GERIS: A Game-Theoretic Framework for Filtering Instance-Dependent Label Noise in License Plate Data Augmentation

1 Introduction

• Instance selection identifies and removes noisy training examples to form a smaller, more focused training set.The introduction cites potential benefits including improved model quality and minimized empirical error.Source: §1 · pp. 1–2
• The paper focuses on character recognition, the fourth step of license plate recognition, rather than the earlier detection, localization, and segmentation steps.Source: §1 · p. 2
• Augmentation can produce unrealistic examples resembling instance-dependent noisy labels, which may lead to inaccurate recognition models.The stated concern is that synthetic data may lack real-world variations such as lighting changes, rotation, and shadows.Source: §1 · p. 2
• Two approaches described for addressing augmentation challenges are filtering synthetic data and methods based on gradient policy.Source: §1 · p. 2

2 Literature Review

• The review organizes relevant work around filtering-based instance selection and learning models, using a high-level comparison to motivate detailed discussion of counterpart algorithms.Source: §2 · pp. 2–3

2.1 Filtering-based Instance Selection

• Filtering-based instance selection is grouped into distance-based, class-distribution, and consistency-based methods for selecting informative and representative instances.Source: §2.1 · p. 3

2.1.1 Distance-based Filtering Methods

• Distance-based methods use feature-space proximity to identify redundant or outlier instances; examples include DBSCAN, KNN, Isolation Forest, K-means, and CNN.Source: §2.1.1 · p. 3

2.1.2 Class Distribution Filtering Methods

• Class-distribution methods seek to preserve dataset representativeness and diversity; examples include ENN, NCR, and Naive Bayes [18].Source: §2.1.2 · p. 3

2.1.3 Consistency-based Filtering Methods

• Consistency-based methods retain instances considered stable with respect to training data or a learning model, including Cross-Validation and One-Class SVM.Source: §2.1.3 · p. 3

2.1.4 Noisy Label Detection Methods

• Noisy-label methods include sample selection, label correction, hybrid techniques, robust losses, regularization, meta-learning, and contrastive learning; the review notes contrastive learning may conflate semantic similarity with noise [22] [23] [24] [27] [28] [30].Source: §2.1.4 · pp. 3–4

2.2 Learning Models

• The review identifies MLP and SVM as learning models that could classify redundant transformation functions and remove them from instances.Source: §2.2 · p. 4

2.3 Policy-gradient Methods

• Policy-gradient methods search for augmentation transformations, while GERIS is presented as game-theoretic pruning that avoids per-iteration model training and uses noise vectors instead of complete images.The paper claims lower computational cost than gradient-policy methods and describes the reduced input dimensionality as addressing the curse of dimensionality.Source: §2.3 · p. 4

3 Proposed methodology

• The section first describes a framework for generating artificial license plates.Source: §3 · p. 5
• It then lists the noises applied to simple plates as part of the generation description.Source: §3 · p. 5
• The second part explains the theory and method of the proposed game and how it is evaluated.Source: §3 · p. 5

3.1 Data generator framework

• The generator loads background templates as plates, adds randomly generated characters, and applies non-perspective and perspective noise.Source: §3.1 · p. 5
• The template layer represents the metal plate, with 13 templates designed to match the categories of license plates in Iran.Source: §3.1 · p. 5
• Noise vectors contain overlay noises in components 0–9 and computed noises in components 10–30.Overlay noises include transparent scratch images; computed noises include formula-based effects such as salt and pepper noise.Source: §3.1 · p. 5

3.2 Instance selection

• GERIS adapts a game-theoretic labeling approach to prune corrupt augmentation instances, using a small manually labeled subset to label the rest.The labeling game is played between an unlabeled noise vector and its neighbors.Source: §3.2 · pp. 5, 8, §3.2.3 · p. 9

3.2.1 Game theory

• Game theory models strategic interactions through players, strategies, and payoffs that reflect the outcomes of their choices.The paper introduces these concepts as the basis for modeling its instance-labeling problem.Source: §3.2.1 · p. 8

3.2.2 Non-cooperative games

• GERIS adapts the NEATER game into a non-cooperative game, where players pursue their own utilities without forming coalitions.The paper defines a normal-form game with players, strategy spaces, and payoff functions.Source: §3.2.2 · p. 8

3.2.3 Modeling the problem into a normal form game

• Each unlabeled vector plays against its h nearest neighbors by Mahalanobis distance, with correct and corrupt as its two strategies.Pairwise payoffs are weighted by the inverse Mahalanobis distance, and each player's utility sums payoffs across its neighbors.Source: §3.2.3 · pp. 9–10

3.2.4 Replicator dynamics

• Replicator dynamics updates strategy frequencies from their payoffs, and GERIS assigns each unlabeled vector the class with the higher probability at convergence.The paper uses discrete-time dynamics for its finite, symmetric game; better-than-average strategies grow while worse-than-average strategies decline.Source: §3.2.4 · pp. 10–11

3.3 Evaluation methodology

• Evaluation compares algorithm labels with manually labeled data and measures an image-to-text model trained on filtered generated plates.Figure 3 depicts these two evaluation stages.Source: §3.3 · p. 12, Figure 3 · p. 13

3.3.1 Measurement

• The pruning mechanism is evaluated with separate F-measures for perspective and non-perspective corruption because their class counts differ.A vector is labeled corrupt if either its perspective or non-perspective label is corrupt.Source: §3.3.1 · pp. 12–13

3.3.2 First stage methodology

• In the first stage, GERIS labels are compared with manual labels on a test set after game hyperparameters are selected by grid search on a validation set.Generated noise vectors are labeled manually, then divided into training, validation, and test sets.Source: §3.3.2 · p. 14

3.3.3 Second stage methodology

• The second stage filters generated noise vectors, trains DenseNet on plates generated from the retained vectors, and evaluates it on a real-world license plate dataset.The paper identifies this stage as more important because it assesses the recognition model's performance.Source: §3.3.3 · p. 14

4 Experimental results

• Noise vectors combined one to three randomly selected noise types; grid search selected h = 40, α = 0.999999, and 20 iterations for convergence.The experiments found that incorporating more than three noise types ensures image corruption.Source: §4 · p. 14

4.1 Sensivity Analysis of Training Data Ratio

• As manually labeled vectors fell from 80% to 10%, mean F1 stayed around 79%, while corrupt recall declined from approximately 87.9% to 69.7%.The study reports that complementary metrics improved or remained flat and characterizes 10% labeling as yielding near-optimal F1 with lower annotation costs.Source: §4.1 · pp. 14–15, Figure 4 · p. 15

4.2 Experimental results of the first stage

• GERIS reached 85.84% corrupt recall, 1.57 pp above Naïve Bayes (84.27%), while corrupt precision was 57.35%, 2.28 pp above Naïve Bayes (55.07%).Correct-label precision was 99.04% versus Naïve Bayes’ 99.15%; GERIS also reduced false positives 2.1× compared with SE Networks.Source: §4.2 · pp. 15–16
• GERIS ran 1.15× faster than Naïve Bayes (2.66s vs. 3.07s) and 4.9× and 12.9× faster than SE Networks and Transformers, respectively.The explicit pattern storage architecture used 1289MB and enabled auditability absent from the compared traditional statistical and neural approaches.Source: §4.2 · p. 16
• GERIS achieved 79.66 F1, 1.17 pp above Naïve Bayes (78.49), and had higher F-measures than the other stated classification algorithms.Table 3 reports averages over 100 trials; the paper identifies corrupt precision and recall as especially important because retaining a corrupt vector is more detrimental than removing a correct one.Source: §4.2 · pp. 15–16, Table 3 · p. 16

4.3 Experimental results of the second stage

• Digits improved by 10.05%, 17%, 17.85%, and 15.32% in accuracy, F1, precision, and recall; alphabet gains were 26.78%, 31.09%, 26.24%, and 33.13%.The paper reports these increases for the baseline model when GERIS-filtered augmentation is used; digit and alphabet recognition use separate models.Source: §4.3 · pp. 17–18, Table 5 · p. 18

5 Discussion

• GERIS selects the neighborhood size h by grid-searching candidates and choosing the value with the highest validation F1-score.The graph is constructed and GERIS is run on the validation set for each candidate h.Source: §5 · p. 18

5.1 Computational Complexity

• Repeated brute-force graph construction during grid search has overall complexity O(H · (n^2d + T)); the paper reports exact search was manageable for its datasets but prohibitive at larger scale.The experiments used 2,000 noise vectors in the first stage and 50,000 in the second; the authors suggest ANN as an alternative.Source: §5.1 · p. 18

5.2 Future Work: Accelerating Neighbor Search with ANN

• The proposed ANN extension constructs the graph once and selects the optimal number of neighbors from search results, avoiding iterative graph construction during hyperparameter optimization.The paper proposes ANN methods to reduce computational cost while sacrificing only a small amount of accuracy.Source: §5.2 · p. 19

5.3 Time Complexity of ANN-Based Graph Construction

• ANN-based graph construction is described as a significant improvement over exact k-NN’s O(n^2d) cost, particularly for large n and moderate-to-high d.The paper says this can reduce runtime while maintaining effectiveness in label propagation and noise filtering.Source: §5.3 · p. 19

Medical Imaging

• Medical imaging applications could use a small set of confirmed noisy labels to identify and prune additional mislabeled scans or tiles through a Mahalanobis-distance k-NN graph.The passage gives histopathology and radiology as examples, where texture, illumination, or artifacts can contribute to instance-dependent mislabeling.Source: §6 · p. 19

Remote Sensing

• In remote sensing, manually reviewed noisy patches could seed detection of similar mislabeled pixels or segments in satellite imagery affected by occlusions such as clouds or shadows.Source: §6 · p. 19

• The authors frame these as potential pattern-recognition applications under the IDN framework, especially when a modest number of seed noisy instances is available.Source: §6 · p. 20

• GERIS models instance selection as a non-cooperative game and uses replicator dynamics to classify synthetic noise vectors as useful or corrupt at Nash equilibrium.Source: §7 · p. 20
• The two-stage evaluation reports that GERIS outperforms classical filtering methods in detecting corrupt instances and improves downstream recognition-task performance.Source: §7 · p. 20
• The study focuses on license plate recognition; medical-imaging adaptation remains future work because noise distinctions may be subtler and manual labeling more difficult, while ANN search is proposed for large-scale deployment.The conclusion also identifies refining the payoff structure or using alternative game-theoretic dynamics as possible improvements.Source: §7 · p. 20