Real-time Localization of a Soccer Ball from a Single Camera

Artem Prosvetov; Dmitrii Vorobev; Karim Elhadji Daou

REVIEW 4 major objections 6 minor 10 references

Real-time Localization of a Soccer Ball from a Single Camera

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A single-camera online filter with four discrete ball states and a fixed-width beam search reconstructs a football's 3D trajectory in real time, matching or exceeding an offline multi-camera MIP baseline on tele-accuracy and kick events…

desk verdict A real-time single-camera 3D ball tracker with a genuinely new mode structure and W-buffer, but its headline accuracy claims are undercut by untested physics, a missing baseline, and no error bars. read the letter →

arxiv 2506.07981 v1 pith:7H3EO5P3 submitted 2025-06-09 cs.CV cs.LG

Dmitrii Vorobev , Artem Prosvetov , Karim Elhadji Daou This is my paper

classification cs.CVcs.LG

keywords SportstechnologyReal-timelocalizationFootballanalytics3Dballtrajectorysingle-cameratrackingbeamsearchstateestimationbroadcastvideo

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 aims to show that a single broadcast camera can deliver the 3D ball tracking that currently requires expensive multi-camera setups, and can do it in real time. It proposes a recursive filter whose hidden state includes four football-specific modes—jumping, possession, waiting, and out-of-pitch—and which keeps only the most likely trajectories through a fixed-width beam search. On 30 minutes of top-league broadcast footage, the filter with a 2-second latency buffer reaches Acc@0.5 m of 0.59 versus 0.56 for the offline multi-camera optimization baseline, and kick F1 of 0.74 versus 0.66, while running at 53 fps on a standard CPU core. The practical point is that accurate ball trajectories and kick events could be generated from the main TV feed without dedicated stadium infrastructure.

What carries the argument

The central object is a recursive Bayes filter over a hybrid state: a 3D ball position with velocity and variance, together with a discrete mode from the set S={J,P,W,O} (jumping, player possession, wait-after-possession, out-of-pitch). Each hypothesis carries an accumulated log-likelihood, and descendants are generated by discretizing the camera's viewing ray into 3 cm steps for visible jumping states, by free-flight extrapolation for occluded frames, and by inheriting player positions for possession states. A fixed-width beam search retains the top K hypotheses at every frame, making per-frame cost linear in the number of detections, and an output buffer of L frames lets the most recent estimates be revised as new observations arrive.

What would settle it

Re-run the same filter on broadcast clips with independent high-frequency ground truth, adding a quadratic drag term to the jumping-mode dynamics with a typical football drag coefficient; if Acc@0.5 m at L=50 changes by more than a few percent relative to the reported 0.59, the idealized free-flight model is carrying the result.

Watch

Extended reading notes

Core claim

The paper's central claim is that the depth ambiguity of a single camera can be resolved online by pairing discrete, interpretable ball states with beam search over physically scored trajectories. Rather than estimating depth frame by frame, the filter generates candidate 3D positions along the camera ray at 3 cm spacing, scores each hypothesis by a log-likelihood that combines a precomputed mode-transition prior, a free-flight dynamics term, and an observation term, and keeps only the top K hypotheses. The waiting mode, which buffers the interval between a kick and the first visible detection, keeps ballistic hypothesis generation to one pass per ball appearance and is what makes real-time beam widths near K=1000 practical. With an L-frame output buffer that revises recent estimates, the filter at L=50 matches or surpasses the offline multi-camera mixed-integer-programming (MIP) baseline on 0.5 m and 1 m tele-accuracy and on kick F1, while running roughly ten times faster.

Load-bearing premise

The filter assumes that whenever the ball is not being touched it follows a simple projectile path under gravity alone, with no air drag or spin, and it uses that assumption both to bridge occlusions and to score visible candidate positions; real trajectories that deviate from this would bias the likelihoods and degrade the reported tele-accuracy.

Editorial extensions

If this is right

A single calibrated broadcast camera can support live 3D ball localization at tele-accuracy (0.5 m), removing the need for multi-camera infrastructure in many analytics and broadcast use cases.
The latency parameter L gives an explicit accuracy-latency dial: at L=1 frame the filter trails the offline baseline, while at L=50 frames it matches or exceeds it, so operators can choose the trade-off per application.
Kick detection becomes a by-product of the discrete mode model, reaching F1 0.74 versus 0.66 for the multi-camera MIP baseline, which is directly useful for shot and pass analytics.
The waiting state W cuts the cost of ballistic hypotheses to one generation per kick appearance, which is what keeps the beam width near 1000 and the throughput at 53 fps on a single CPU.
Out-of-pitch events are also recovered with F1 0.79 against 0.81 for the offline baseline, so the same filter covers ball-out and re-entry events.

Reading between the lines

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

The same mode-based beam-search structure should transfer to other ball sports—tennis, volleyball, basketball—by replacing the possession and out-of-pitch states with the sport's own discrete events, such as serves and out-of-bounds.
The reported parity with the offline multi-camera baseline may narrow on footage with heavy spin, air drag, or deflections, because the jumping mode uses a simple projectile model; adding a drag term to the dynamics is a direct sensitivity test.
A public benchmark dataset would be needed to know how far the single-camera advantage extends, since the evidence here is one proprietary 30-minute dataset and one offline baseline.
The latency buffer L could be made adaptive rather than fixed, increasing during occluded or crowded phases to stabilize accuracy exactly when the model is most uncertain.

Share X Bluesky LinkedIn Reddit HN

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

Quick take: this is a serious engineering paper with a genuinely new algorithmic idea (the W-state and the latency-controlled beam search), and it deserves referee time. But the strongest claims — centimeter-level accuracy and beating offline MIP — are not convincingly supported by the evidence as written.

What's actually new: the J/P/W/O discrete state model, especially the W-state that defers ballistic initialization until first visible detection. That is a clever move that keeps beam width manageable. The online beam-search filter with a controllable latency buffer L is also a nice practical contribution. The comparison against Maksai's MIP, even with the caveats below, suggests the method is in the right ballpark for real-time use.

Where it gets soft. First, the J-mode free-flight assumption is load-bearing and untested. The paper itself says in Section 1 that a football's path 'rarely follows a simple parabola,' yet J→J extrapolation and the Gaussian scoring of visible candidates assume pure gravity, no drag or spin. With roughly half of frames occluded, the gravity-only prior can persist and bias the depth estimates. There is no ablation or sensitivity test over this choice. That is a real gap, not a nitpick.

Second, the evaluation. The abstract promises 'centimeter-level accuracy,' but the finest metric is Acc@0.5m, and the best value is 0.59 — meaning 41% of frames are off by more than half a meter. That's not centimeter-level. Also, the comparison omits Van Zandycke 2022, which is cited in related work as the most recent single-camera method; leaving it out is a noticeable omission.

Third, no confidence intervals or per-match variance. The gains over MIP are +0.03 Acc@0.5 and +0.08 kick F1. With ten 3-minute segments, those differences could easily move. The filter's transition matrix, thresholds, and variances are 'precomputed from historical data' with no description of how that data relates to the test matches. That's a circularity risk the authors need to close.

On the positive side, the writing is clear, the algorithm is described precisely enough to reimplement, and the authors are candid about the latency trade-off. The proprietary dataset is a problem for reproducibility, but the method itself is well specified.

Bottom line: conditional accept if the authors add an ablation on the ballistic model, report variance, and include the missing baseline. It deserves a serious referee.

Referee Report

4 major / 6 minor

Summary. The paper proposes an online, single-camera 3D football trajectory reconstruction method based on a hybrid continuous-discrete state filter with four discrete modes (Jumping, Possession, Wait-after-Possession, Out-of-Pitch), beam-search pruning, and a tunable latency buffer. The system is evaluated on a proprietary Russian Premier League dataset at 6K resolution, comparing against three single-camera baselines and the multi-camera MIP method of Maksai et al. The authors report that at latency L=50 frames the method reaches or slightly exceeds MIP accuracy on threshold-based localization metrics and kick-event F1, while running at 53 fps on a CPU.

Significance. If the results are robust, this is a practically valuable contribution: it demonstrates that a carefully designed online filter with interpretable discrete states and a latency buffer can approach offline multi-camera optimization accuracy using only a single broadcast camera and standard CPU hardware. The W-state design and the linear-complexity beam search are reasonable engineering contributions, and the empirical comparison against MIP is a useful reference point. However, the strength of the central claim depends on several points that are currently insufficiently supported: the most recent single-camera competitor is not evaluated, the reported differences over MIP are small and lack statistical grounding, and the load-bearing free-flight assumption is not ablated or stress-tested. The paper also does not release code or data, which further limits verification.

major comments (4)

[Sec. 7.2 / Table 2] The baseline evaluation omits Van Zandycke and De Vleeschouwer 2022 [8], which is the most recent single-camera online method and is explicitly cited in Section 1 as an approach whose accuracy 'remains inadequate.' Since the paper's central claim is about single-camera reconstruction quality, the absence of this comparison leaves the claim that the proposed method improves over prior single-camera work unestablished. Please add this baseline or justify its exclusion.
[Sec. 6.3 / Sec. 6.4 / Table 2] The J-mode free-flight dynamics (motion purely under gravity, with no air drag, spin, or wind) are load-bearing: they are used both to extrapolate occluded J-states via j() and to score every visible ray hypothesis through the Gaussian centered at the gravity-only extrapolation. Section 1 itself concedes that a ball's path 'rarely follows a simple parabola,' and roughly half of the frames are occluded, so a biased extrapolation can persist until the next detection. No ablation or sensitivity analysis over this modeling choice is provided. The reported gains over MIP (+0.03 Acc@0.5, +0.08 kick F1) could be an artifact of this scoring bias. Please add experiments with a drag term or a sensitivity study over the gravitational model, the velocity variance, and the invisible penalty.
[Table 2 / Sec. 7.4] The headline improvements over MIP are small (Acc@0.5 0.59 vs 0.56, Acc@1 0.66 vs 0.64, kick F1 0.74 vs 0.66) and are reported without confidence intervals, per-match variance, or significance tests. The evaluation comprises only ten 3-minute segments (30 minutes total), so the differences may be within noise. Please report per-match results and specify whether the differences are statistically significant.
[Sec. 4.2 / Sec. 6.1 / Sec. 6.3] The transition matrix p_s, the threshold thrsld, the velocity variance Sigma_v, and the invisible penalty p_invisible_z are described as 'precomputed from historical data' or 'derived from historical data,' but the paper never states whether this historical data is disjoint from the ten test matches. If the same matches or similar segments were used to fit these parameters and to evaluate the filter, the comparison with MIP becomes circular. Please clarify the provenance of these parameters and confirm that the test segments were not used for fitting.

minor comments (6)

[Abstract / Sec. 1] The abstract and introduction claim 'centimeter-level accuracy,' but the finest reported metric is Acc@0.5m; no sub-decimeter threshold is reported. Please either add a finer-grained metric or temper the wording to match the evidence.
[Sec. 3] The phrase 'The solution is infered online' contains a typo: 'infered' should be 'inferred.'
[Sec. 6.3] The sentence 'the likelihood component px is computed as the value of a of a Gaussian' contains a duplicated article; please correct.
[Sec. 6.4] The W->J velocity initialization is described verbally as using 'the free-flight equation,' but the actual equation is not written. Please give the explicit formula so that the initialization is reproducible.
[Sec. 7.4] The phrase '∼10 time reduction of the inference time' is unclear; please restate as 'an order-of-magnitude reduction' and specify how this is computed from the reported fps values (53 vs 6).
[Sec. 2 / Table 1] In the related-work text, 'Strachan et al. [4]' is mentioned, but reference [4] is Ren et al.; please check the citation mapping.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the filter's parameters are not shown to be fitted to the test set, and reported accuracy is measured against an independent multi-camera triangulation ground truth.

full rationale

The paper's derivation chain is self-contained. It formulates the problem as posterior maximization over a Markovian latent state (Eq. 1, Sec. 4), generates hypotheses from single-camera detections and calibrated rays (Sec. 6.2), and scores them using a fixed ballistic extrapolation and a Gaussian likelihood (Sec. 6.3). The reported accuracies are evaluated against ground-truth positions obtained independently via four-camera triangulation with a stated mean error below 10 cm (Sec. 7.1). None of the reported numbers reduces by construction to a fitted quantity. The filter constants ps, thrsld, and Σv are said to be 'precomputed from historical data' (Secs. 4.2, 6.1, 6.3), but the paper does not state that these historical data coincide with the ten-match evaluation set, so no circular fit is established. The baseline MIP method is an independent multi-camera optimizer, and the comparison is not definitionally forced. The paper contains no load-bearing self-citation and imports no uniqueness theorem from the authors' own prior work. The gravity-only jumping model, acknowledged in Section 1 to be an idealization, is an untested modeling assumption and a correctness risk, but it is not equivalent by construction to the outputs or to the evaluation metric, so it does not constitute circularity.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The method depends on several hand-fitted or historically precomputed parameters (transition probabilities, thresholds, variances) and domain assumptions about calibration, detections, and ball physics. None of these are given numerical values or validation splits, so the central accuracy claim rests on unquantified tuning choices.

free parameters (7)

p_s transition matrix = not disclosed
Mode transition probabilities 'precomputed from historical data' (Sections 4.2, 6), used to score every hypothesis; if tuned on the evaluation set, results would be inflated.
thrsld (distance threshold for possession) = not disclosed
Precomputed from historical data (Section 6.1); controls all transitions into P mode.
Sigma_v (velocity variance in J state) = not disclosed
Derived from historical data (Section 6.3); used in the variance update Sigma'_t+1 = Sigma_t + dt*Sigma_v.
p_invisible_z (penalty for no detection) = not disclosed
Pre-computed value (Section 6.3); penalizes missing ball detections and shapes the trade-off between occlusion and false negatives.
Sigma_g (initial variance of J state after W) = not disclosed
Predetermined value (Section 6.4); encodes uncertainty in kick origin and body part, affecting subsequent likelihoods.
Beam width K = up to 1000
Hand-set hypothesis limit (Section 5.1); controls runtime and accuracy.
Ray discretization step = 3 cm
Design choice for candidate depth positions along the camera ray (Section 6.2); too coarse could miss true position.

assumptions (5)

domain assumption Camera calibration (K, R, T) is available at every frame.
Input to the system (Section 3.1); if calibration is wrong or changes with zoom or pan, the ray geometry and depth recovery fail.
domain assumption Ball detections from RTMDet-t and player detections projected via homography are reliable.
The filter consumes these detections (Sections 3.1, 7.1); detection misses or false positives directly drive hypotheses.
domain assumption The ball's trajectory during J mode is ballistic under gravity with possible bounces and no aerodynamic drag.
Extrapolation j(Xt, vt, dt) and W-to-J initialization use free-flight equations (Sections 6.3, 6.4); drag or spin would break the Gaussian likelihood.
ad hoc to paper Precomputed historical statistics (transition matrix, thresholds, variances) are representative of the evaluation matches.
Parameters are derived from undisclosed historical data (Sections 6.1, 6.3, 6.4); the paper does not demonstrate train/test separation, so these may be tuned to the league or season being evaluated.
domain assumption Ground truth from 4-camera triangulation has mean error below 10 cm.
Used as reference for all accuracy metrics (Section 7.1); any bias in this reference limits the meaningfulness of Acc@0.5m.

invented entities (1)

W-state (Wait-after-Possession)
purpose: A latent mode that stores kick time and kicker position between the moment a player kicks and the ball's first visible detection, so ballistic hypotheses are generated only once the ball reappears (Sections 5.1, 6.4).
The W state is a modeling construct, not a measured quantity. The paper gives no external evidence for its existence, but it is an internal variable of the filter, not a physical claim.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Real-time Localization of a Soccer Ball from a Single Camera." pith.science (2026). https://pith.science/paper/7H3EO5P3

@misc{pith2026250607981,
  author       = {Pith},
  title        = {Pith review of: Real-time Localization of a Soccer Ball from a Single Camera},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7H3EO5P3}},
  note         = {Machine review of arXiv:2506.07981}
}

abstract

We propose a computationally efficient method for real-time three-dimensional football trajectory reconstruction from a single broadcast camera. In contrast to previous work, our approach introduces a multi-mode state model with $W$ discrete modes to significantly accelerate optimization while preserving centimeter-level accuracy -- even in cases of severe occlusion, motion blur, and complex backgrounds. The system operates on standard CPUs and achieves low latency suitable for live broadcast settings. Extensive evaluation on a proprietary dataset of 6K-resolution Russian Premier League matches demonstrates performance comparable to multi-camera systems, without the need for specialized or costly infrastructure. This work provides a practical method for accessible and accurate 3D ball tracking in professional football environments.

Figures

Figures reproduced from arXiv: 2506.07981 by the authors.

**Figure 1.** Uncertainty in ball position determined from only a single camera frame. To address these challenges, we developed a multi-mode state model that distinguishes phases such as free flight, player possession, post-kick buffering, and out-of-play. The method applies limited discretization and a fixed-width beam search, ensuring linear time complexity for each filter step. We introduce a controllable latency parameter … view at source ↗

**Figure 2.** The scheme of the proposed pipeline. 5 Ball State Modes 5.1 Discrete Modes of Ball Motion To model the variety of game events, we define a finite set of discrete ball states S = {J ,P, W, O}. For each frame t the discrete variable st, included in the latent state Ht, specifies which kinematic model applies [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Possible types of state transitions. by the distance between Xt+1 and Xt: px(Xt+1 | Xt, st+1 = P) = ∥Xt+1 − Xt∥ < thrsld Here, thrsld is a distance threshold precomputed from historical data. Thus, ∆ℓ = log ps(st+1 = P | st) if the new position Xt+1 is sufficiently close to the previous one; otherwise, ∆ℓ = −∞, effectively eliminating improbable transitions. 6.2 Hypothesis Generation from Visible Detections Given t… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Generated positions for visible J-states 6.3 J → J transition When in jumping mode, the current J -state generates both visible and invisible J-states, depending on whether a detection is associated with it. First, the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

10 extracted references · 8 canonical work pages

[8]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

Van Zandycke, G., De Vleeschouwer, C.: 3d ball localization from a single calibrated image. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 3472--3480 (2022)

work page 2022
[1]

In: Sixth International Conference on Computer Vision (IEEE Cat

Kim, T., Seo, Y., Hong, K.S.: Physics-based 3d position analysis of a soccer ball from monocular image sequences. In: Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271). pp. 721--726. IEEE (1998)

work page 1998
[2]

In: Proceedings of the IEEE conference on computer vision and pattern recognition

Maksai, A., Wang, X., Fua, P.: What players do with the ball: A physically constrained interaction modeling. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 972--981 (2016)

work page 2016
[3]

Metzler, J., Pagel, F.: 3d trajectory reconstruction of the soccer ball for single static camera systems. In: MVA. pp. 121--124 (2013)

work page 2013
[4]

IEEE Transactions on Circuits and Systems for Video Technology 18(3), 350--362 (2008)

Ren, J., Orwell, J., Jones, G.A., Xu, M.: Real-time modeling of 3-d soccer ball trajectories from multiple fixed cameras. IEEE Transactions on Circuits and Systems for Video Technology 18(3), 350--362 (2008)

work page 2008
[5]

IEEE transactions on pattern analysis and machine intelligence 31(5), 938--944 (2008)

Ribnick, E., Atev, S., Papanikolopoulos, N.P.: Estimating 3d positions and velocities of projectiles from monocular views. IEEE transactions on pattern analysis and machine intelligence 31(5), 938--944 (2008)

work page 2008
[6]

In: Symposium on Computer Science in Sports (IACSS 2015)

Shen, L., Liu, Q., Li, L., Yue, H.: 3d reconstruction of ball trajectory from a single camera in the ball game international. In: Symposium on Computer Science in Sports (IACSS 2015). pp. 33--39 (2015)

work page 2015
[7]

In: RoboCup 2011: Robot Soccer World Cup XV 15

Silva, H., Dias, A., Almeida, J., Martins, A., Silva, E.: Real-time 3d ball trajectory estimation for robocup middle size league using a single camera. In: RoboCup 2011: Robot Soccer World Cup XV 15. pp. 586--597. Springer (2012)

work page 2012

Show all 10 references

[9]

, " * write output.state after.block = add.period write

ENTRY address author booktitle chapter doi edition editor eid howpublished institution journal key month note number organization pages publisher school series title type url volume year label INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION in...
[10]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [8]

In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

Van Zandycke, G., De Vleeschouwer, C.: 3d ball localization from a single calibrated image. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 3472--3480 (2022)

work page 2022

[2] [1]

In: Sixth International Conference on Computer Vision (IEEE Cat

Kim, T., Seo, Y., Hong, K.S.: Physics-based 3d position analysis of a soccer ball from monocular image sequences. In: Sixth International Conference on Computer Vision (IEEE Cat. No. 98CH36271). pp. 721--726. IEEE (1998)

work page 1998

[3] [2]

In: Proceedings of the IEEE conference on computer vision and pattern recognition

Maksai, A., Wang, X., Fua, P.: What players do with the ball: A physically constrained interaction modeling. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 972--981 (2016)

work page 2016

[4] [3]

Metzler, J., Pagel, F.: 3d trajectory reconstruction of the soccer ball for single static camera systems. In: MVA. pp. 121--124 (2013)

work page 2013

[5] [4]

IEEE Transactions on Circuits and Systems for Video Technology 18(3), 350--362 (2008)

Ren, J., Orwell, J., Jones, G.A., Xu, M.: Real-time modeling of 3-d soccer ball trajectories from multiple fixed cameras. IEEE Transactions on Circuits and Systems for Video Technology 18(3), 350--362 (2008)

work page 2008

[6] [5]

IEEE transactions on pattern analysis and machine intelligence 31(5), 938--944 (2008)

Ribnick, E., Atev, S., Papanikolopoulos, N.P.: Estimating 3d positions and velocities of projectiles from monocular views. IEEE transactions on pattern analysis and machine intelligence 31(5), 938--944 (2008)

work page 2008

[7] [6]

In: Symposium on Computer Science in Sports (IACSS 2015)

Shen, L., Liu, Q., Li, L., Yue, H.: 3d reconstruction of ball trajectory from a single camera in the ball game international. In: Symposium on Computer Science in Sports (IACSS 2015). pp. 33--39 (2015)

work page 2015

[8] [7]

In: RoboCup 2011: Robot Soccer World Cup XV 15

Silva, H., Dias, A., Almeida, J., Martins, A., Silva, E.: Real-time 3d ball trajectory estimation for robocup middle size league using a single camera. In: RoboCup 2011: Robot Soccer World Cup XV 15. pp. 586--597. Springer (2012)

work page 2012