Restoring Geometric and Probabilistic Symmetry for Tiny Football Localization in Dynamic Environments

Abstract

The precise identification of minute, high-velocity entities within unconstrained visual fields represents a significant hurdle in computational perception. This difficulty primarily arises from the geometric degradation stemming from scale volatility, motion-induced asymmetry, and heterogeneous background clutter. To mitigate the critical deficit of high-fidelity benchmarks for dynamic micro-targets, we present Soccer-Wild. This comprehensive dataset is characterized by the extreme visual complexity of microscopic objects in diverse ecological settings. Built upon this empirical foundation, we introduce GOAL (Global Object Alignment for Localization). This novel computational paradigm is designed to enhance the weak features of tiny targets by integrating frequency-domain filtering, dynamic feature routing, and entropy-guided probabilistic modeling. The GOAL framework rigorously preserves spatial-structural equilibrium and information fidelity through three synergetic mechanisms: (1) Spectral Purification: We implement a Frequency-aware Spectral Gating approach that operates in the Fourier manifold, suppressing stochastic noise to accentuate the spectral signatures of the targets; (2) Geometric Adaptation: A Multi-Granularity Mixture of Experts (MG-MoE) is formulated with heterogeneous receptive fields to dynamically rectify anisotropic distortions caused by kinetic blurring. This adaptive routing ensures cross-state representation consistency; (3) Information Recovery: We propose Information-Guided Gaussian Distribution Estimation (IGDE), which utilizes information entropy to conceptualize target coordinates as radially symmetric probability densities. This facilitates the implicit recovery of latent signals typically discarded by rigid deterministic regression. Empirical validations on the Soccer-Wild and VisDrone2019 benchmarks reveal that the proposed methodology yields substantial gains in precision. Specifically, our model achieves 40.0% and 40.4% AP (Average Precision), respectively, establishing a new state-of-the-art for localizing highly dynamic, micro-scale objects.

1. Introduction

In modern sports analytics, computer vision has evolved from a supportive tool to a cornerstone technology, powering systems ranging from Video Assistant Referee (VAR) to granular tactical analysis [1,2,3]. At the heart of these applications lies a singular, critical task: the precise localization and tracking of the soccer ball. From a geometric perspective, a soccer ball represents a simple spherical object. However, in unconstrained match footage, this theoretical symmetry is frequently compromised by dynamic environmental factors, posing a formidable challenge to standard object detection paradigms, such as the YOLO series [4,5] and detection transformers [6,7].

The unique difficulty of this task is visually dissected in Figure 1. Unlike standard objects in the COCO dataset, a soccer ball in broadcast footage suffers from severe visual degradations. Specifically, we define geometric degradation as the severe loss of the object’s structural integrity and clear boundaries at extremely low resolutions. This degradation is directly driven by scale volatility, which refers to the rapid and extreme changes in the apparent size of the target (e.g., abruptly oscillating between a few pixels and dozens of pixels) caused by unpredictable camera zooms and fast object movements. As illustrated in Figure 1a, the primary obstacle is the extreme scale variation. In typical wide-angle views, the target occupies fewer than $8\times 8$ pixels. Under such conditions, the hierarchical downsampling inherent in deep neural networks [8] inevitably erodes the target’s structural symmetry, rendering it virtually indistinguishable from background noise. Furthermore, Figure 1b highlights how high-speed motion (e.g., during a powerful shot or long pass) induces severe blur, distorting the ball’s isotropic sphericity into an anisotropic streak, thereby invalidating shape-based geometric priors. This is compounded by complex background interference and occlusion (Figure 1c), where the ball’s visual signature is partially or fully hidden, causing generic detectors to lose the spatiotemporal consistency required for stable tracking.

Compounding these visual challenges is a fundamental data gap. As quantitatively contrasted in Figure 1d, existing benchmarks fail to adequately represent the very tiny regime. While datasets like VisDrone [9] and DOTA [10] have pushed the boundaries of small object detection, their mean object sizes generally hover above 30 pixels. In stark contrast, our proposed Soccer-Wild dataset occupies a distinct distribution space, with a mean object size of only $18.8\pm 15.4$ pixels. This places the vast majority of our instances squarely within the Very Tiny Object Regime, a domain where standard feature extractors struggle to retain spatial-structural information.

To address this fundamental deficiency, we construct Soccer-Wild, a benchmark that serves as a rigorous testbed for micro-object research. With the data gap bridged, the core challenge shifts to the algorithmic domain: how to reconstruct stable geometric representations from a few noisy, blurred pixels? To this end, we propose GOAL (Global Object Alignment for Localization), a unified framework engineered to restore the information symmetry of tiny targets through a purification-adaptation-recovery paradigm.

GOAL systematically tackles the visual degradations highlighted in Figure 1 through three coupled innovations. First, addressing the signal-to-noise ratio bottleneck, we introduce Frequency-aware Spectral Gating (SG) for background noise suppression. This module operates in the Fourier domain to globally disentangle high-frequency target signals from low-frequency background redundancies, acting as a signal purifier that preserves the intrinsic spectral symmetry of the ball. Second, to resolve the motion-induced distortion, we design a Multi-Granularity Mixture of Experts (MG-MoE) for adaptive feature refinement. By dynamically routing features to heterogeneous experts—Focus Experts for sharp details and Context Experts for blurred trajectories—this module ensures adaptive feature alignment across varying velocity states. Finally, to counter feature erosion, we propose Information-Guided Gaussian Distribution Estimation (IGDE) for probabilistic target localization. Moving beyond rigid bounding box regression, IGDE leverages Information Entropy theory [11] to model the ball as a probabilistic Gaussian distribution. This approach implicitly recovers the probabilistic symmetry of the target position, capturing weak signals that are otherwise discarded by deterministic thresholding.

In summary, our main contributions are:

• We introduce Soccer-Wild, the first large-scale, high-precision dataset dedicated to the Very Tiny Object Regime, providing a new foundation for studying geometric perception limits in the wild.
• We propose the GOAL framework, which integrates spectral gating, dynamic expert routing, and entropy-guided estimation to maintain feature consistency and solve the dilemmas of scale erosion and motion-induced asymmetry.
• Extensive experiments demonstrate that GOAL establishes a new state-of-the-art on both Soccer-Wild and VisDrone2019, significantly outperforming generic detectors in localizing tiny, dynamic targets through enhanced representation alignment.

2. Related Work

2.1. Feature Enhancement for Tiny Objects

Tiny object detection [12] is fundamentally constrained by the feature erosion phenomenon, where objects occupying few pixels (e.g., <$16\times 16$) lose their semantic information during the hierarchical downsampling of deep networks [13,14]. Early solutions focused on multi-scale feature fusion. FPN [15] and its variants like PANet [16] and BiFPN [17] established the baseline by constructing pyramidal pathways to propagate high-resolution details. To further alleviate the semantic gap, DetectoRS [18] introduced recursive feature pyramids with switchable atrous convolution. However, these spatial-domain methods often amplify background noise when upsampling low-level features, which is detrimental for distinguishing soccer balls from field textures.

Recent advances have shifted towards frequency-domain learning and dynamic representations. Recognizing that tiny objects manifest as high-frequency signals, Global Filter Networks [19] demonstrated the efficacy of learning global filters in the Fourier domain. This paradigm has been extended to object detection by MSF-DETR [20], which utilizes spectral gating to separate targets from clutter, aligning with our Spectral Gating strategy. Furthermore, addressing the challenge of variable motion blur in sports, dynamic neural networks have gained prominence. Mixture of Experts (MoE) [21,22], originally successful in NLP, has been adapted to vision tasks to scale model capacity. Sparse MoE [23] and Soft MoE [24] enable adaptive computation by routing tokens to specialized experts. However, adapting such mechanisms to explicitly disentangle the representations of sharp versus severely blurred tiny targets remains a perspective largely unexplored in previous generic detectors.

2.2. Regression-Based vs. Distribution-Aware Localization

Standard detectors typically formulate localization as a deterministic bounding box regression task, assuming that object boundaries are crisp and discernible. However, in the tiny object regime (e.g., <$8\times 8$ pixels), this “hard” regression paradigm becomes ill-posed. The extreme sensitivity of the Intersection over Union (IoU) metric means that a positional deviation of merely one or two pixels can cause the IoU to plummet to zero, leading to the collapse of label assignment in anchor-based detectors [25]. To mitigate this sensitivity, the field has gravitated towards distribution-aware modeling. NWD (Normalized Wasserstein Distance) [26] pioneered this shift by modeling objects as 2D Gaussian distributions and utilizing optimal transport theory to measure similarity, fundamentally relaxing the strict overlap requirements of IoU. Building on this, RFLA [27] introduced Gaussian receptive field priors to re-weight anchor assignment, acknowledging the spatial uncertainty inherent in tiny targets.

Beyond label assignment, the regression loss function itself has evolved from ensuring geometric alignment to optimizing probability distributions. Generalized Focal Loss (GFL) [28] bridged the gap between classification and localization by learning discrete probability distributions for box edges, effectively modeling the uncertainty of ambiguous boundaries. LD [29] further advanced this by integrating localization distillation, transferring the “dark knowledge” of distribution from teacher to student networks.

Most recently, information-theoretic approaches have emerged as a powerful frontier for recovering eroded features. DCEDet [30] employed dual-contrast mechanisms to enhance weak feature responses. Notably, PFIM [31] proposed an information entropy-driven framework that unsupervisedly mines information-rich regions to estimate position distributions. Resonating with this entropy-based philosophy, applying these concepts to dynamic sports scenarios presents a unique challenge. Existing methods like PFIM primarily operate on static features. When visual cues are severely smeared by motion blur or partially occluded, there is a critical need for frameworks that can integrate entropy priors with dynamic feature routing. Developing robust probabilistic models that can recover weak representations without relying on explicit trajectory supervision remains an open problem in this domain.

2.3. Benchmarks for Tiny and Dynamic Scenarios

Data drives the evolution of detection algorithms. In the general domain of tiny object detection, benchmarks like VisDrone [32] and AI-TOD [33] have catalyzed significant progress. However, these datasets are predominantly sourced from aerial platforms, characterized by a birds-eye viewpoint and targets that are mostly rigid (e.g., vehicles) with relatively stable motion patterns. SODA [34] offers a large-scale benchmark for small objects, yet it lacks the high-velocity motion blur and complex occlusion dynamics inherent in ground-level sports footage, creating a substantial domain gap when transferring these models to athletic scenes.

In the specific domain of sports analytics, SoccerNet [35,36] stands as the premier ecosystem for action spotting and replay grounding. While its recent extension, SoccerNet-v3 [37], introduces tracking tasks, the annotations are often temporally sparse or centered on player trajectories, lacking the dense, pixel-level spatial supervision required to train high-precision regression heads for tiny balls. Other datasets, such as FootAndBall [38], are constrained by limited scale and diversity, failing to capture the in-the-wild variability of weather and lighting. Consequently, the field lacks a benchmark that simultaneously challenges detectors with extreme scale degradation, non-stationary motion, and severe background interference. To bridge this critical gap, we introduce Soccer-Wild, a large-scale dataset with high-precision annotations specifically curated for tiny ball detection in unconstrained environments, providing a rigorous testbed to push the boundaries of dynamic micro-object perception.

3. Proposed Method

In this section, we present GOAL, a unified framework specifically designed for the robust localization of tiny, dynamic soccer balls by restoring their representation consistency. At a high level, GOAL operates as an end-to-end Transformer-based detector. Its main structure consists of a dual-stream backbone for initial feature extraction, a hybrid encoder-decoder for filtering noise and adaptively refining features, and a prediction head that estimates the target’s location as a probabilistic heatmap. We first reformulate the tiny object detection task as a probabilistic estimation problem under conditions of geometric symmetry breaking caused by signal degradation. Subsequently, we detail the core architectural components: Frequency-aware Spectral Gating, Multi-Granularity Mixture of Experts, and Information-Guided Gaussian Distribution Estimation.

3.1. Problem Formulation and Overall Architecture

Problem Formulation. Let $\mathcal{I}\in {\mathbb{R}}^{H\times W\times 3}$ denote an input video frame from a broadcast soccer match, and $\mathcal{B}={\left\{b_i\right\}}_{i=1}^N$ be the set of ground-truth states, where each $b_i=(x_i,y_i,w_i,h_i)$ represents the center coordinates and scale. In our context, targets are characterized by extreme sparsity and minimal spatial support ($\sqrt{w_i{h}_i}\le 16$ pixels), leading to a vanishing signal-to-noise ratio (SNR).

Standard detectors typically assume a deterministic mapping ${\mathcal{F}}_{\theta }:\mathcal{I}\to \widehat{\mathcal{Y}}$. However, this mapping degenerates when the target’s rotational symmetry is distorted into an anisotropic blur $\mathcal{S}$ or submerged in background noise $\eta$. We thus formulate the task as the recovery of the latent target distribution $\mathcal{P}$ from a corrupted observation:

$${\mathcal{I}}_{obs}=\mathcal{T}(\mathcal{P}\otimes \mathcal{K})+\eta$$

(1)

where $\mathcal{K}$ represents the motion-induced blur kernel that breaks the target’s spatial symmetry, and $\mathcal{T}$ denotes the downsampling transformation. To solve this ill-posed inverse problem, we decompose the detection process into three sequential phases: spectral purification, adaptive representation, and probabilistic recovery.

Overall Architecture. As illustrated in Figure 2, the GOAL framework operates in a coarse-to-fine manner, employing three strategic modules to maintain feature invariance across varying environmental conditions:

• Signal Enhancement Phase (Spectral Purification): Before hierarchical feature extraction, the raw image $\mathcal{I}$ is processed by the Frequency-aware Spectral Gating (SG) module. By transforming the spatial signal into the Fourier domain $\mathcal{F}\left(\mathcal{I}\right)$, SG applies a learnable global mask $\mathcal{M}$ to filter out low-frequency background redundancies while amplifying high-frequency components that represent the target’s structural singularities. This yields a spectral-enhanced tensor ${\mathcal{I}}^{\prime }$ with restored signal-background balance.
• Dynamic Representation Phase (Motion Adaptation): We adopt a hierarchical backbone to extract multi-scale features. To adapt to the ball’s transition from static states to high-speed streaks (which represent a shift from isotropic to anisotropic geometry), we implement a Multi-Granularity Mixture of Experts (MG-MoE). A gating network $G(·)$ dynamically routes features to specific experts $E_k(·)$ with heterogeneous receptive fields, ensuring that features of different granularities are aligned into a consistent latent space.
• Information Recovery Phase (Probabilistic Alignment): The detection head employs the Information-Guided Gaussian Distribution Estimation (IGDE) module. Instead of regressing deterministic coordinates which are sensitive to noise, IGDE leverages Information Entropy $H\left(\mathbf{F}\right)$ to mine informative regions. It models the ball’s position as a radially symmetric 2D Gaussian distribution $\mathcal{N}(\mu ,\Sigma )$, thereby recovering the target’s probabilistic center even when the visual evidence is partially eroded.

The entire framework is optimized end-to-end using a composite loss function ${\mathcal{L}}_{total}$, ensuring that the model learns to maintain structural consistency from the spectral input to the final probabilistic output.

3.2. Frequency-Aware Spectral Gating

In the spatial domain $\mathcal{I}(x,y)$, a tiny soccer ball often manifests as a discrete impulse signal with minimal spatial support, while the playing pitch presents a continuous, wide-range texture pattern. Standard Convolutional Neural Networks (CNNs), constrained by local receptive fields, struggle to distinguish the target impulse from background noise when their intensities are similar. To overcome this, we introduce the Frequency-aware Spectral Gating (SG) module (Figure 3). By projecting features into the frequency domain, we obtain a global receptive field that inherently captures long-range dependencies [39]. Unlike local spatial operations, this spectral projection allows for the explicit and global decoupling of periodic background noise from sparse target signals. Leveraging this property, we observe that the soccer ball, characterized by sharp edges, dominates the high-frequency spectrum, whereas the homogeneous grass texture exhibits a concentration in the low-frequency domain with global translational symmetry.

Formulation. Let $X\in {\mathbb{R}}^{H\times W\times C}$ denote the input feature tensor. The SG module restores the signal-to-noise balance through three sequential steps:

(1) Spectral Transformation. We first apply a 2D Fast Fourier Transform (FFT) to convert the spatial feature X into its spectral representation $\mathcal{Z}$. Leveraging the Hermitian symmetry of the Fourier transform for real-valued signals, we utilize the Real-FFT (RFFT) to ensure computational efficiency without loss of information:

$$\mathcal{Z}(u,v)=\mathcal{F}\left(X\right)(u,v)=\sum _{h=0}^{H-1}\sum _{w=0}^{W-1}X(h,w)e^{-j2\pi (\frac{uh}{H}+\frac{vw}{W})}$$

(2)

where $\mathcal{Z}\in {\mathbb{C}}^{H\times (\frac{W}{2}+1)\times C}$ represents the complex-valued spectrum. In this domain, each frequency coordinate $(u,v)$ encapsulates global spatial information, effectively transforming the local convolutional bias into a global structural perspective.

(2) Global Gating and Symmetry Filtering. To suppress background redundancies, we introduce a learnable global filter $\mathcal{G}\in {\mathbb{C}}^{H\times (\frac{W}{2}+1)\times C}$. This filter acts as a frequency-domain mask that modulates the spectrum via element-wise multiplication:

$$\tilde{\mathcal{Z}}=\mathcal{Z}\odot \mathcal{G}$$

(3)

where ⊙ denotes the Hadamard product. Unlike spatial filters, $\mathcal{G}$ learns to adaptively adjust the spectral weights, assigning lower values to frequencies associated with repetitive background patterns (which exhibit periodic symmetry) and higher weights to the non-redundant high-frequency components of the soccer ball.

(3) Spatial Reconstruction and Residual Alignment. Finally, the modulated spectrum $\tilde{\mathcal{Z}}$ is transformed back to the spatial domain via the Inverse FFT (IFFT), ensuring the restoration of spatial–temporal consistency:

$$\tilde{X}={\mathcal{F}}^{-1}(\tilde{\mathcal{Z}})=\mathrm{Real}(\sum _{u=0}^{H-1}\sum _{v=0}^{W-1}\tilde{\mathcal{Z}}(u,v)e^{j2\pi (\frac{uh}{H}+\frac{vw}{W})})$$

(4)

To facilitate gradient flow and maintain the structural equilibrium of the features, we implement a residual connection followed by Layer Normalization:

$$Y=\mathrm{LayerNorm}(X+\tilde{X})$$

(5)

By integrating this global frequency gating mechanism, the framework ensures that subsequent layers operate on purified signal representations where the target’s geometric saliency is significantly amplified against the background clutter.

3.3. Multi-Granularity Mixture of Experts

Following spectral enhancement, the feature maps contain amplified target signals. However, a critical challenge remains: the non-stationary geometric state of the target. As established in Section 1, high-speed motion distorts the target from a static, symmetric sphere into an anisotropic motion streak. Standard Convolutional Neural Networks (CNNs), constrained by fixed $3\times 3$ kernels, exhibit a rigid inductive bias that fails to adapt to these morphological transitions.

To address this, we propose the Multi-Granularity Mixture of Experts (MG-MoE) module. Unlike standard MoEs that focus on parameter scaling, MG-MoE is designed to achieve structural adaptation across varying receptive fields. As depicted in Figure 4, we replace the static feed-forward layers with a dynamic routing mechanism that dispatches features to heterogeneous experts, effectively restoring the representational balance across different motion dynamics.

Formulation. Let $F_{in}\in {\mathbb{R}}^{H\times W\times C}$ be the input feature tensor. The MG-MoE consists of a Gating Network $\mathcal{G}$ and a set of N experts $\mathcal{E}=\{E_1,\dots ,E_N\}$. The output $F_{out}$ is formulated as a weighted combination:

$$F_{out}=\sum _{k=1}^N\mathcal{G}{\left(F_{in}\right)}_k·E_k\left(F_{in}\right)$$

(6)

where $\mathcal{G}{\left(F_{in}\right)}_k$ represents the routing weight for the k-th expert, satisfying ${\sum }_{k=1}^N\mathcal{G}{\left(F_{in}\right)}_k=1$.

Heterogeneous Expert Design. To disentangle the representation of sharp versus blurred targets—thereby addressing the isotropic-anisotropic transition—we construct two distinct categories of experts:

• Focus Experts ($E_{focus}$): Optimized for local geometric conservation. These experts utilize Depthwise Convolutions with a small $3\times 3$ kernel, ensuring the extraction of fine-grained textures and the preservation of the ball’s inherent rotational symmetry during static or slow-moving states.
• Context Experts ($E_{context}$): Optimized for structural recovery under deformation. To compensate for the “broken” local features caused by motion blur or occlusion, these experts employ Dilated Convolutions with a larger receptive field. This design allows the network to capture the global spatiotemporal context (e.g., motion trajectories), enabling the inference of the ball’s position even when its local symmetry is severely eroded.

Dynamic Routing and Symmetry Alignment. The Gating Network $\mathcal{G}$ acts as a state-aware controller. It analyzes the statistical variance of the input features to determine the degree of target deformation:

$$\mathcal{G}\left(F_{in}\right)=\mathrm{Softmax}(W_g·\mathrm{GlobalAvgPool}\left(F_{in}\right)+b_g)$$

(7)

By adaptively assigning weights between $E_{focus}$ and $E_{context}$, the MG-MoE ensures that the feature representation remains invariant to motion-induced distortions, effectively aligning diverse visual states into a unified, robust latent space.

3.4. Information-Guided Gaussian Distribution Estimation (IGDE)

While MG-MoE enhances dynamic feature representation, a fundamental bottleneck persists at the detection head: Feature Erosion. As the spatial resolution decreases, a tiny soccer ball often collapses into a single pixel or vanishes due to quantization. Standard detection heads employing Deterministic Bounding Box Regression are inherently unstable in this regime, as minor pixel deviations cause gradient explosion. To resolve this, we propose the IGDE module (Figure 5), which shifts the paradigm from deterministic regression to probabilistic distribution estimation, guided by self-guided information mining. Specifically, a Gaussian distribution is inherently suited for this micro-regime: rather than forcing the prediction of ambiguous rigid boundaries, its peak identifies the most likely object center, while its variance smoothly absorbs the spatial uncertainty caused by feature erosion and motion blur. This module aims to restore the probabilistic symmetry of the target position.

The IGDE module operates on the encoded features $F\in {\mathbb{R}}^{H^{\prime }\times W^{\prime }\times C}$ through two coupled streams:

(1) Entropy-driven Information Mining. Drawing from Shannon’s Information Theory, salient targets (soccer balls) represent high-information, low-probability events against a redundant background. We employ a lightweight estimator ${\Phi }_{info}$ to predict the pixel-wise mean $\mu$ and standard deviation $\sigma$, where the predicted scale map $\sigma$ effectively serves as an Information Map ${\mathcal{M}}_{info}$. This map acts as a “soft attention mask” that highlights regions with high entropy, recovering weak signals by maintaining a balance between expected and observed signal intensity.

(2) Position Gaussian Prediction. Guided by ${\mathcal{M}}_{info}$, we explicitly model the ball’s position as a radially symmetric 2D Gaussian distribution. Instead of regressing discrete coordinates, we predict a heatmap $\mathcal{P}\in {[0,1]}^{H^{\prime }\times W^{\prime }}$. The ground-truth heatmap ${\mathcal{Y}}_{gt}$ is formulated by a Gaussian kernel centered at $(c_x,c_y)$:

$${\mathcal{Y}}_{gt}(x,y)=exp\left(-{\displaystyle \frac{{(x-c_x)}^2+{(y-c_y)}^2}{2{\sigma }_{adapt}^2}}\right)$$

(8)

where ${\sigma }_{\mathrm{adapt}}=min(w,h)/3$ is an adaptive radius dynamically scaled by the target’s spatial dimensions. This formulation ensures that the target representation possesses isotropic spatial support, making the optimization invariant to small quantization errors. The final prediction is conditioned on the fused information prior:

$$\mathcal{P}={\Phi }_{pos}\left([F;{\mathcal{M}}_{info}]\right)$$

(9)

Optimization Objective. The IGDE module is optimized using a weighted Mean Squared Error (MSE) loss for Gaussian prediction, balanced with an Information Entropy loss ${\mathcal{L}}_{ent}$:

$${\mathcal{L}}_{\mathrm{IGDE}}=\sum _{x,y}{\omega }_{x,y}{|\mathcal{P}(x,y)-{\mathcal{Y}}_{\mathrm{gt}}(x,y)|}^2+\lambda {\mathcal{L}}_{\mathrm{ent}}$$

(10)

where ${\omega }_{x,y}$ addresses the extreme foreground-background imbalance. By modeling the ball as a probabilistic density function with inherent spatial symmetry, the network retains a spatially smoothed belief distribution, ensuring robust recall even when the exact pixel location is ambiguous.

4. The Soccer-Wild Benchmark

4.1. Data Collection and Annotation

Data Collection. To construct a robust benchmark reflecting the complexity of real-world sports production, we adhered to the “In-the-Wild” principle. Instead of relying on static surveillance cameras or drones, we aggregated raw footage from diverse public broadcast sources, covering over 20 different leagues (e.g., Premier League, La Liga) and varying tournament levels. This ensures a rich semantic diversity in terms of: (1) Environmental Conditions: Ranging from sunny days with hard shadows to rainy nights with reflections; (2) Viewpoints: Including high-angle panoramic views, dynamic zoom-in shots, and spider-cam perspectives; (3) Background Clutter: Encompassing various pitch patterns, advertising boards, and crowded penalty areas.

Data Annotation. To guarantee precision for micro-object evaluation, we implemented a rigorous Human-in-the-Loop annotation pipeline using CVAT (Computer Vision Annotation Tool) tailored for tiny, high-speed targets. Unlike standard datasets that rely heavily on interpolation, we enforced frame-by-frame manual verification to capture non-linear motion trajectories caused by collisions or rebounds. First, a dedicated team of trained sports video analysts manually drew tight bounding boxes around the soccer ball in keyframes. Then, a tracker generated pseudo-labels for adjacent frames, which were subsequently refined by human verifiers. To ensure high inter-annotator agreement, a secondary blind review was enforced on a 20% validation split, resolving any boundary discrepancies via panel consensus. To address the Motion Blur challenge, we adopted a consistent annotation strategy where the bounding box is adjusted to cover the visible region of the target, ensuring that the model learns to recognize robust motion patterns. In cases of full occlusion, the target is marked as invisible to prevent noisy supervision. In total, the annotation process involved significant manual effort, resulting in a high-fidelity ground truth set.

4.2. Comparison with Existing Benchmarks

As quantitatively detailed in

Table 1. Comparison of Soccer-Wild with existing object detection datasets.

Dataset	Pub.	Year	Image Height	Image Count	Type	Object Size
MS COCO [41]	ECCV	2014	800–1333	163,957	HBB	$99.5\pm 107.5$
DIOR [42]	P&RS	2020	800	23,463	HBB	$65.6\pm 91.7$
DIOR-R [42]	P&RS	2020	800	23,463	OBB	$57.7\pm 80.2$
DOTA-v1.0 [10]	CVPR	2018	800–13,000	2423	H/OBB	$55.3\pm 63.1$
VisDrone [9]	ICCVW	2018	2000	8629	HBB	$35.8\pm 32.8$
xView [43]	arXiv	2018	3000	1127	HBB	$34.9\pm 39.9$
DOTA-v1.5 [40]	TPAMI	2019	800–13,000	2423	H/OBB	$34.0\pm 47.8$
DOTA-v2 [40]	TPAMI	2021	800–13,000	11,268	H/OBB	$24.8\pm 32.6$
VEDAI (512) [44]	JVCIR	2015	512, 1024	1210	HBB	$33.4\pm 11.3$
SODA-D [12]	TPAMI	2023	3407	24,828	OBB	$25.4\pm 10.0$
Soccer-Wild (ours)	-	2026	416–1080	14,773	HBB	$18.8\pm 15.4$

, Soccer-Wild establishes a distinct benchmark frontier that diverges significantly from existing generic and aerial datasets. Firstly, regarding the absolute scale, while datasets like VisDrone [9] and DOTA-v2 [40] have pushed the envelope for small object detection, their average object sizes hover around 35.8 and 24.8 pixels, respectively. In stark contrast, Soccer-Wild targets a much more aggressive “micro-object” regime with an average size of only 18.8 pixels. This nearly 50% reduction in spatial support implies that most targets in our dataset lack sufficient distinct textures for standard CNNs, making feature erosion a dominant challenge rather than an edge case. Secondly, regarding scale variation, the standard deviation of ±15.4 pixels—comparable in magnitude to the mean itself—indicates extreme scale volatility. Unlike aerial surveillance where objects maintain relatively consistent scales due to fixed flight altitudes, broadcast footage involves frequent zooming and camera movements, demanding detectors to handle dramatic resolution shifts within the same domain. Finally, unlike SoccerNet-v3 [37] which focuses on sparse action spotting or trajectory points, Soccer-Wild provides dense, pixel-level Horizontal Bounding Boxes (HBB). This dense supervision is critical for training regression-based detectors (like GOAL) to learn precise localization and shape estimation under severe motion blur, a capability unattainable with point-level supervision.

5. Experiments

5.1. Datasets

To comprehensively evaluate the performance and generalization capability of GOAL, we conducted experiments on two distinct benchmarks. The primary evaluation is performed on our proposed Soccer-Wild (see Section 4), which contains 14,773 images with high-precision annotations. This dataset is specifically designed to challenge detectors in the “micro-dynamic” regime, featuring extreme scale variations and significant motion blur (30% of instances) typical of complex sports environments. To further validate the model’s versatility beyond the sports domain, we extend our evaluation to VisDrone2019 [9], a widely recognized large-scale benchmark for aerial detection. It comprises 8629 high-resolution images ($2000\times 1500$) covering 10 categories. While VisDrone targets predominantly rigid and stable objects (e.g., vehicles), testing on this standard benchmark verifies that GOAL’s architectural advantages in feature enhancement are generalizable to generic tiny object detection tasks.

5.2. Implementation Details

Implementation Details. We implemented the GOAL framework using PyTorch 2.7.0 and Python 3.11 on an Ubuntu 24.04 workstation equipped with NVIDIA 5090 GPUs (CUDA 12.8). The model input resolution is set to $640\times 640$. For the architecture, we employ a DINOv3-Tiny backbone (embedding dimension of 192 and 3 attention heads) initialized with distilled weights to extract multi-scale features, followed by our proposed Hybrid SG-MG-MoE Encoder and a 4-layer Transformer Decoder with 300 object queries. The network is trained for a total of 132 epochs with a global batch size of 32 using the AdamW optimizer. The initial learning rate is set to $1\times {10}^{-4}$ for the encoder-decoder and $2.5\times {10}^{-5}$ for the backbone, with a weight decay of $1\times {10}^{-4}$. We utilize a Flat-Cosine learning rate schedule, where the learning rate remains constant for the first 64 epochs before decaying. Regarding data augmentation, we adopt a robust “strong-to-weak” strategy: rigorous augmentations including Mosaic (prob = 1.0), Mixup (prob = 0.5), and CopyBlend (prob = 0.5) are applied during the initial training phase to enhance sample diversity, but are disabled in the final 12 epochs to ensure precise convergence. The objective function is a weighted combination of losses, with coefficients set to ${\lambda }_{cls}=2.0$, ${\lambda }_{bbox}=5.0$, ${\lambda }_{giou}=2.0$, and the proposed IGDE loss weight ${\lambda }_{igde}=1.0$. During inference, all evaluations are strictly conducted at a single scale ($640\times 640$) without employing any Test-Time Augmentation (TTA). The top-300 queries are selected based on confidence scores without requiring additional Non-Maximum Suppression (NMS).

5.3. Evaluation Metrics

To provide a comprehensive and rigorous assessment of the proposed GOAL framework, we employ a multi-dimensional evaluation protocol covering both detection accuracy and computational efficiency.

Detection Accuracy Metrics. We adopt the standard COCO evaluation protocol [41] to quantify detection performance. The foundation of our evaluation lies in the confusion matrix metrics: Precision (P) and Recall (R). Precision measures the accuracy of positive predictions, while Recall quantifies the model’s ability to retrieve all positive instances. They are mathematically formulated as:

$$P={\displaystyle \frac{TP}{TP+FP}},R={\displaystyle \frac{TP}{TP+FN}}$$

(11)

where $TP$, $FP$, and $FN$ denote the number of True Positives, False Positives, and False Negatives, respectively.

To evaluate overall performance, we calculate the Average Precision ($AP$), which represents the area under the Precision–Recall (PR) curve. For a specific class, $AP$ is defined as the integral of precision at varying recall levels:

$$AP={\int }_0^{1}P\left(R\right)dR$$

(12)

In practice, the Mean Average Precision (mAP) is calculated by averaging $AP$ across all categories and multiple Intersection over Union (IoU) thresholds. This is expressed as:

$$mAP={\displaystyle \frac{1}{N_{cls}}}\sum _{i=1}^{N_{cls}}\left({\displaystyle \frac{1}{K}}\sum _{j=1}^{K}A{P}_{i,Io{U}_j}\right)$$

(13)

where $N_{cls}$ represents the number of categories and $K=10$ corresponds to the IoU thresholds ranging from 0.50 to 0.95 with a step of 0.05. In our experiments, we report three key indicators: the mean Average Precision (mAP or $A{P}_{50:95}$), which serves as the primary metric reflecting overall robustness across different localization strictness levels; $A{P}_{50}$, which measures the model’s basic detection capability at a single IoU threshold of 0.50; and $A{P}_{75}$, which highlights high-precision localization performance critical for tiny objects at a stricter IoU threshold of 0.75.

Efficiency Metrics. To assess the practical feasibility of GOAL for real-time deployment in sports broadcasting, we evaluate model complexity and speed using three primary metrics. First, we report the total number of learnable parameters (Params in millions) to indicate the spatial complexity and storage requirement of the model. Second, we calculate Giga Floating-point Operations Per Second (GFLOPs) to represent the theoretical computational cost required to process a single image. Finally, we measure Frames Per Second (FPS) to evaluate the actual inference speed on a single NVIDIA RTX 4090 GPU with a batch size of 1, encompassing the latency of both network inference and post-processing steps.

5.4. Comparison with State-of-the-Art

To strictly validate the effectiveness of GOAL, we conducted comprehensive comparative experiments against representative detectors, ranging from classic frameworks to the latest real-time YOLO series and Transformer-based models, including a wide array of recent post-2023 state-of-the-art methods specialized for efficient detection (e.g., YOLOv10-v12, D-FINE, DEIM) and tiny object perception (e.g., Drone-DETR and the recently proposed DAU-YOLO [45]).

Performance on Soccer-Wild. As reported in

Table 2. Benchmarking results on the proposed Soccer-Wild test set. The best results are highlighted in bold, and the second best are underlined.

Method	Year	Pub.	Backbone	Params (M)	GFLOPs	mAP	AP50	AP75
FRCNN [48]	2015	ICCV	ResNet-50	41.35	185.50	27.45	49.80	26.10
SSD [49]	2016	ECCV	VGG-16	26.28	61.32	19.85	38.50	18.20
YOLOv5 [50]	2020	Github	CSPDarknet	9.12	24.04	24.80	52.43	23.38
YOLOv6 [51]	2022	arXiv	CSPDarknet	16.31	44.21	30.43	55.47	28.06
YOLOv8 [52]	2023	Github	CSPDarknet	11.14	28.65	30.93	61.05	25.77
YOLOv9 [53]	2024	ECCV	GELAN	7.29	27.39	28.22	54.03	19.03
YOLOv10 [54]	2024	NeurIPS	CSPDarknet	8.07	24.77	30.82	58.86	24.94
YOLO11 [55]	2024	Github	-	9.43	21.55	28.63	56.38	21.20
YOLOv12 [56]	2025	NeurIPS	R-ELAN	9.25	21.52	28.80	54.25	23.77
YOLO26 [57]	2026	arXiv	-	9.95	22.50	31.25	60.41	25.38
RT-DETR [7]	2024	CVPR	ResNet-50	42.76	130.47	27.66	55.23	22.16
D-FINE [46]	2025	ICLR	ResNet-50	9.85	24.50	31.95	61.50	27.10
DEIM [47]	2025	CVPR	ResNet-50	10.23	20.55	32.6	71.5	25.7
GOAL (Ours)	-	-	MG-MoE	12.41	29.66	40.0	77.9	33.9

, generic real-time detectors struggle significantly in the proposed micro-dynamic regime. While the latest iterations of the YOLO family (e.g., YOLOv10, YOLO11, and the YOLO26) have optimized efficiency, their accuracy hits a bottleneck around 31% mAP, primarily due to the loss of fine-grained features during downsampling. Recent DETR-based methods like D-FINE [46] and DEIM [47] show improved performance by leveraging global context, achieving 31.95% and 32.6% mAP, respectively.

In stark contrast, GOAL establishes a new state-of-the-art with an mAP of 40.0%, outperforming the second-best DEIM by a substantial margin of +7.4%. Most notably, under the strict localization threshold of $A{P}_{75}$, GOAL achieves an 8.2% improvement (33.9% vs. 25.7%). This qualitative leap confirms that our IGDE module effectively mitigates the “feature erosion” problem, allowing for precise bounding box regression even when the target is blurred or occluded.

Efficiency-Accuracy Trade-off. Beyond raw accuracy, GOAL maintains a highly competitive inference efficiency. As shown in Table 2, our model requires only 12.41 M parameters and 29.66 GFLOPs.Compared to heavy-weight transformer models like RT-DETR-R50 (42.76 M Params, 130 GFLOPs), GOAL achieves a +12.34% accuracy gain while requiring less than 30% of the computational cost. Although slightly heavier than the nano-scale YOLOv8/v9 models, the dramatic performance improvement justifies the marginal increase in complexity, making GOAL well-suited for high-performance sports analytics where precision is paramount.

Generalization on VisDrone2019. To verify that our improvements are not limited to specific ball features, we further evaluated GOAL on the general-purpose VisDrone2019 benchmark. As detailed in

Table 3. Quantitative comparison with state-of-the-art detectors on the VisDrone2019 benchmark.

Method	Year	Pub.	Backbone	AP95	AP50	FPS
FRCNN [48]	2015	ICCV	Hourglass	21.8	41.8	17
CornerNet [58]	2018	ECCV	ResNet-50	17.4	34.1	-
ARFP [59]	2022	Appl. Intell.	ResNet-50	20.4	33.9	-
DMNet [60]	2020	CVPRW	ResNet-50	29.4	49.3	-
DSHNet [61]	2021	WACV	ResNet-50	30.3	51.8	-
CRENet [62]	2020	ECCV	ResNet-50	33.7	54.3	-
YOLOv5 [50]	2020	GitHub	CSPDarknet	21.9	42.3	85
YOLOv7 [63]	2023	CVPR	CSPDarknet	23.0	41.1	55
TPH-YOLOv5 [64]	2021	ICCV	CSPDarknet	23.1	41.5	25
YOLOv8 [52]	2023	GitHub	CSPDarknet	25.5	42.1	90
HIC-YOLOv5 [65]	2024	ICRA	CSPDarknet	26.0	44.3	-
YOLO-DCTI [66]	2023	Remote Sens.	CSPDarknet	27.4	49.8	15
Drone-YOLO-L [67]	2023	Drones	CSPDarknet	31.9	51.3	-
DAU-YOLO-L [45]	2025	Remote Sens.	CSPDarknet	-	43.8	24.6
Deformable-DETR [68]	2020	arXiv	ResNet-50	27.1	43.1	19
RT-DETR [7]	2024	CVPR	ResNet-50	27.7	45.8	76
Drone-DETR [69]	2024	Sensor	ResNet-50	33.9	53.9	30
GOAL (Ours)	2026	-	MG-MoE	40.4	55.1	28

, GOAL continues to dominate, achieving 40.4% AP, significantly surpassing specialized aerial detectors such as Drone-DETR (33.9%) and TPH-YOLOv5 (23.1%).While some lightweight YOLO variants achieve higher FPS (e.g., YOLOv8 at 90 FPS), their detection capability for dense, tiny crowds is far inferior. GOAL maintains a real-time speed of 28 FPS, striking an optimal balance between accuracy and speed for complex surveillance scenarios.

5.5. Ablation Studies

In this section, we perform a comprehensive ablation analysis to evaluate the effectiveness of the proposed GOAL framework. Specifically, we aim to dissect the individual contribution of each core component—Spectral Gating, MG-MoE, and IGDE—and verify their synergistic effects in the micro-dynamic regime. Furthermore, we investigate the impact of critical architectural designs and hyperparameter settings to justify our optimal configuration. Unless otherwise specified, all experiments are conducted on the Soccer-Wild dataset, employing the ResNet-50 based DEIM [47] as the baseline detector.

5.5.1. Contribution of Individual Components

As shown in

Table 4. Component-wise effectiveness analysis on the Soccer-Wild dataset. SG: Spectral Gating; MG-MoE: Multi-Granularity Mixture of Experts; IGDE: Information-Guided Gaussian Distribution Estimation. The baseline is DEIM [47] with a ResNet-50 backbone.

Exp.	SG	MG-MoE	IGDE	mAP	AP50	AP75
1	-	-	-	32.6	71.5	25.7
2	✔	-	-	36.4 (+3.8)	75.2 (+3.7)	29.8 (+4.1)
3	✔	✔	-	38.2 (+5.6)	76.5 (+5.0)	32.1 (+6.4)
4	✔	-	✔	38.9 (+6.3)	77.1 (+5.6)	32.9 (+7.2)
5	✔	✔	✔	40.0 (+7.4)	77.9 (+6.4)	33.9 (+8.2)

, each proposed module addresses a specific bottleneck in the micro-dynamic regime. Integrating the Spectral Gating (SG) module (Exp. 2) delivers an immediate gain of +3.8% mAP over the baseline, validating that frequency-domain filtering effectively enhances the signal-to-noise ratio by suppressing background texture. Building on this, the MG-MoE module (Exp. 3) further boosts performance to 38.2% mAP, confirming that dynamic expert routing successfully adapts to varying motion states—such as motion blur—that static backbones struggle to resolve. Most notably, the IGDE module demonstrates its critical role in high-precision localization; even when applied individually (Exp. 4), it drives a massive +7.2% jump in AP₇₅. This proves that probabilistic distribution modeling is far superior to deterministic regression for recovering eroded features. Ultimately, the full framework (Exp. 5) achieves a peak mAP of 40.0%, demonstrating that these components function synergistically to solve the detection challenges of tiny, high-speed targets.

5.5.2. Efficacy of Heterogeneous Expert Design

We investigate the internal architecture of the expert module in

Table 5. Ablation study on Expert Design and Granularity. We compare the standard CNN block, MLP-based mixing block, Homogeneous Experts, and our Heterogeneous MG-MoE. Our method achieves the best trade-off between parameter efficiency and detection accuracy.

Exp.	Expert Design	Params	mAP	AP50
1	Standard ResNet Block	11.25 M	36.4	75.2
2	MLP-Mixer Block (Dense)	14.80 M	36.9	75.6
3	Homogeneous MoE ($k=4,3\times 3$)	12.15 M	37.3	75.9
4	MG-MoE (Heterogeneous)	12.35 M	38.2	76.5

. While the MLP-Mixer Block (Exp. 2) offers a slight improvement over the standard ResNet block, it incurs a significant computational penalty (14.80 M params), suggesting that dense connectivity alone is inefficient for this task. Similarly, the Homogeneous MoE (Exp. 3), which stacks identical $3\times 3$ kernels to increase capacity, yields only limited gains (37.3% mAP) because it lacks the structural diversity required to handle the multi-scale nature of motion blur. In contrast, our Heterogeneous MG-MoE (Exp. 4) achieves the optimal trade-off. By explicitly decoupling experts into “Focus” and “Context” roles, it achieves the highest accuracy (38.2% mAP) with only a marginal increase in parameters (12.35 M) compared to the baseline. This result validates the necessity of a physics-aware design that can adaptively process both fine-grained details and broader contextual semantics.

5.5.3. Impact of Expert Quantity in MG-MoE

Table 6. Ablation on the Number of Experts (N) in MG-MoE. We evaluate different combinations of Focus ($3\times 3$) and Context ($5\times 5$) experts. $N=4$ achieves the best balance between efficiency and accuracy, while $N=6$ suffers from slight overfitting.

Total Experts (N)	Configuration	Params (M)	GFLOPs	mAP	AP50
2	1 Focus + 1 Context	11.85	28.82	37.4	75.8
4 (Default)	2 Focus + 2 Context	12.41	29.66	38.2	76.5
6	3 Focus + 3 Context	30.08	23.45	38.1	76.3

explores the impact of expert quantity (N) on model performance, which is a critical hyperparameter governing the balance between capacity and complexity. Setting $N=2$ results in suboptimal performance (37.4% mAP), indicating that a single pair of Focus and Context experts provides insufficient representational diversity to capture complex motion patterns. Increasing the number of experts to $N=4$ (2 Focus + 2 Context) yields the best results (38.2% mAP), effectively expanding the model’s capacity to handle diverse object scales without excessive computational cost. However, further increasing N to 6 leads to a slight performance degradation (38.1% mAP) and a substantial increase in parameters (30.08 M). This drop suggests that an over-parameterized expert pool tends to overfit on the sparse tiny object samples, confirming that $N=4$ is the optimal configuration for efficiency and robustness.

5.5.4. Sensitivity to Gaussian Kernel Radius

In

Table 7. Sensitivity analysis of the Gaussian Kernel Radius $\mathit{\sigma }$ in IGDE. We investigate the impact of fixed radius settings versus our adaptive strategy.

Exp.	Radius Strategy	Value	mAP	AP50
1	Fixed (Very Strict)	$\sigma =0.5$	34.2	71.5
2	Fixed (Small)	$\sigma =1.0$	36.1	73.8
3	Fixed (Optimal)	$\sigma =1.5$	37.8	76.1
4	Fixed (Medium)	$\sigma =2.0$	37.6	75.9
5	Fixed (Large)	$\sigma =3.0$	36.8	75.1
6	Fixed (Very Large)	$\sigma =4.0$	35.2	72.4
7	Adaptive (Ours)	$\sigma \approx {\displaystyle \frac{min(w,h)}{3}}$	38.2	76.5

, we investigate the sensitivity of the Gaussian kernel radius $\sigma$, which defines the spatial extent of the supervision signal. The results clearly demonstrate the limitations of static radius settings. As seen in Exp. 1, an overly strict radius ($\sigma =0.5$) results in the lowest performance (34.2% mAP), indicating that the supervision signal is too sparse to guide effective feature learning. Conversely, blindly increasing the radius is detrimental; Exp. 6 reveals that a very large radius ($\sigma =4.0$) introduces excessive background noise by labeling surrounding pixels as positives, causing accuracy to drop to 35.2%. Although a moderate fixed value ($\sigma =1.5$ in Exp. 3) achieves a reasonable compromise, it lacks flexibility. Our Adaptive Strategy (Exp. 7), which dynamically scales $\sigma$ proportional to the object size ($\sigma \approx min(w,h)/3$), achieves the highest mAP of 38.2%. This confirms that maintaining semantic consistency between the distribution and the target’s physical scale is crucial for robust detection.

5.5.5. Balancing the Entropy Loss Weight

Finally, we examine the influence of the auxiliary loss weight ${\lambda }_{igde}$ in

Table 8. Sensitivity analysis of the IGDE loss weight ${\mathit{\lambda }}_{\mathit{igde}}$. We vary the weight of the auxiliary loss to find the optimal balance. Setting ${\mathit{\lambda }}_{\mathit{igde}}=\mathbf{1.0}$ yields the best performance, while excessively large weights dominate the main detection task, leading to performance degradation.

Exp.	Loss Weight (${\mathit{\lambda }}_{\mathit{igde}}$)	mAP	AP50
1	0.0	37.3	75.8
2	0.1	37.6	76.0
3	0.5	38.0	76.3
4	1.0 (Ours)	38.2	76.5
5	2.0	37.9	76.2
6	5.0	36.5	74.9

. The results exhibit a clear trade-off between the primary detection task and the auxiliary distribution estimation task. When ${\lambda }_{igde}$ is set to low values (e.g., $0.1$ or $0.5$), the supervision signal from the entropy map is too weak to significantly impact feature learning, resulting in limited performance gains over the baseline (${\lambda }_{igde}=0$). The performance peaks at ${\lambda }_{igde}=1.0$, achieving the best mAP of 38.2%. This indicates an optimal equilibrium where the IGDE module effectively guides feature recovery without interfering with the main optimization objective. However, increasing the weight further leads to degradation; specifically, at ${\lambda }_{igde}=5.0$, the mAP drops sharply to 36.5%. This suggests that an excessively large auxiliary weight dominates the total loss gradient, distracting the model from learning precise bounding box coordinates.

5.6. Visualization and Qualitative Analysis

Figure 6 visualizes the qualitative comparison between GOAL and state-of-the-art detectors on the Soccer-Wild test set. The results highlight three distinct advantages of our framework in the micro-dynamic regime:

Robustness to Motion Blur. As seen in the rightmost column, high-speed balls often degenerate into motion streaks, losing their spherical geometry. Standard detectors (e.g., YOLOv8, YOLO11) fail to recognize these non-rigid shapes, resulting in missed detections. In contrast, GOAL successfully recovers the target. This is attributed to the IGDE module, which utilizes probabilistic modeling to pinpoint the distribution peak (center of mass) even when visual boundaries are dissolved.

Suppression of Visual Distractors. In crowded penalty areas (Middle column), baseline models suffer from severe False Positives, frequently confusing players’ white socks or shoes with the ball due to local texture similarity. GOAL significantly reduces these false alarms through the synergy of Spectral Gating (SG) and MG-MoE. The SG module filters out background clutter frequencies, while context experts in MG-MoE distinguish true targets from visual mimics based on semantic context.

Precision in Localization. For extremely tiny objects (Left column), regression-based models often exhibit spatial drift or low IoU due to feature erosion. GOAL achieves pixel-level tightness (as shown in the green insets), validating our Adaptive Gaussian Kernel strategy. By dynamically adjusting the supervision scope based on object scale, our model ensures precise boundaries where fixed-regression methods fail.

5.7. Limitations

The state-of-the-art performance achieved by GOAL on the Soccer-Wild benchmark, we identify two primary limitations that merit further investigation.

First, there remains a trade-off between detection accuracy and inference speed. While GOAL operates at a real-time speed of 28 FPS on a high-end GPU, it incurs a higher computational overhead compared to ultra-lightweight detectors like YOLOv8 (90 FPS). This latency may pose a bottleneck for deployment on resource-constrained edge devices or in high-frame-rate (e.g., >60 FPS) broadcasting scenarios. Future work could explore model quantization or knowledge distillation to alleviate this burden without compromising the focus-and-context mechanism.

Second, although our IGDE module effectively handles standard motion blur and partial occlusion, the model still struggles under extreme visual degradation, as illustrated by the failure cases in Figure 7. Specifically, the detector is prone to false negatives (missed detections) in three severe edge cases: (1) Extreme background clutter, where a fast-moving ball merges with complex crowd textures or stadium infrastructure; (2) Zero-contrast blending, such as a white ball camouflaged against the white mesh of a goal net or thick penalty lines; and (3) Extreme scale degradation in ultra-wide broadcast angles, where the target collapses to a sub-pixel footprint. In these specific scenarios, the single-frame spatial contrast drops to near zero, causing the IGDE module to lose its vital information entropy cues. Since our current framework operates purely on single-frame inputs, it lacks the temporal memory to infer the ball’s position based on trajectory history. Integrating temporal sequence modeling (e.g., 3D-CNNs or temporal attention) would be a promising direction to bridge these extreme frame-level discontinuities.

6. Conclusions

In this paper, we addressed the challenging problem of detecting tiny, high-speed objects in unconstrained broadcast environments—a “micro-dynamic” regime characterized by the interplay of feature erosion, severe motion blur, and background clutter. To bridge the data gap impeding research in this domain, we introduced Soccer-Wild, the first large-scale benchmark providing high-precision annotations for objects undergoing extreme scale degradation and motion streaks. By exposing the limitations of generic detectors, Soccer-Wild establishes a rigorous testbed for evaluating future micro-object perception algorithms.

Building upon this foundation, we proposed GOAL, a unified framework that reconstructs the representation paradigm for tiny objects through three physics-aware innovations. First, we introduced Spectral Gating to suppress background redundancy in the frequency domain, enhancing the signal-to-noise ratio at the source. Second, we designed a Heterogeneous MG-MoE to dynamically disentangle the representation of sharp versus blurred targets, resolving the conflict between fine-grained detail preservation and contextual semantic abstraction. Crucially, we shifted the localization paradigm from unstable deterministic regression to Information-Guided Gaussian Distribution Estimation (IGDE). By leveraging an adaptive Gaussian kernel and entropy constraints, IGDE effectively recovers weak signals from minimal pixel support, enabling precise sub-pixel localization.

Extensive experiments demonstrate that GOAL achieves state-of-the-art performance on the Soccer-Wild benchmark (40.0% mAP), outperforming existing methods by a significant margin, particularly in the high-precision regime ($A{P}_{75}$). Furthermore, its superior generalization on the VisDrone2019 dataset confirms its robustness across diverse tiny object scenarios. While GOAL sets a new baseline, future work will focus on integrating temporal consistency constraints to resolve full occlusion in long-shot views and exploring model quantization to optimize the inference efficiency of the MoE architecture for edge deployment. We hope this work inspires further exploration into the limits of micro-object perception in dynamic scenes.