Gravity as a Reference for Estimating a Person's Height from Video

Didier Bieler; Helge Rhodin; Pascal Fua; Semih G\"unel

REVIEW 2 major objections 6 minor 31 references

Gravity as a Reference for Estimating a Person's Height from Video

T0 review · 2 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The known acceleration of gravity can convert pixel measurements in ordinary video into a person's metric height, without calibrating the camera or ground plane.

desk verdict A clever and sound physics-based scale estimator for monocular video, but the headline accuracy is a median over selected on-spot jumps and the constant-depth precondition is understated. read the letter →

arxiv 1909.02211 v2 pith:4QUP3NF6 submitted 2019-09-05 cs.CV

Didier Bieler , Semih Günel , Pascal Fua , Helge Rhodin This is my paper · ORCID

classification cs.CV

keywords heightestimationgravityreferencefree-fallmonocularvideoscalerecoverycenterofmasscamerauncalibratedjumpingmotion

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that the omnipresent constant $g = 9.81\,\mathrm{m/s^2}$ can replace a calibration object when measuring a person's height from video. It shows that the quadratic term of a projected free-fall trajectory, measured purely in pixels, can be equated to $g$ to yield a scale factor $q$, and that multiplying a standing person's pixel height by $q$ recovers metric height with a mean absolute error of 3.9 cm on jumping motions. The method requires only that the video contains a free-fall phase, that the camera is static, and that air friction is negligible. Its appeal is that it works on legacy, uncalibrated monocular footage where existing methods need extra sensors, reference objects, or manual calibration.

What carries the argument

The load-bearing identity is the ratio between the known gravitational acceleration and the measured image acceleration: $q = g / a_{px}$, obtained by matching the quadratic coefficient of the projected free-fall parabola (Eq. 4 and Eq. 5). The companion identity $h = h_{px} q$ (Eq. 7) then rescales any pixel measurement aligned with gravity into meters. The argument is carried through for people by replacing the body with its center of mass, whose projected trajectory must still follow the same parabola regardless of internal articulation.

What would settle it

A controlled video of a person of known height jumping at constant distance to a static camera should reproduce the paper's 3.9 cm MAE; the same person jumping while walking one meter toward the camera during the clip should produce a systematically biased estimate if the distance-consistency assumption breaks.

Watch

Extended reading notes

Core claim

Under scaled-orthographic projection, a rigid object in free fall traces a parabola on the image plane. Writing the projected trajectory as $p_{px}(t)=\frac{1}{2}a_{px}t^2 + v_{0,px}t + p_{0,px}$, the paper equates the measured image acceleration $a_{px}$ to the known gravitational constant $g$ through $q = g/a_{px}$ (Eq. 5). Because any pixel length aligned with gravity equals metric length times $1/q$, the standing person's head-to-heel pixel extent $h_{px}$ converts to height $h = h_{px} q$ (Eq. 7). This requires no knowledge of camera intrinsics, object distance, or gravity direction. For articulated people, the same derivation is carried out on the center of mass, using conservation of momentum so that internal body motions do not invalidate the projectile model.

Load-bearing premise

The scale ratio measured during free fall is applied to the standing height measured in a different set of frames; this only works when the person's distance to the camera is the same in both parts of the video and the camera does not move.

Editorial extensions

If this is right

Metric height becomes recoverable from uncalibrated monocular video of a jump, without reference objects or camera/ground-plane calibration.
Legacy video and consumer footage can be rescaled to meters, making forensic or surveillance height estimates possible on footage that existing calibrated methods cannot process.
The recovered scale factor $q$ can be applied to the output of an off-the-shelf monocular 3D pose estimator to turn it into metric 3D pose, which the paper demonstrates in a qualitative experiment.
Because $q$ is measured per jump, taking the median over several jumps reduces the effect of occasional pose-detection failures and improves accuracy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same ratio-symmetric identity would apply to any scene containing a moving object whose only external acceleration is known (e.g., a dropped tool), not just to human jumpers.
A practical self-check suggested by this reasoning: if the person moves toward or away from the camera between the jump and the standing measurement, the estimate degrades; errors of 12.3–18.9 cm in the running experiments indicate that distance consistency can serve as a quality control metric.
One could extend the method to temporally varying scale by estimating $q$ continuously during the jump and rescaling each frame's height, rather than transferring a single $q$ to standing frames, which would avoid the distance-consistency assumption.
For applications like person re-identification, the unbiased, per-person height estimate could serve as a geometric fingerprint complementary to appearance cues.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague, here's my read on 1909.02211.

The thing to know: this paper actually delivers something new — a way to turn free-fall acceleration into a pixel-to-meter scale for uncalibrated monocular video, applied to articulated humans via COM tracking. The derivation in Sec. 3 is simple and internally consistent under scaled orthographic projection. The authors are honest that it only recovers height, the gravity-aligned extent, and not arbitrary 3D scale. The new 12-subject dataset and the ball-dropping sanity check are useful contributions. Credit where due: the COM argument is well made, the RANSAC/polynomial fitting for acceleration is sensible, and the paper beats the appearance-based baseline [13] on their own data with lower bias.

Soft spots, in order of importance. First, the abstract's 'MAE of up to 3.9 cm' applies to a median across four on-spot jumps per subject, not to per-jump predictions. Table 2 shows low jumps have MAE of 13–21 cm. That's not hiding a broken method, but it's an optimistic summary. Second — and this is the one I'd want fixed before publication — the scale q is measured during the jump, while the height h_px is measured in the first standing frames. That only works if the person-camera distance is the same in both. The paper never states this as a precondition. The authors mention 'static camera' and 'free fall', but not constant depth between the two measurements. The lateral-motion results in Table 3 (12–19 cm MAE) are consistent with depth change being a load-bearing failure mode, even though the authors attribute them to occlusion and short flight phases. The appendix simulation covers non-fronto-parallel trajectories, but doesn't test the exact standing-vs-jump depth mismatch. Third, the comparison with [13] uses different aggregation protocols for the two methods (median over jumps vs median over all frames), so the 'nearly half the error' claim should be taken with a grain of salt. Fourth, flight-phase detection requires a hand-selected snippet; the paper says this, so it's a stated limitation, not a hidden one.

None of these kill the central idea. For on-spot jumps with roughly constant depth, the method works, the math checks out, and the errors are reasonable. People working on monocular metric scale estimation, forensic video analysis, or person re-id will get value from this paper. It deserves a serious referee. With revisions — state the constant-depth condition explicitly, redo the abstract numbers, and align the comparison protocol — it would be a solid contribution. I'd send it out.

Referee Report

2 major / 6 minor

Summary. The paper proposes to estimate a person's metric height from monocular video by using the gravitational acceleration g as an absolute reference. Under a scaled-orthographic projection model, the pixel acceleration measured during a free-fall phase yields a conversion factor q = g / a_px, which is then applied to the pixel height of a standing person to recover metric height h = c * h_px * q. The method is validated on a falling tennis ball and on a new dataset of 12 subjects performing on-spot jumps, lateral runs, and lateral jumps at two distances, reporting a median MAE of 3.9 cm on on-spot jumps. The paper also demonstrates the use of the height estimate to rescale a monocular 3D pose estimator and makes code and data available.

Significance. The core idea is elegant and the derivation (Eqs. 1-7) is clean and internally consistent under scaled orthographic projection. A notable strength is that the scale factor q requires no camera intrinsics, extrinsics, ground-plane knowledge, or any reference object in the scene, making it a genuinely complementary cue to appearance-based or geometry-based height estimation. The appendix simulation, the ablation study, and the public release of the ArticulatedFreeFall dataset are valuable contributions. If the boundary conditions of the method are stated precisely and the headline claims are qualified, the paper would offer a useful new tool for forensic, surveillance, and monocular reconstruction applications.

major comments (2)

[Section 3.1, Eq. (7), and Section 4.4] The derivation assumes a single constant scale q = d/f, but the algorithm estimates q from the free-fall segment and applies it to h_px measured 'at the first frames of the video' (Section 4.4). This is valid only if the person's distance to the camera is identical at the two times. The paper never states this constant-depth precondition; the limitation section names the static-camera assumption but not the depth-constancy requirement. The appendix simulation (Table 4) shows the magnitude of the resulting failure: for a jump straight toward the camera at d = 4 m, the error is 21 cm even in a noise-free simulation. This is a load-bearing boundary condition on the central claim, and it should be stated explicitly. The authors should either restrict the claim to on-spot/fronto-parallel motions or add an experiment in which the subject changes depth between the standing measurement and the jump, demonstrating the expected degradation.
[Abstract and Section 5.2 (Tables 1 and 2)] The abstract and Section 5.2 state 'reaching a MAE of up to 3.9 cm on jumping motions.' According to Table 1, this number is the median over four on-spot jumps per subject. Table 2 shows that per-jump MAE is substantially higher: for example, low jumps have MAE of 13.1 cm at 4 m and 20.7 cm at 7 m, and even the best single-jump category remains above 5 cm. The headline therefore overstates the accuracy available from a single jump, which is the realistic operating condition for many applications. The abstract should be reworded to say 'a median over four on-spot jumps per subject yields 3.9 cm MAE,' and the per-jump variability should be highlighted more prominently in the discussion.

minor comments (6)

[Section 1] There is a typo in 'demonstrates the success our our method'; 'our our' should be 'of our'.
[Section 5.2] The sentence 'The naive Baseline-population-mean, predicting the population mean height of 168.9 m' should read '168.9 cm'.
[Sections 5.2 and 8] Table references are inconsistent: the accuracy and ablation results are discussed as 'Table 4', but the relevant tables in the main text are Tables 1 and 3; the appendix also contains a Table 4, which is confusing.
[Section 3.1] The word 'dominante' should be 'dominates'.
[Section 8] The sentence 'the COM estimation generally decreases with the dirstance' contains a typo: 'dirstance' should be 'distance'.
[Figure 7 caption] The caption line 'Distance d in [m] 400' appears malformed; the axis label and numeric tick should be formatted as a normal axis.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: q is estimated directly from measured pixel acceleration and known g; the target height is never used to fit q, and the only self-citation is a non-load-bearing baseline comparison.

full rationale

The derivation is self-contained. The scale factor q is obtained by equating the quadratic coefficients of the projected Newton trajectory and the observed pixel parabola (Eqs. 2-5): q = g / a_px, where a_px is measured by a least-squares quadratic fit to the COM trajectory during free fall (Section 4.3). The height is then h = h_px q (Eq. 7), with h_px measured from AlphaPose keypoints in standing frames. The ground-truth person height never enters the estimation of q, a_px, or h_px at test time, so there is no fitted-input-called-prediction and no self-definitional reduction. The only fitted component, the nose-to-ankle correction c = 1.17 ± 0.03, is calibrated on 29 independent web images, not on the test subjects, and the paper reports its small SD. The self-cited work Gün el et al. [13] is used solely as an external baseline in Tables 1 and 4, not as an input to the derivation, so the self-citation is not load-bearing. The lateral-motion errors in Table 3 and the appendix's depth/perspective simulation concern an unstated precondition about constant person-camera depth, which is a boundary condition on validity rather than a circularity: the derivation would still be non-circular even in the regimes where its assumptions fail. Thus no step reduces, by construction or by self-citation, to the target quantity being estimated.

Assumptions & free parameters 3 free parameters · 8 assumptions · 0 invented entities

The central claim rests on standard Newtonian physics plus several domain assumptions about the capture setup (static camera, free-fall phases, scaled orthographic projection, and approximate COM from keypoints). No new physical entities are introduced. The only fitted numerical constants are the nose-ankle correction factor and the hand-chosen flight-selection thresholds.

free parameters (3)

c (nose-ankle to full-height correction) = 1.17 ± 0.03
Fitted on 29 web images in Section 4.4 to convert AlphaPose nose-ankle pixel distance into total body height. Used for all final height estimates.
flight-phase selection threshold = 15% of jump peak above floor for on-spot jumps; upper half of peak-to-minimum range for lateral motion
Hand-chosen in Section 4.2 to identify airborne frames for the parabola fit. This choice directly affects the estimated pixel acceleration a_px and hence q.
floor-median window = first 100 frames
Section 4.2 uses the median vertical position in the first 100 frames as the floor. This is a dataset-specific hand choice with no sensitivity study.

assumptions (8)

standard math Newton's equation of motion, p(t) = 1/2 g t^2 + v0 t + p0, describes the center-of-mass trajectory during free fall.
Invoked in Section 3 (Eq. 1) and used to equate the quadratic image acceleration term to gravity.
domain assumption The gravitational acceleration is constant and known, g = 9.81 m/s^2.
Section 3 states g is roughly constant with variation below 4%. The method uses this single value as the metric reference without propagating the geographic variation.
domain assumption The camera is static during the recorded video.
Stated in Section 6 as the strongest limitation; if the camera moves, measured image acceleration includes camera motion and cannot be attributed solely to gravity.
domain assumption Scaled orthographic projection is an adequate model for the tested capture conditions.
Section 3.1 (Eq. 2) uses this model; the appendix simulation shows perspective error grows for near and non-fronto-parallel motion, so the model is only approximate at 4-7 m for frontal jumps.
domain assumption During the selected flight-phase frames, gravity is the only external force (air friction is negligible).
Section 4.2 explicitly assumes this; the flight detection attempts to exclude ground-contact phases, but residual aerodynamic drag and body-air interaction are not modeled.
domain assumption The weighted sum of AlphaPose 2D keypoints, using Clauser et al. body-mass ratios, approximates the projected center of mass of the person.
Section 4.1 defines the COM this way; the appendix states the simulation removes this approximation, and real-experiment errors are an order of magnitude larger, showing this is a major error source.
domain assumption The person is at the same distance from the camera when the standing height is measured as during the jump used to estimate q.
Section 4.4 applies the jump-derived q to a height measured in the first frames; the running results in Table 3 show the assumption fails when the subject moves in depth.
domain assumption The nose-to-ankle pixel distance, scaled by c = 1.17, is a valid proxy for total body height across the test population.
Section 4.4 fits c on 29 web images and reports SD 0.03, but no cross-validation or per-subject validation is reported.

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Cite this review

Pith. "Pith review of Gravity as a Reference for Estimating a Person's Height from Video." pith.science (2026). https://pith.science/paper/4QUP3NF6

@misc{pith2026190902211,
  author       = {Pith},
  title        = {Pith review of: Gravity as a Reference for Estimating a Person's Height from Video},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4QUP3NF6}},
  note         = {Machine review of arXiv:1909.02211}
}

read the original abstract

Estimating the metric height of a person from monocular imagery without additional assumptions is ill-posed. Existing solutions either require manual calibration of ground plane and camera geometry, special cameras, or reference objects of known size. We focus on motion cues and exploit gravity on earth as an omnipresent reference 'object' to translate acceleration, and subsequently height, measured in image-pixels to values in meters. We require videos of motion as input, where gravity is the only external force. This limitation is different to those of existing solutions that recover a person's height and, therefore, our method opens up new application fields. We show theoretically and empirically that a simple motion trajectory analysis suffices to translate from pixel measurements to the person's metric height, reaching a MAE of up to 3.9 cm on jumping motions, and that this works without camera and ground plane calibration.

Figures

Figures reproduced from arXiv: 1909.02211 by the authors.

**Figure 1.** Idea. We exploit gravity as a reference object for mapping image height measurements in pixel [px] to metric height [m]. initial speed and position, with the curvature determined by the acceleration induced by constant external forces [22]. To this end, we restrict ourselves to cases where gravitation is the only source of external acceleration and the camera is static, so that acceleration in the image can be uniq… view at source ↗

**Figure 2.** Application to metric 3D pose estimation. Left: Input and output of LCRNet, a 3D human pose estimation method [25], which does not recover the correct scales (marked in red). Right: Using our height estimate from directed on-spot jumping recovers the scale and relative depth of the hip locations (marked in green). We validate our findings on a new test set containing 12 persons performing seven different jumping and… view at source ↗

**Figure 3.** Projection of height. The projected height, h px is the distance between two projected points Π(pu) and Π(pb) that are aligned with the direction of gravity n in 3D and span height h. We now turn to the height estimation using q. We define height as the distance between two 3D points pu and pb that are in a line with the direction of gravity n, see [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Bodypart keypoint detections using AlphaPose on frontal and lateral motion, displayed as colored skeleton overlay [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: COM trajectory for on-spot jumping, with the polynomial fit,detected start, maximum, and end points marked. 4.2. Detecting Free-Fall We assume that gravity is the only external force applied on the person (neglecting air friction). However, this is only true during ju…

**Figure 6.** Figure 6: Outlier removal example. The red diamond marks the outlier and the red curve is the one that excludes it during fitting, leading to significantly improved fits. height measurements to meters with Eq. 7 and multiplying the result with c. 5. Experimental Evaluation We fi…

**Figure 7.** Figure 7: Illustration of the tennisball experiment. The ball is dropped in front of the camera so that it is still in the field of view. Running and jumping ( 4m) Close (4m) on-spot jump Far (7m) on-spot jump [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]

**Figure 9.** Figure 9: Example of funny and jumping jack poses. The wooden reference object is used to estimate relative errors of q. For quantitative evaluation of estimated height hˆ and conversion factor qˆ we compute absolute and signed errors to report: • accuracy across trials as the M…

**Figure 11.** Figure 11: COM trajectory comparison, for 3 on-spot jumps (left) and 6 running steps (right). Running has shorter flight phases and contains temporal jitter around the peaks. MAE of 6.5 cm, and strong bias of 3.7 cm, see bottom of [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [13]

What Face and Body Shapes Can Tell About Height

S. G ¨unel, H. Rhodin, and P. Fua. What Face and Body Shapes Can Tell About Height. In arXiv preprint arXiv:1805.10355, 2018

work page Pith review arXiv 2018

[2] [1]

Adjeroh, D

D. Adjeroh, D. Cao, M. Piccirilli, and A. Ross. Predictability and Correlation in Human Metrology. In IEEE International Workshop on Information Forensics and Security, 2010

work page 2010

[3] [2]

Agarwala, K.C

A. Agarwala, K.C. Zheng, C. Pal, M. Agrawala, M. Cohen, B. Curless, D. Salesin, and R. Szeliski. Panoramic video tex- tures. In ACM Transactions on Graphics, volume 24, pages 821–827. ACM, 2005

work page 2005

[4] [3]

BenAbdelkader and Y

C. BenAbdelkader and Y . Yacoob. Statistical Body Height Estimation from a Single Image. In Automated Face and Gesture Recognition, pages 1–7, 2008

work page 2008

[5] [4]

Clauser, J.T

C.E. Clauser, J.T. McConville, and J.W. Young. Weight, V ol- ume, and Center of Mass Segments of the Human Body. Journal of Occupational and Environmental Medicine , 13(5):270, 1971

work page 1971

[6] [5]

Criminisi, I

A. Criminisi, I. Reid, and A. Zisserman. Single view metrol- ogy. International Journal of Computer Vision , 40(2):123– 148, 2000

work page 2000

[7] [6]

Show me your face and i will tell you your height, weight and body mass index

Antitza Dantcheva, Francois Bremond, and Piotr Bilinski. Show me your face and i will tell you your height, weight and body mass index. pages 3555–3560, 08 2018

work page 2018

[8] [7]

R. Dey, M. Nangia, W. Ross, W. Keith, and Y . Liu. Esti- mating Heights from Photo Collections: A Data-Driven Ap- proach. In ACM conference on Online social network, 2014

work page 2014