SO-HOTA: Small-Object-Aware HOTA Metric

• SO-HOTA is a small-object-aware metric that replaces IoU with Dot Distance to evaluate tiny object tracking in UAV videos.
• It retains HOTA’s balanced structure between detection and association while applying threshold averaging over multiple DotD criteria.
• Challenge results demonstrate that SO-HOTA better discriminates slight localization errors in UAV bird tracking compared to standard HOTA.

SO-HOTA is a small-object-aware variant of HOTA for multi-object tracking, introduced in the SMOT4SB challenge to evaluate small multi-object tracking in UAV video where birds often occupy only a few dozen pixels and IoU-based matching becomes unstable (Kondo et al., 17 Jul 2025). It preserves HOTA’s balanced treatment of detection and association, but replaces IoU-driven matching with Dot Distance (DotD), a center-distance-based similarity designed to remain informative under tiny spatial displacements that would otherwise cause overlap-based scores to collapse (Kondo et al., 17 Jul 2025). In the cited literature, SO-HOTA is therefore a metric, not a tracker: it is intended to rank SMOT systems more faithfully in regimes where standard HOTA’s localization sensitivity becomes a dominant source of evaluation error (Kondo et al., 17 Jul 2025).

1. Conceptual origin and problem setting

SO-HOTA arises from a specific failure mode of conventional MOT evaluation on very small targets. In SMOT4SB, birds are frequently smaller than $32\times 32$ pixels, and many are around $16\times 16$ or similarly small scales; at that size, a localization error of only a few pixels can radically change IoU even when the prediction remains visually close to the target (Kondo et al., 17 Jul 2025). The motivating example is explicit: for a $16\times 16$ box, an 8-pixel horizontal or vertical shift already reaches the conventional IoU threshold boundary of $0.5$, and once the shift exceeds half the box size, IoU becomes zero (Kondo et al., 17 Jul 2025).

The paper identifies two pathologies of overlap-based evaluation in this regime. First, the metric becomes overly sensitive: trivial-looking localization errors can produce a large score drop. Second, IoU becomes non-discriminative once overlap is lost: a prediction that is barely non-overlapping and one that is far away both receive IoU $=0$ (Kondo et al., 17 Jul 2025). In UAV bird tracking, where both camera motion and bird motion are unconstrained in 3D, near-but-non-overlapping predictions occur frequently, so a pure IoU criterion can undervalue tracking quality (Kondo et al., 17 Jul 2025).

This setting explains why SO-HOTA was proposed inside a challenge paper rather than a general MOT benchmark paper. The SMOT4SB challenge introduces three main contributions: the SMOT4SB dataset with 211 UAV video sequences and 108,192 annotated frames, SO-HOTA as the primary ranking metric, and a competitive challenge with 78 participants and 308 submissions (Kondo et al., 17 Jul 2025). The metric is thus inseparable from the small-object tracking regime for which it was designed.

2. Relation to standard HOTA

SO-HOTA is structurally derived from HOTA, the Higher Order Tracking Accuracy metric introduced to balance detection and association while incorporating localization through threshold averaging (Luiten et al., 2020). At a localization threshold $\alpha$, standard HOTA decomposes as

$$\mathrm{HOTA}_{\alpha}=\sqrt{\mathrm{DetA}_{\alpha}\cdot \mathrm{AssA}_{\alpha}},$$

with

$$\mathrm{DetA}_{\alpha}=\frac{|\mathrm{TP}|}{|\mathrm{TP}|+|\mathrm{FN}|+|\mathrm{FP}|},$$

and

$$\mathrm{AssA}_{\alpha}=\frac{1}{|\mathrm{TP}|}\sum_{c\in\{\mathrm{TP}\}} \mathcal{A}(c),$$

where $\mathcal{A}(c)$ is a Jaccard-style association score defined from $16\times 16$0, $16\times 16$1, and $16\times 16$2 over the matched predicted and ground-truth trajectories (Luiten et al., 2020). Final HOTA is then averaged over thresholds $16\times 16$3 (Luiten et al., 2020).

The essential design choice in SO-HOTA is not to discard this decomposition. Instead, the paper keeps HOTA’s “optimization structure for detection, association, and localization accuracy,” but changes the similarity notion used at the matching stage from IoU to DotD (Kondo et al., 17 Jul 2025). This means SO-HOTA is best understood as a HOTA-family metric with a different admissibility criterion for true positives, rather than as a wholly unrelated evaluation framework.

That continuity matters methodologically. HOTA was introduced precisely because prior metrics such as MOTA and IDF1 overemphasized different parts of the tracking problem, whereas HOTA explicitly balances detection and association (Luiten et al., 2020). SO-HOTA preserves that balance, but adapts the underlying geometric primitive to the small-object regime (Kondo et al., 17 Jul 2025).

3. Formal definition and matching procedure

The core similarity in SO-HOTA is Dot Distance:

$16\times 16$4

where

$16\times 16$5

and $16\times 16$6 is the average size of all objects in the dataset, described as the square root of average box area over all labeled objects (Kondo et al., 17 Jul 2025). DotD therefore measures center proximity relative to a dataset-level characteristic object scale.

A predicted box and a ground-truth box are considered a true positive at threshold $16\times 16$7 when

$16\times 16$8

The paper states that SO-HOTA “follows the same matching procedure as HOTA, using the Hungarian algorithm to assign predicted and ground-truth detections in a one-to-one manner,” with DotD used as the similarity measure instead of IoU (Kondo et al., 17 Jul 2025). The practical consequence is that the matched set, and therefore the downstream TP, FP, FN, TPA, FNA, and FPA counts, are all DotD-defined rather than IoU-defined.

For detection accuracy, the paper defines SO-DetA by replacing IoU-based true positives with DotD-based true positives (Kondo et al., 17 Jul 2025). For association accuracy, it likewise defines SO-AssA by computing the HOTA-style association score over the DotD-defined matched set (Kondo et al., 17 Jul 2025). The per-threshold metric is then

$16\times 16$9

and the final score is

$16\times 16$0

This threshold averaging mirrors standard HOTA’s multi-threshold philosophy, but substitutes DotD for IoU in the matching backbone (Kondo et al., 17 Jul 2025).

The metric therefore changes HOTA primarily at the matching/similarity stage. A plausible implication is that SO-HOTA should be viewed as a DotD-based adaptation of HOTA’s DetA/AssA machinery, not as a new association formalism. The paper is explicit that it does not provide an explicit separate formula for a modified localization-accuracy term, even though it says the method preserves HOTA’s overall optimization structure (Kondo et al., 17 Jul 2025).

4. Behavior in the SMOT4SB challenge

SO-HOTA was the primary ranking criterion in the SMOT4SB challenge: teams were ranked by their highest achieved SO-HOTA score, with public evaluation through CodaBench and private evaluation performed by the organizers on submitted code (Kondo et al., 17 Jul 2025). In addition to SO-HOTA, the challenge also reported conventional HOTA, MOTA, IDF1, Mostly Tracked, and Mostly Lost for reference, alongside the SO-HOTA suite metrics SO-HOTA, SO-DetA, SO-AssA, SO-DetRe, and SO-DetPr (Kondo et al., 17 Jul 2025).

The reported scores illustrate the intended effect of the new metric. On the private test set, the winning DL Team achieved SO-HOTA = 50.59 and HOTA = 36.74, while the baseline scored SO-HOTA = 9.90 and HOTA = 6.51 (Kondo et al., 17 Jul 2025). On the public test set, DL Team achieved SO-HOTA = 54.90 and HOTA = 41.67 (Kondo et al., 17 Jul 2025). The challenge paper interprets the persistent gap between SO-HOTA and standard HOTA as evidence that conventional overlap-based HOTA is harsher in the tiny-object regime, whereas SO-HOTA retains discriminative power under slight localization offsets (Kondo et al., 17 Jul 2025).

The paper’s synthetic displacement analysis clarifies this behavior. When a prediction is vertically displaced by $16\times 16$1 pixels from the ground truth for a box of size $16\times 16$2, IoU falls sharply and reaches zero when overlap disappears, whereas DotD decays smoothly with center distance (Kondo et al., 17 Jul 2025). The corresponding HOTA-versus-SO-HOTA comparison shows HOTA reacting dramatically even to 1-pixel displacement and collapsing once overlap is lost, while SO-HOTA continues to provide graded evaluation based on proximity (Kondo et al., 17 Jul 2025). This is the metric’s main empirical justification.

The challenge results also align with tracker design trends. The paper notes that several top methods moved away from pure IoU for association, instead using adaptive similarity, distance penalties, DIoU, box expansion, or motion compensation (Kondo et al., 17 Jul 2025). This suggests that evaluation and algorithm design converged on the same operational insight: in tiny-object tracking, spatial tolerance is often necessary because overlap may vanish even for semantically correct correspondences.

5. Scope, neighboring literature, and recurrent misreadings

The most common misreading is to treat SO-HOTA as a generic synonym for “HOTA-style tracking” or for strong association performance. That is incorrect. Several MOT papers are relevant to SO-HOTA-oriented literature searches because they report strong HOTA or AssA results, but they do not define SO-HOTA. SearchTrack, for example, is an online MOTS/MOT method whose relevance comes from reporting HOTA, DetA, and AssA and from demonstrating large association gains, especially through motion-aware features, but it does not propose a new higher-order metric (Tsai et al., 2022). Deep HM-SORT is similarly centered on sports MOT and reports strong HOTA and AssA, yet it does not mention SO-HOTA explicitly (Gran-Henriksen et al., 2024). RTAT ranks first on MOT17 and MOT20 in several HOTA-family metrics through a two-stage association design, but again its contribution is a tracker, not an evaluation metric (Guo et al., 2024).

A second misreading is to attribute SO-HOTA to sparse-label long-horizon tracking benchmarks. The multi-camera traffic paper “So you think you can track?” uses standard HOTA terminology and modifies the detection term to

$16\times 16$3

because false positives cannot be counted under sparse GPS-based ground truth, but it explicitly does not define SO-HOTA (Gloudemans et al., 2023). That work motivates a recall-oriented HOTA adaptation for sparse labels, not the DotD-based small-object metric introduced in SMOT4SB.

A third source of confusion is acronym overload. “HOTA” does not uniquely refer to the MOT metric family.

Term	Meaning	Relation to SO-HOTA
HOTA	Higher Order Tracking Accuracy	Metric foundation (Luiten et al., 2020)
SO-HOTA	DotD-based small-object HOTA variant	Topic of SMOT4SB (Kondo et al., 17 Jul 2025)
$16\times 16$4 usage	Recall-oriented HOTA modification under sparse labels	Not named SO-HOTA (Gloudemans et al., 2023)
HOTA-FedGradNorm	Hierarchical Over-the-Air FedGradNorm	Unrelated acronym (Vahapoglu et al., 2022)
HOTA in OT	Hamiltonian framework for Optimal Transport Advection	Unrelated acronym (Buzun et al., 23 Jul 2025)

This terminological ambiguity matters in bibliographic practice. A literature search for “SO-HOTA” can return work on HOTA-family tracking metrics, traffic datasets with modified HOTA components, or entirely unrelated “HOTA” acronyms in federated learning and optimal transport. In the tracking literature represented here, only the SMOT4SB challenge paper explicitly introduces SO-HOTA as a named metric (Kondo et al., 17 Jul 2025).

6. Limitations and methodological implications

The challenge paper does not present SO-HOTA as a universal replacement for HOTA. Several limitations are either stated directly or are structurally apparent. First, SO-HOTA still depends on bounding boxes and still inherits HOTA’s framework, so it does not address annotation ambiguity in object extent or uncertainty beyond box-level correspondence (Kondo et al., 17 Jul 2025). Second, DotD depends only on center distance. Two boxes with similar centers but different sizes or aspect ratios can therefore score highly, which the paper treats as an acceptable trade-off for tiny birds whose center location is more informative than exact extent (Kondo et al., 17 Jul 2025).

Third, the normalization scale $16\times 16$5 is computed globally from all labeled boxes in the dataset, not per-image, per-sequence, or per-instance (Kondo et al., 17 Jul 2025). This makes the metric simple and reproducible, but it also implies that heterogeneous scale distributions may not be perfectly represented by a single characteristic size. Fourth, although the paper states that SO-HOTA preserves HOTA’s optimization structure, it does not formalize a separate SO-localization term; implementers seeking a full analogue of every HOTA submetric would therefore need to infer or design that component themselves (Kondo et al., 17 Jul 2025).

These limitations imply a narrower but clearer interpretation. SO-HOTA is most appropriately understood as a small-object-aware HOTA: it preserves HOTA’s balanced treatment of detection and association, but replaces IoU with DotD in the matching and thresholding logic so that tiny spatial displacements do not cause catastrophic evaluation changes (Kondo et al., 17 Jul 2025). Within that scope, it is not merely a benchmark convenience. It expresses a specific evaluative thesis: for SMOT in UAV bird tracking, especially when boxes are very small and motion is highly dynamic, spatial proximity is often a better primitive than overlap for deciding whether a tracker is “close enough” to deserve credit (Kondo et al., 17 Jul 2025).