusions

The aim of this study was to assess the relevance of using ML motion capture to estimate the performance metrics commonly used to evaluate CMJ tests. Although a good overall consistency was found between ML analysis and force plates measures, a further agreement analysis for peak power estimation is to be conducted to assess if ML methods are sufficiently sensitive to accurately and reliably quantify CMJ performance.

## Conflict of Interest Statement

The authors declare no conflict of interest during this study.

## Contributor Roles

AS: Conceptualization, Methodology, Software, Data curation, Writing original draft, Visualization; AM: Methodology, Data curation, Supervision, Writing review & editing. GS: Supervision, Project administration, Writing review & editing; LR.: Conceptualization, Supervision, Writing review & editing, Project administration, Funding acquisition.

## References

Lahkar, B., Chaumeil, A., Dumas, R., Muller, A., & Robert, T. (2022). Description, development and dissemination of two consistent marker-based and markerless multibody models. bioRxiv. https://doi.org/10.1101/2022.11.08.515577

Samozino, P., Morin, J., Hintzy, F., & Belli, A. (2008). A simple method for measuring force, velocity and power output during squat jump. *Journal of Biomechanics, 41*(14), 2940–2945. https://doi.org/10.1016/j.jbiomech.2008.07.028

Carpentier, J., Saurel, G., Buondonno, G., Mirabel, J., Lamiraux, F., Stasse, O., & Mansard, N. (2019). The Pinocchio C++ library : A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives. *2022 IEEE/SICE International Symposium on System Integration (SII)*, 614–619. https://doi.org/10.1109/sii.2019.8700380

Cao, Z., Hidalgo, G., Simon, T., Wei, S., & Sheikh, Y. (2019). OpenPose: Realtime multi-person 2D pose estimation using part affinity fields. *IEEE Transactions on Pattern Analysis and Machine Intelligence, 43*(1), 172–186. https://doi.org/10.1109/tpami.2019.2929257

Colyer, S., Needham, L., Evans M., et al. (2023). Estimation of ground reaction forces from markerless kinematics and comparison against measured force plate data. Paper presented at International Society of Biomechanics in Sports, Milwaukee, USA United States.