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REVIEW 3 major objections 6 minor 44 references

TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A distance threshold or minimum duration sets the TGOSPA track-switch penalty.

desk verdict Useful parameter-selection rules for TGOSPA, honestly bounded but empirically thin where it matters most: the switch-calibration claim is proven only in a toy scenario. read the letter →

arxiv 2412.08321 v3 pith:SKWMU6SQ submitted 2024-12-11 eess.SY cs.CVcs.SY

Jan Krejčí , Oliver Kost , Ondřej Straka , Yuxuan Xia , Lennart Svensson , Ángel F. García-Fernández This is my paper · ORCID
classification eess.SYcs.CVcs.SY
keywords multi-objecttrackingTGOSPAmetrictrackswitchesperformanceevaluationswitchingpenaltyIoUcomputervisionaxioms
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

The paper tries to establish that TGOSPA, a metric on finite sets of trajectories, is the right evaluation tool for visual multi-object tracking because its parameters can be chosen to match an application. Its main result is that the switching penalty $\gamma$ does not have to be guessed: choosing a threshold distance $g_1 < c$ and setting $\gamma = ((c^p - g_1^p)/2)^{1/p}$ makes short interim track changes count as switches, while setting $\gamma = n^{1/p} c$ makes TGOSPA ignore switches shorter than $n+1$ time steps. These rules turn a counterintuitive hyperparameter into an interpretable tolerance for track changes. The paper also proves that HOTA and $1 - \text{HOTA}$ are not mathematical metrics, and it recommends three concrete parameter triples for detector training, online surveillance, and offline scene understanding.

What carries the argument

The carrying object is the TGOSPA metric $d^{(c,\gamma)}_p$ (Definition 1), a metric between finite sets of discrete-time trajectories that minimizes over time-indexed assignment vectors and decomposes (equation 14) into a localization term, a missed-objects term, a false-alarms term, and a switch term. The parameter-selection rules are produced by equating the cost of a no-switch assignment with the cost of a switch assignment in a simplified two-trajectory, one-estimate scenario; the equality gives closed-form formulas for $\gamma$ in terms of $g_1$ or $n$. Because exact TGOSPA is NP-hard, the numerical evaluations use the LP relaxation from [16], which is itself a metric and agreed with exact TGOSPA in all cases tested in the paper.

What would settle it

Construct the exact two-trajectory scenario, set $\gamma$ by (19) for a fixed $g_1$, and vary the wrong-track distance $d$ around $g_1$: the optimal TGOSPA assignment should flip from no switch to two switches exactly at $d = g_1$; if the boundary shifts when a third trajectory is added or when $c$ is enlarged, the threshold interpretation is refuted.

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Extended reading notes

Core claim

The central claim is that the TGOSPA switching penalty $\gamma$ can be set through threshold distances. In a scenario where one estimate briefly tracks the wrong ground-truth trajectory, TGOSPA counts the episode as two switches exactly when $\gamma < ((c^p - d^p)/2)^{1/p}$, where $d$ is the estimate's distance to the wrong trajectory at the switched time step; hence a user-provided threshold $g_1$ yields $\gamma = ((c^p - g_1^p)/2)^{1/p}$. For permanent changes, TGOSPA counts the change as one switch when $\gamma < (\ell c^p - \sum d_k^p)^{1/p}$, and setting $\gamma = n^{1/p} c$ guarantees that changes lasting at most $n$ time steps are ignored. The authors validate the interpretation on a two-pedestrian occlusion segment of MOT17-09, show that different $\gamma$ choices reorder BoT SORT and Tracktor++v2, and propose the three recommended setups. They further show that HOTA and $1 - \text{HOTA}$ violate the metric axioms, and that the TGOSPA decomposition into localization, missed, false, and switch terms gives reasons for algorithm orderings that CV scores cannot provide.

Load-bearing premise

The load-bearing assumption is that the two-trajectory, one-estimate derivation describes real scenes: the estimate is correctly assigned before the change, the wrong-track distance at the change is below the relevant threshold, and no third trajectory competes for the assignment; the paper itself flags that this interpretation is no longer valid with more trajectories or larger $c$, and its Observation 11 records a real BoT SORT case where the predicted threshold does not hold.

Editorial extensions

If this is right

  • Users can replace the opaque switching penalty $\gamma$ with a distance tolerance $g_1$ or a minimum switch duration $n$, making evaluation results interpretable before the metric is computed.
  • Setting $\gamma = n^{1/p} c$ implements 'ignore switches shorter than $n+1$ time steps' as a hard specification, which is directly relevant for scene-understanding applications that only care about long track fragmentations.
  • Detector training should use $\gamma = 0$, because with any positive $\gamma$ the temporary disconnections of a per-frame detector are counted as switches and the detector ranking becomes misleading.
  • The three recommended parameter triples produce different orderings of the same trackers, so application-specific scoring is not cosmetic: the same algorithm can be the right choice for online surveillance and the wrong choice for offline scene understanding under TGOSPA.

Reading between the lines

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

  • My inference (not the paper's claim): in crowded scenes the effective threshold will be stricter than $g_1$ because nearby third trajectories compete for the same assignment; a practical workaround would be to set $g_1$ from the observed distribution of inter-object distances and verify switch counts on validation data.
  • A testable extension the paper does not pursue: use the same cost-equality argument to derive thresholds for other event types, such as a track that splits into two estimates for a few frames, rather than only for temporary or permanent switches.
  • Since the paper's $\gamma = 0$ case reduces TGOSPA to per-frame GOSPA and forfeits the metric property, any use of TGOSPA as a true metric between two algorithms' outputs requires a positive switching penalty; this makes the parameter-selection rules not just a convenience but a prerequisite for the metric interpretation.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper introduces the TGOSPA metric to computer-vision multi-object tracking evaluation, argues that common CV scores such as HOTA and 1−HOTA are not mathematical metrics, and proposes principled rules for selecting the TGOSPA parameters (cut-off c, exponent p, and switching penalty γ). The central methodological contribution is an indirect calibration of γ: Eq. (19) sets γ from a short-term threshold distance g1, and Eq. (24) sets γ from a minimum switch length n, with derivations carried out in simplified two-ground-truth, one-estimate scenarios. The paper also proposes a histogram-based c and p selection procedure, recommends three concrete parameter setups for detector training, online surveillance, and offline scene understanding, and evaluates several trackers on the MOT17-09 sequence. The algebraic derivations are presented transparently, and the paper explicitly discloses conditions under which its interpretation breaks, including after Eq. (20), after Eq. (24), and in Observation 11.

Significance. If the proposed calibration survives contact with realistic scenarios, the paper provides a useful bridge between the mathematically principled TGOSPA metric and practical CV evaluation, giving users an intuitive handle on the otherwise unintuitive switching penalty. The paper is honest about the scope of its derivations and ships concrete parameter recommendations with decomposition-style evaluation tables, which is valuable for practitioners. The main significance hinges on whether the recommended g1- and n-based settings actually deliver the intended switch behavior in scenes with multiple trajectories and moderate c; the paper's own Observation 11 shows a violation of the threshold interpretation in exactly such a setting, so the practical claim currently rests on an extrapolation from a toy scenario.

major comments (3)
  1. [III-D1, III-D2 and VI] The central claim that γ can be set indirectly through g1 or n is proved only for the simplified scenario with two ground-truth trajectories, one estimated trajectory, and a fixed pre-switch assignment. The paper itself states after Eq. (20) and after Eq. (24) that the interpretation is no longer valid with more trajectories or considerably larger c, and Observation 11 concretely shows a BoT SORT estimate with distance larger than g1=0.255 still producing four switches because d(x^t_1,y^t_1)>c fails. Section VI nevertheless recommends γ=0.31 (from g1=0.17) and γ=5 (from n=10) and evaluates them on the full MOT17-09 video, where the simplifying assumptions are violated. The manuscript therefore does not establish that the recommended γ values realize the intended g1 or n switch thresholds in the evaluated scenes. Please add a quantitative robustness analysis, for example by measuring effective switch thresholds as a function of target count and c, or by calibrating on controlled scenarios with the same trajectory density and showing the deviation from the intended g1/n.
  2. [IV-B, IV-C and VI-A] The values of c, p, and γ used in the recommended setups in Section VI are selected using the same MOT17-09 data that is later used for the evaluations in Tables V and VI. In particular, Combinations A-C are read off the histograms in Fig. 11 and the visualization in Fig. 12, which are computed from the algorithms that are subsequently ranked. This creates a mild in-sample selection, and the paper does not report how sensitive the rankings or the metric decompositions are to the chosen parameter values. Please add a sensitivity analysis, for example by varying c and p within interval I2 and reporting the resulting rankings, or by validating the recommended setups on an additional MOT17 sequence, so that the recommendations can be distinguished from an overfit to a single video.
  3. [III-D2, Section V] The statement around Eq. (24) that setting n>K/2 makes TGOSPA behave as if γ→∞ deserves a more careful justification. The maximum possible length of a track-change segment depends on the pre-switch segment length, and the paper's own caveat that the assumption of a sufficiently long pre-switch assignment is 'crucial for the validity of the interpretation of (24)' makes the claim nontrivial. In particular, the text uses both K and K+1 inconsistently in this discussion, and the derivation leading to Eq. (21) does not cover the case where a tracker switches after a very short initial segment and then persists on the wrong target for the remainder of the sequence. Please clarify the exact conditions under which the 'n>K/2 implies no switches' statement holds, or restrict the claim accordingly.
minor comments (6)
  1. [II-C] There is a typo in the phrase 'the funciton dHOTA(X, Y)' near Eq. (1); it should read 'the function dHOTA(X, Y)'.
  2. [II-B] The tracker name is written as 'Bot SORT' in the description 'Bag-of-tricks for simple online and real-time tracking (Bot SORT)', while everywhere else it is 'BoT SORT'; please unify the capitalization.
  3. [V] The observations are numbered starting from Observation 2, but there is no Observation 1 in the manuscript; either renumber or add the missing observation.
  4. [VI-A, Table VI] The caption 'online surveillance and offline scene understanding tracking algorithms evaluation using the IoU metric, MOT17-09 video processing the public FRCNN detections' should be reworded, for example 'evaluation on the MOT17-09 video using the public FRCNN detections', since the current phrasing is grammatically incomplete.
  5. [III-C and Observation 7] The notation 'γ> c 2√p' is ambiguous; it should be written as γ > c/2^{1/p} or, equivalently, γ^p > c^p/2, to make the comparison with the missed/false-object cost cp/2 explicit.
  6. [III-D2] The text 'Setting n> K/2 results in TGOSPA behaving as if γ→+∞' should use n>(K+1)/2 consistently with the preceding sentence that refers to the total number of time steps K+1.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the gamma-calibration rules are algebraic consequences of the TGOSPA definition, not fitted to outcomes.

full rationale

The paper's central contribution is a set of rules translating user-chosen threshold quantities (g1 or n) into the TGOSPA switching penalty gamma. These rules are derived by equating the TGOSPA costs of two explicitly written candidate assignment matrices in two simplified scenarios: Eq. (19) follows from Eq. (17), which sets the no-switch cost (15) equal to the two-switch cost (16), and Eq. (24) follows analogously from Eq. (22) with h_l=0. These are algebraic consequences of the published TGOSPA definition, so the threshold behavior is not an input renamed as an output. The paper is explicit that the interpretation is valid only under the stated two-trajectory assumptions, with qualifications after Eq. (20) and Eq. (24), and Observation 11 demonstrates a real violation in the MOT17-09 data; this is a limitation of the parameter-selection method's applicability in dense scenes, not circularity, because the derivation does not assume the conclusion it uses the scenario to illustrate. Self-citations to [16], [17], and [27] supply the metric definition, the LP-relaxation implementation, and the c-selection guideline functions, but the novel gamma-calibration claim does not reduce to those citations. The recommended c, p, and gamma values are chosen with the aid of MOT17-09 distance histograms and later illustrated on the same video, which is in-sample parameter tuning; however, the paper does not present a statistical prediction from a fitted parameter, and the numerical tables are computed evaluations rather than forced forecasts. No step in the derivation chain is equivalent to its own input by construction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim depends on the TGOSPA metric theorem from prior literature, the Jaccard metric property, and the assumption that LP relaxation matches TGOSPA in the evaluated cases. The gamma-selection rules additionally assume simplified two-trajectory scenarios. The recommended parameter values are explicit user choices, not hidden fitted constants.

free parameters (6)
  • cut-off c = 0.34, 0.255, 0.5 (recommended setups)
    Selected by hand from histogram interval I2 of MOT17-09 distances; controls the maximum localization error counted as proper.
  • exponent p = 1, 1.71, 2.409, 1.8
    Computed from chosen c and a via Eq. (32); controls outlier penalization.
  • maximum admissible error a = 0.17, 0.255, 0.34, 0.25
    User-chosen distance; indirectly sets p through Eq. (32).
  • switching penalty gamma = 0, 0.043, 0.079, 0.149, 0.31, 0.981, 3.4, 5
    Set via g1, n, or the extreme limit; penalizes track switches.
  • short-term threshold g1 = 0.75c in examples
    User-chosen distance for short-term switches; determines gamma via Eq. (19).
  • minimum switch length n = 10, 31
    User-chosen number of frames; determines gamma via Eq. (24).
assumptions (5)
  • standard math TGOSPA is a metric on the space of finite sets of trajectories
    Proven in [16]; the paper's evaluation framework depends on it.
  • standard math dIoU = 1 - IoU is a metric on bounding boxes
    The paper extends the finite-set Jaccard metric proof of [34] to Lebesgue-measurable boxes.
  • domain assumption The LP relaxation coincides with the exact TGOSPA metric for all computations in this paper
    The paper states all optimal assignments were hard in its runs, but this is an empirical claim, not a guarantee.
  • ad hoc to paper Simplified switch scenarios with one estimate, two ground truths, and a fixed pre-switch assignment are representative for gamma selection
    The derivations of Eqs. (18) through (25) rely on this setup; the paper acknowledges it can fail in real scenes.
  • domain assumption The interval I2 in the histogram can be identified by hand
    The c-selection method requires the user to pick a stable interval from guideline functions.

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Cite this review

Pith. "Pith review of TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking." pith.science (2026). https://pith.science/paper/SKWMU6SQ

@misc{pith2026241208321,
  author       = {Pith},
  title        = {Pith review of: TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SKWMU6SQ}},
  note         = {Machine review of arXiv:2412.08321}
}
read the original abstract

Multi-object tracking algorithms are deployed in various applications, each with different performance requirements. For example, track switches pose significant challenges for offline scene understanding, as they hinder the accuracy of data interpretation. Conversely, in online surveillance applications, their impact is often minimal. This disparity underscores the need for application-specific performance evaluations that are both simple and mathematically sound. The trajectory generalized optimal sub-pattern assignment (TGOSPA) metric offers a principled approach to evaluate multi-object tracking performance. It accounts for localization errors, the number of missed and false objects, and the number of track switches, providing a comprehensive assessment framework. This paper illustrates the effective use of the TGOSPA metric in computer vision tasks, addressing challenges posed by the need for application-specific scoring methodologies. By exploring the TGOSPA parameter selection, we enable users to compare, comprehend, and optimize the performance of algorithms tailored for specific tasks, such as target tracking and training of detector or re-ID modules.

Figures

Figures reproduced from arXiv: 2412.08321 by the authors.

Figure 1
Figure 1. Part of the publicly available MOT17-09 scenario studied in this paper. The ground truth objects are depicted in blue. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FRCNN detector results depicted in red. The detector [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Tracktor++v2 tracker results. The pedestrian [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (15 more)
Figure 4
Figure 4. Figure 4: BoT SORT tracker results. The estimates switch positions at time step k=415, see Figure 4b. (a) k = 416 (b) k = 442 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: GMPHDOGM17 tracker results. Estimates are of [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: Example assignment matrix π 0:K for two sets of trajectories X = {X1, X2} depicted in blue and Y = {Y1} depicted in red. For instance, the trajectories X2 and Y1 are assigned at k = 7, which is indicated by ρ(π 7 ) = {(2, 1)}. Similarly, the trajectories X1 and Y1 are …
Figure 7
Figure 7. Figure 7: Short-term track change scenario illustration. [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Long-term track change scenario illustration. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Track fragmentation scenario illustration.  q [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Graphical sketch of expected properties of the incre [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: Increments of the guideline functions diff N(c)  (30) and diff L(c)  (31) for the entire MOT17-09 video and sample distances collected from all the algorithms described in Section II-B. At this point, the sample distances  d(x k i , yk j ) [PITH_FULL_IMAGE:figures…
Figure 12
Figure 12. Figure 12: It should be emphasized that the data used for drawing both [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 12
Figure 12. Figure 12: Examples of bounding box pairs ordered using the IoU-induced metric. The value of the metric is given above each [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: The IoU-induced distance of individual estimates from each ground truth bounding box. Note that the F-RCNN [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 14
Figure 14. Figure 14: Description of a single cell of Tables II, III and IV. The example is taken from Table III: Tracktor++v2. [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]
Figure 15
Figure 15. Figure 15: With this notation, according to [10], the HOTA score is defined as follows. Definition 12 (HOTA score): Given two trajectories X and Y, the HOTA score is defined and approximated as HOTA(X, Y) = R 1 0 HOTA(α) (X,Y) dα (40a) ≈ 1 19 P19 l=1 HOTA(0.05·l) (X,Y), (40b) […
Figure 15
Figure 15. Figure 15: Illustration of sets involved in the HOTA score [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]
Figure 16
Figure 16. Figure 16: Illustrative toy examples. d (c,γ) p (X,Y)=4× c 2=2c and two pairs of missed and false estimates resut. The HOTA score for Ex1 is HOTA(X,Y) = s 4 × 1 1+1+1 2 + 1 + 1 ≈ 0.577. (50) Ex2 (perfect localization, one missed, and one false): For this and the following Ex3, E…

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.