| Literature DB >> 35891060 |
Mingkun Tan1, Daniel Langenkämper1, Tim W Nattkemper1.
Abstract
Data augmentation is an established technique in computer vision to foster the generalization of training and to deal with low data volume. Most data augmentation and computer vision research are focused on everyday images such as traffic data. The application of computer vision techniques in domains like marine sciences has shown to be not that straightforward in the past due to special characteristics, such as very low data volume and class imbalance, because of costly manual annotation by human domain experts, and general low species abundances. However, the data volume acquired today with moving platforms to collect large image collections from remote marine habitats, like the deep benthos, for marine biodiversity assessment and monitoring makes the use of computer vision automatic detection and classification inevitable. In this work, we investigate the effect of data augmentation in the context of taxonomic classification in underwater, i.e., benthic images. First, we show that established data augmentation methods (i.e., geometric and photometric transformations) perform differently in marine image collections compared to established image collections like the Cityscapes dataset, showing everyday traffic images. Some of the methods even decrease the learning performance when applied to marine image collections. Second, we propose new data augmentation combination policies motivated by our observations and compare their effect to those proposed by the AutoAugment algorithm and can show that the proposed augmentation policy outperforms the AutoAugment results for marine image collections. We conclude that in the case of small marine image datasets, background knowledge, and heuristics should sometimes be applied to design an effective data augmentation method.Entities:
Keywords: data augmentation; deep learning; marine objects classification; underwater computer vision
Mesh:
Year: 2022 PMID: 35891060 PMCID: PMC9322900 DOI: 10.3390/s22145383
Source DB: PubMed Journal: Sensors (Basel) ISSN: 1424-8220 Impact factor: 3.847
Figure 1dataset. (a) Ophiuroidea; (b) Cnidaria; (c) Amperima; (d) Foraminifera. Reproduced with permission from Henry Ruhl.
Figure 2Dataset structure. The datasets were randomly subdivided into train, validation, and test set.
Figure 3Construction of the training sets. Experiments were conducted using training sets of different sizes to investigate the influence of training set size on the impact of augmentation.
Sample sizes of each category per subset in the dataset.
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| Ophiuroidea | Cnidaria | Amperima | Foraminifera |
|---|---|---|---|---|
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| 50 | 50 | 50 | 50 |
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| 100 | 100 | 100 | 100 |
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| 200 | 200 | 200 | 200 |
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| 300 | 300 | 300 | 300 |
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| 200 | 200 | 200 | 200 |
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| 8883 | 8861 | 5202 | 2132 |
Figure 4dataset. (a) Sponge; (b) Coral.
Sample sizes of category per subset in the dataset.
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| Sponge | Coral |
|---|---|---|
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| 50 | 50 |
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| 100 | 100 |
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| 150 | 150 |
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| 150 | 150 |
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| 1236 | 700 |
Figure 5dataset. (a) Car; (b) Bicycle.
Sample sizes of each category per subset in the dataset.
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| Car | Bicycle |
|---|---|---|
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| 50 | 50 |
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| 100 | 100 |
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| 150 | 150 |
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| 200 | 200 |
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| 24,371 | 3208 |
Figure 6Flowchart of the work. Each DA method was applied to each train data and an individual model was trained and optimized using the validation data. The accuracy of the individually trained model was evaluated using the test data.
Performance of DA methods on . The impact of DA methods and parameters on classification performance for is revealed. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy).
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| 1° | 3.82% | 0.1 | 2.79% | 0.1 | 1.97% | 0.1 | 0.92% | 0.1 | 2.68% | 0.1 | 1.65% |
| 2° | 5.11% | 0.2 | 3.95% | 0.2 | 2.85% | 0.2 | 1.35% | 0.2 | 3.15% | 0.2 | 1.93% |
| 3° | 5.69% | 0.3 | 4.38% | 0.3 | 3.34% | 0.3 | 1.96% | 0.3 | 3.24% | 0.3 | 1.95% |
| 4° | 5.89% | 0.4 | 4.40% | 0.4 | 3.71% | 0.4 | 2.18% | 0.4 | 3.51% | 0.4 | 1.99% |
| 5° | 6.11% | 0.5 | 4.90% | 0.5 | 4.15% | 0.5 | 2.46% | 0.5 | 3.57% | 0.5 | 2.11% |
| 6° | 6.01% | 0.6 | 5.35% | 0.6 | 4.53% | 0.6 | 2.81% | 0.6 | 3.66% | 0.6 | 2.14% |
| 7° | 6.03% | 0.7 | 5.61% | 0.7 | 4.66% | 0.7 | 3.11% | 0.7 | 3.57% | 0.7 | 2.11% |
| 8° | 6.30% | 0.8 | 5.64% | 0.8 | 5.19% | 0.8 | 3.06% | 0.8 | 3.31% | 0.8 | 1.80% |
| 9° | 6.10% | 0.9 | 6.24% | 0.9 | 5.59% | 0.9 | 2.97% | 0.9 | 3.12% | 0.9 | 1.56% |
| 10° | 6.01% | 1 | 6.82% | 1 | 6.22% | 1 | 2.95% | 1 | 0.34% | 1 | –1.16% |
| 20° | 6.85% | 1.1 | 6.25% | 1.3 | 6.33% | 1.5 | 3.27% | Shear | |||
| 30° | 6.97% | 1.2 | 6.87% | 1.5 | 5.87% | 2 | 3.29% | ||||
| 40° | 6.71% | 1.3 | 6.75% | 1.8 | 6.18% | 3 | 4.08% | 5° | 4.05% | ||
| 50° | 6.96% | 1.4 | 7.01% | 2 | 6.29% | 4 | 4.67% | 10° | 3.92% | ||
| 60° | 7.41% | 1.5 | 7.22% | 2.5 | 5.86% | 5 | 4.97% | 20° | 4.34% | ||
| 70° | 7.17% | 1.6 | 6.56% | 3 | 7.13% | 6 | 5.43% | 30° | 4.93% | ||
| 80° | 7.39% | 1.7 | 6.95% | 3.5 | 7.00% | 7 | 5.49% | 40° | 5.48% | ||
| 90° | 7.61% | 1.8 | 7.01% | 4 | 6.88% | 8 | 5.72% | (0°, 0°, −5°, 5°) | 4.20% | ||
| 100° | 8.02% | 1.9 | 7.11% | 4.5 | 6.59% | 9 | 5.83% | (0°, 0°, −10°, 10°) | 5.38% | ||
| 110° | 7.84% | 2 | 7.74% | 5 | 7.70% | 10 | 5.99% | (0°, 0°, −20°, 20°) | 6.20% | ||
| 120° | 7.70% | Hue | Translate | (0°,0°, −30°, 30°) | 6.06% | ||||||
| 130° | 7.69% | (0°, 0°, −40°, 40°) | 6.47% | ||||||||
| 140° | 7.76% | 0.1 | 4.17% | (0.1, 0.1) | 5.59% | (−5°, 5°, −5°, 5°) | 5.89% | ||||
| 150° | 7.31% | 0.2 | 5.13% | (0.2, 0.2) | 4.72% | (−10°, 10°, −10°, 10°) | 5.75% | ||||
| 160° | 7.47% | 0.3 | 4.86% | (0.3, 0.3) | 4.21% | (−20°, 20°, −20°, 20°) | 6.22% | ||||
| 170° | 7.11% | 0.4 | 4.52% | (0.4, 0.4) | 2.53% | (−30°, 30°, −30°, 30°) | 6.68% | ||||
| 180° | 7.55% | 0.5 | 4.70% | (0.5, 0.5) | 1.40% | (−40°, 40°, −40°, 40°) | 6.58% | ||||
Performance of DA methods on . The DA methods and parameters impact on classification performance is shown. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy).
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| 1° | 1.30% | 0.1 | 1.19% | 0.1 | 0.69% | 0.1 | 0.25% | 0.1 | 0.94% | 0.1 | 0.77% |
| 2° | 1.55% | 0.2 | 1.22% | 0.2 | 1.41% | 0.2 | 0.34% | 0.2 | 0.81% | 0.2 | 0.92% |
| 3° | 2.18% | 0.3 | 1.38% | 0.3 | 1.41% | 0.3 | 0.42% | 0.3 | 1.01% | 0.3 | 0.80% |
| 4° | 2.11% | 0.4 | 1.70% | 0.4 | 1.48% | 0.4 | 0.57% | 0.4 | 0.86% | 0.4 | 0.88% |
| 5° | 2.01% | 0.5 | 1.75% | 0.5 | 1.56% | 0.5 | 0.74% | 0.5 | 1.31% | 0.5 | 0.79% |
| 6° | 1.94% | 0.6 | 1.85% | 0.6 | 1.76% | 0.6 | 1.11% | 0.6 | 0.89% | 0.6 | 0.82% |
| 7° | 2.08% | 0.7 | 2.13% | 0.7 | 1.95% | 0.7 | 1.24% | 0.7 | 0.77% | 0.7 | 0.74% |
| 8° | 1.55% | 0.8 | 2.15% | 0.8 | 2.12% | 0.8 | 0.38% | 0.8 | 0.56% | 0.8 | 0.70% |
| 9° | 2.18% | 0.9 | 2.59% | 0.9 | 1.82% | 0.9 | 1.09% | 0.9 | 0.78% | 0.9 | 0.62% |
| 10° | 2.15% | 1 | 2.57% | 1 | 2.05% | 1 | 1.27% | 1 | −0.43% | 1 | −0.43% |
| 20° | 2.14% | 1.1 | 2.34% | 1.3 | 1.84% | 1.5 | 0.81% | Shear | |||
| 30° | 2.53% | 1.2 | 2.43% | 1.5 | 2.15% | 2 | 1.49% | ||||
| 40° | 2.17% | 1.3 | 2.34% | 1.8 | 2.32% | 3 | 1.75% | 5° | 1.70% | ||
| 50° | 2.62% | 1.4 | 2.35% | 2 | 1.81% | 4 | 1.72% | 10° | 1.85% | ||
| 60° | 2.74% | 1.5 | 2.06% | 2.5 | 1.94% | 5 | 1.80% | 20° | 1.78% | ||
| 70° | 2.86% | 1.6 | 2.43% | 3 | 2.15% | 6 | 1.85% | 30° | 1.53% | ||
| 80° | 2.45% | 1.7 | 2.35% | 3.5 | 2.26% | 7 | 1.86% | 40° | 2.13% | ||
| 90° | 3.06% | 1.8 | 2.47% | 4 | 2.19% | 8 | 1.61% | (0°, 0°, −5°, 5°) | 1.63% | ||
| 100° | 3.17% | 1.9 | 2.52% | 4.5 | 2.40% | 9 | 1.76% | (0°, 0°, −10°, 10°) | 2.34% | ||
| 110° | 3.09% | 2 | 2.39% | 5 | 2.28% | 10 | 1.72% | (0°, 0°, −20°, 20°) | 1.72% | ||
| 120° | 3.25% | Hue | Translate | (0°, 0°, −30°, 30°) | 2.06% | ||||||
| 130° | 2.96% | (0°, 0°, −40°, 40°) | 2.33% | ||||||||
| 140° | 3.14% | 0.1 | 1.45% | (0.1, 0.1) | 2.00% | (−5°, 5°, −5°, 5°) | 2.20% | ||||
| 150° | 3.27% | 0.2 | 1.61% | (0.2, 0.2) | 1.67% | (−10°, 10°, −10°, 10°) | 2.22% | ||||
| 160° | 3.08% | 0.3 | 1.94% | (0.3, 0.3) | 1.57% | (−20°, 20°, −20°, 20°) | 2.40% | ||||
| 170° | 3.29% | 0.4 | 1.73% | (0.4, 0.4) | 0.69% | (−30°, 30°, −30°, 30°) | 2.29% | ||||
| 180° | 3.23% | 0.5 | 1.72% | (0.5, 0.5) | 0.21% | (−40°, 40°, −40°, 40°) | 2.40% | ||||
Performance of DA methods on . The impact of different DA methods and parameters on classification performance is displayed. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy).
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| 1° | 3.07% | 0.1 | 1.86% | 0.1 | 2.12% | 0.1 | 0.77% | 0.1 | 2.93% | 0.1 | 2.27% |
| 2° | 4.13% | 0.2 | 2.77% | 0.2 | 2.40% | 0.2 | 1.20% | 0.2 | 3.05% | 0.2 | 2.67% |
| 3° | 3.99% | 0.3 | 3.18% | 0.3 | 3.08% | 0.3 | 1.26% | 0.3 | 3.24% | 0.3 | 2.60% |
| 4° | 4.39% | 0.4 | 4.03% | 0.4 | 4.01% | 0.4 | 1.66% | 0.4 | 3.01% | 0.4 | 2.53% |
| 5° | 4.91% | 0.5 | 4.26% | 0.5 | 4.32% | 0.5 | 1.82% | 0.5 | 2.80% | 0.5 | 2.60% |
| 6° | 4.98% | 0.6 | 4.50% | 0.6 | 4.88% | 0.6 | 1.37% | 0.6 | 3.04% | 0.6 | 2.85% |
| 7° | 5.00% | 0.7 | 4.94% | 0.7 | 4.91% | 0.7 | 1.76% | 0.7 | 3.01% | 0.7 | 2.78% |
| 8° | 5.12% | 0.8 | 4.51% | 0.8 | 5.36% | 0.8 | 2.07% | 0.8 | 3.15% | 0.8 | 2.65% |
| 9° | 4.97% | 0.9 | 4.44% | 0.9 | 4.77% | 0.9 | 2.08% | 0.9 | 2.63% | 0.9 | 2.31% |
| 10° | 5.31% | 1 | 5.32% | 1 | 4.97% | 1 | 2.29% | 1 | −0.93% | 1 | −0.99% |
| 20° | 5.70% | 1.1 | 5.35% | 1.3 | 4.86% | 1.5 | 2.21% | Shear | |||
| 30° | 5.54% | 1.2 | 5.19% | 1.5 | 5.06% | 2 | 1.27% | ||||
| 40° | 6.35% | 1.3 | 5.10% | 1.8 | 5.03% | 3 | 1.67% | 5° | 2.70% | ||
| 50° | 6.11% | 1.4 | 5.43% | 2 | 5.15% | 4 | 1.42% | 10° | 3.39% | ||
| 60° | 5.81% | 1.5 | 5.16% | 2.5 | 5.39% | 5 | 2.09% | 20° | 4.95% | ||
| 70° | 6.17% | 1.6 | 4.71% | 3 | 4.95% | 6 | 2.20% | 30° | 5.55% | ||
| 80° | 6.48% | 1.7 | 5.53% | 3.5 | 4.56% | 7 | 2.03% | 40° | 5.44% | ||
| 90° | 6.69% | 1.8 | 5.09% | 4 | 4.88% | 8 | 2.43% | (0°, 0°, −5°, 5°) | 4.71% | ||
| 100° | 6.31% | 1.9 | 5.54% | 4.5 | 5.30% | 9 | 2.19% | (0°, 0°, −10°, 10°) | 5.16% | ||
| 110° | 6.57% | 2 | 5.28% | 5 | 5.16% | 10 | 1.85% | (0°, 0°, −20°, 20°) | 4.95% | ||
| 120° | 6.85% | Hue | Translate | (0°, 0°, −30°, 30°) | 5.23% | ||||||
| 130° | 6.66% | (0°, 0°, −40°, 40°) | 5.51% | ||||||||
| 140° | 6.31% | 0.1 | 3.18% | (0.1, 0.1) | 4.98% | (−5°, 5°, −5°, 5°) | 5.55% | ||||
| 150° | 7.14% | 0.2 | 3.96% | (0.2, 0.2) | 4.19% | (−10°, 10°, −10°, 10°) | 5.60% | ||||
| 160° | 6.95% | 0.3 | 3.98% | (0.3, 0.3) | 3.76% | (−20°, 20°, −20°, 20°) | 5.64% | ||||
| 170° | 6.80% | 0.4 | 3.48% | (0.4, 0.4) | 3.09% | (−30°, 30°, −30°, 30°) | 5.91% | ||||
| 180° | 6.73% | 0.5 | 2.95% | (0.5, 0.5) | −0.15% | (−40°, 40°, −40°, 40°) | 6.11% | ||||
Performance of DA methods on . The effect of different DA methods and different parameters on classification improvement is shown. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy).
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| 1° | 1.84% | 0.1 | 0.73% | 0.1 | 0.53% | 0.1 | 0.32% | 0.1 | 1.50% | 0.1 | 0.92% |
| 2° | 2.01% | 0.2 | 1.40% | 0.2 | 0.91% | 0.2 | 0.40% | 0.2 | 1.29% | 0.2 | 0.92% |
| 3° | 1.81% | 0.3 | 1.59% | 0.3 | 1.18% | 0.3 | 0.60% | 0.3 | 1.26% | 0.3 | 0.99% |
| 4° | 2.02% | 0.4 | 1.74% | 0.4 | 1.76% | 0.4 | 1.06% | 0.4 | 1.25% | 0.4 | 1.26% |
| 5° | 2.18% | 0.5 | 1.73% | 0.5 | 1.72% | 0.5 | 1.32% | 0.5 | 1.10% | 0.5 | 1.14% |
| 6° | 1.82% | 0.6 | 1.65% | 0.6 | 1.87% | 0.6 | 1.29% | 0.6 | 1.17% | 0.6 | 1.24% |
| 7° | 1.80% | 0.7 | 2.47% | 0.7 | 2.34% | 0.7 | 1.48% | 0.7 | 0.95% | 0.7 | 1.20% |
| 8° | 2.12% | 0.8 | 1.93% | 0.8 | 2.52% | 0.8 | 1.56% | 0.8 | 0.84% | 0.8 | 0.90% |
| 9° | 2.26% | 0.9 | 2.13% | 0.9 | 2.55% | 0.9 | 1.91% | 0.9 | 0.73% | 0.9 | 0.87% |
| 10° | 2.39% | 1 | 2.57% | 1 | 3.08% | 1 | 2.05% | 1 | −1.07% | 1 | −0.19% |
| 20° | 2.71% | 1.1 | 2.22% | 1.3 | 3.33% | 1.5 | 2.46% | Shear | |||
| 30° | 3.19% | 1.2 | 2.83% | 1.5 | 3.22% | 2 | 2.46% | ||||
| 40° | 2.45% | 1.3 | 2.41% | 1.8 | 3.32% | 3 | 2.40% | 5° | 1.36% | ||
| 50° | 2.60% | 1.4 | 2.49% | 2 | 3.00% | 4 | 2.35% | 10° | 1.59% | ||
| 60° | 2.18% | 1.5 | 2.66% | 2.5 | 3.10% | 5 | 2.13% | 20° | 1.96% | ||
| 70° | 3.09% | 1.6 | 2.87% | 3 | 3.03% | 6 | 1.88% | 30° | 2.37% | ||
| 80° | 3.16% | 1.7 | 2.90% | 3.5 | 3.13% | 7 | 1.53% | 40° | 2.99% | ||
| 90° | 3.76% | 1.8 | 2.43% | 4 | 3.10% | 8 | 1.73% | (0°, 0°, −5°, 5°) | 1.88% | ||
| 100° | 3.57% | 1.9 | 2.54% | 4.5 | 3.19% | 9 | 2.00% | (0°, 0°, −10°, 10°) | 1.66% | ||
| 110° | 3.68% | 2 | 3.14% | 5 | 3.33% | 10 | 2.18% | (0°, 0°, −20°, 20°) | 1.85% | ||
| 120° | 3.66% | Hue | Translate | (0°, 0°, −30°, 30°) | 2.32% | ||||||
| 130° | 3.56% | (0°, 0°, −40°, 40°) | 2.75% | ||||||||
| 140° | 3.32% | 0.1 | 1.40% | (0.1, 0.1) | 1.63% | (−5°, 5°, −5°, 5°) | 2.02% | ||||
| 150° | 3.17% | 0.2 | 1.68% | (0.2, 0.2) | 1.44% | (−10°, 10°, −10°, 10°) | 2.14% | ||||
| 160° | 3.74% | 0.3 | 1.69% | (0.3, 0.3) | 1.02% | (−20°, 20°, −20°, 20°) | 2.30% | ||||
| 170° | 3.93% | 0.4 | 1.57% | (0.4, 0.4) | −0.66% | (−30°, 30°, −30°, 30°) | 2.16% | ||||
| 180° | 3.64% | 0.5 | 1.62% | (0.5, 0.5) | −0.90% | (−40°, 40°, −40°, 40°) | 2.11% | ||||
Performance of DA methods on . The impact of different DA methods and parameters on classification performance, which is very different from the impact on and , is displayed. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy).
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| 1° | −0.08% | 0.1 | −0.12% | 0.1 | −0.09% | 0.1 | 0.07% | 0.1 | −1.95% | 0.1 | 0.59% |
| 2° | 0.32% | 0.2 | 0.06% | 0.2 | −0.14% | 0.2 | 0.17% | 0.2 | −1.43% | 0.2 | 0.46% |
| 3° | 0.63% | 0.3 | 0.12% | 0.3 | −0.06% | 0.3 | 0.42% | 0.3 | −1.52% | 0.3 | 0.63% |
| 4° | 0.39% | 0.4 | −0.16% | 0.4 | −0.08% | 0.4 | 0.63% | 0.4 | −1.39% | 0.4 | 0.68% |
| 5° | 0.30% | 0.5 | −0.04% | 0.5 | −0.16% | 0.5 | 0.62% | 0.5 | −1.69% | 0.5 | 0.59% |
| 6° | 0.52% | 0.6 | 0.27% | 0.6 | −0.06% | 0.6 | 0.69% | 0.6 | −1.82% | 0.6 | 0.57% |
| 7° | 0.42% | 0.7 | 0.20% | 0.7 | 0.18% | 0.7 | 0.61% | 0.7 | −2.07% | 0.7 | 0.56% |
| 8° | 0.34% | 0.8 | 0.17% | 0.8 | −0.35% | 0.8 | 0.77% | 0.8 | −2.49% | 0.8 | 0.51% |
| 9° | 0.31% | 0.9 | −0.18% | 0.9 | −0.08% | 0.9 | 0.75% | 0.9 | −2.80% | 0.9 | 0.37% |
| 10° | 0.19% | 1 | −0.19% | 1 | −0.56% | 1 | 0.90% | 1 | −8.53% | 1 | −0.30% |
| 20° | −0.67% | 1.1 | −0.60% | 1.3 | −0.67% | 1.5 | 1.18% | Shear | |||
| 30° | −0.98% | 1.2 | −0.67% | 1.5 | −0.25% | 2 | 1.33% | ||||
| 40° | −1.61% | 1.3 | −0.33% | 1.8 | 0.02% | 3 | 1.36% | 5° | −0.14% | ||
| 50° | −0.47% | 1.4 | 0.19% | 2 | −0.25% | 4 | 1.30% | 10° | 0.25% | ||
| 60° | −0.88% | 1.5 | 0.07% | 2.5 | −0.33% | 5 | 1.22% | 20° | −0.06% | ||
| 70° | −1.87% | 1.6 | −0.40% | 3 | −0.08% | 6 | 1.16% | 30° | −0.42% | ||
| 80° | −2.67% | 1.7 | 0.03% | 3.5 | 0.22% | 7 | 1.26% | 40° | −0.25% | ||
| 90° | −2.35% | 1.8 | 0.11% | 4 | 0.04% | 8 | 1.30% | (0°, 0°, −5°, 5°) | 0.92% | ||
| 100° | −2.79% | 1.9 | 0.57% | 4.5 | 0.59% | 9 | 1.15% | (0°, 0°, −10°, 10°) | 0.89% | ||
| 110° | −2.57% | 2 | 0.40% | 5 | 1.13% | 10 | 1.25% | (0°, 0°, −20°, 20°) | 0.31% | ||
| 120° | −2.94% | Hue | Translate | (0°, 0°, −30°, 30°) | 0.19% | ||||||
| 130° | −3.85% | (0°, 0°, −40°, 40°) | −0.10% | ||||||||
| 140° | −3.81% | 0.1 | 0.53% | (0.1, 0.1) | −0.38% | (−5°, 5°, −5°, 5°) | 0.37% | ||||
| 150° | −3.89% | 0.2 | 0.27% | (0.2, 0.2) | −0.14% | (−10°, 10°, −10°, 10°) | 0.55% | ||||
| 160° | −4.80% | 0.3 | 0.16% | (0.3, 0.3) | −0.57% | (−20°, 20°, −20°, 20°) | 0.14% | ||||
| 170° | −4.31% | 0.4 | −0.01% | (0.4, 0.4) | −2.02% | (−30°, 30°, −30°, 30°) | −0.37% | ||||
| 180° | −4.28% | 0.5 | 0.10% | (0.5, 0.5) | −2.46% | (−40°, 40°, −40°, 40°) | −1.18% | ||||
Performance of DA methods on . The heatmap shows the DA methods and parameters impact on classification performance. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy).
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| 1° | 0.35% | 0.1 | 0.23% | 0.1 | 0.25% | 0.1 | 0.13% | 0.1 | −1.22% | 0.1 | 0.26% |
| 2° | 0.55% | 0.2 | 0.40% | 0.2 | 0.46% | 0.2 | 0.24% | 0.2 | −1.37% | 0.2 | 0.53% |
| 3° | 0.74% | 0.3 | 0.34% | 0.3 | 0.55% | 0.3 | 0.23% | 0.3 | −1.78% | 0.3 | 0.50% |
| 4° | 0.09% | 0.4 | 0.62% | 0.4 | 0.53% | 0.4 | 0.29% | 0.4 | −1.82% | 0.4 | 0.44% |
| 5° | 0.55% | 0.5 | 0.73% | 0.5 | 0.62% | 0.5 | 0.21% | 0.5 | −2.21% | 0.5 | 0.37% |
| 6° | 0.75% | 0.6 | 0.91% | 0.6 | 0.37% | 0.6 | 0.29% | 0.6 | −2.31% | 0.6 | 0.65% |
| 7° | 0.83% | 0.7 | 0.51% | 0.7 | 0.90% | 0.7 | 0.42% | 0.7 | −2.33% | 0.7 | 0.47% |
| 8° | 0.55% | 0.8 | 0.86% | 0.8 | 0.59% | 0.8 | 0.49% | 0.8 | −2.33% | 0.8 | 0.32% |
| 9° | 0.84% | 0.9 | 0.86% | 0.9 | 0.18% | 0.9 | 0.48% | 0.9 | −1.64% | 0.9 | 0.57% |
| 10° | −0.21% | 1 | 0.81% | 1 | 1.07% | 1 | 0.49% | 1 | −8.28% | 1 | 0.48% |
| 20° | 0.32% | 1.1 | 0.91% | 1.3 | 0.35% | 1.5 | 0.70% | Shear | |||
| 30° | 0.31% | 1.2 | 1.18% | 1.5 | 1.37% | 2 | 0.81% | ||||
| 40° | −0.16% | 1.3 | 1.33% | 1.8 | 0.87% | 3 | 0.82% | 5° | 0.28% | ||
| 50° | −0.18% | 1.4 | 1.11% | 2 | 1.00% | 4 | 0.94% | 10° | 0.78% | ||
| 60° | −0.14% | 1.5 | 1.24% | 2.5 | 0.83% | 5 | 1.02% | 20° | 0.50% | ||
| 70° | −0.08% | 1.6 | 1.33% | 3 | 0.93% | 6 | 1.09% | 30° | 0.17% | ||
| 80° | −0.64% | 1.7 | 0.56% | 3.5 | 0.75% | 7 | 1.27% | 40° | −0.11% | ||
| 90° | −2.72% | 1.8 | 0.96% | 4 | 1.40% | 8 | 1.31% | (0°, 0°, −5°, 5°) | 0.56% | ||
| 100° | −2.48% | 1.9 | 0.96% | 4.5 | 0.73% | 9 | 1.31% | (0°, 0°, −10°, 10°) | −0.18% | ||
| 110° | −3.08% | 2 | 1.26% | 5 | 1.08% | 10 | 1.11% | (0°, 0°, −20°, 20°) | 0.32% | ||
| 120° | −2.34% | Hue | Translate | (0°, 0°, −30°, 30°) | 0.31% | ||||||
| 130° | −2.49% | (0°, 0°, −40°, 40°) | −0.27% | ||||||||
| 140° | −3.21% | 0.1 | 0.60% | (0.1, 0.1) | 0.13% | (−5°, 5°, −5°, 5°) | 0.87% | ||||
| 150° | −3.02% | 0.2 | 0.54% | (0.2, 0.2) | −1.52% | (−10°, 10°, −10°, 10°) | 0.91% | ||||
| 160° | −2.56% | 0.3 | 0.56% | (0.3, 0.3) | −0.62% | (−20°, 20°, −20°, 20°) | −0.72% | ||||
| 170° | −3.26% | 0.4 | 0.61% | (0.4, 0.4) | −1.47% | (−30°, 30°, −30°, 30°) | −0.14% | ||||
| 180° | −4.57% | 0.5 | 0.48% | (0.5, 0.5) | −0.79% | (−40°, 40°, −40°, 40°) | −0.06% | ||||
Figure 7Impacts comparison of Rotation and Shear. The figure reveals the impacts of the different parameters of Rotation and Shear on , , and classification performance improvement.
Figure 8Impacts comparison of Brightness, Contrast and Saturation. The impacts of Brightness, Contrast and Saturation on improving the classification performance on , , and are plotted in the figure.
DA combination policies.
| DA Policy | Function of Each Policy |
|---|---|
| RBC_1 |
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| RBC_2 |
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| RBC_3 |
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| RBC_4 |
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| RBC_5 |
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| RBCS |
Performance of policies applied on and . The best performing policy is highlighted in yellow.
| AA_IP | AA_CP | RBC_1 | RBC_2 | RBC_3 | RBC_4 | RBC_5 | RBCS | |
|---|---|---|---|---|---|---|---|---|
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| +9.59% | +9.43% | +10.63% | +10.45% | +10.49% | +10.38% | +10.86% | +10.57% |
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| +5.48% | +5.07% | +6.32% | +6.35% | +6.26% | +6.07% | +5.86% | +6.14% |
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| +3.19% | +2.89% | +3.73% | +3.66% | +3.72% | +3.80% | +3.61% | +3.66% |
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| +2.48% | +2.66% | +2.76% | +2.84% | +2.80% | +2.91% | +2.83% | +2.88% |
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| +6.23% | +5.06% | +6.78% | +6.77% | +6.73% | +7.31% | +7.05% | +7.10% |
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| +4.26% | +3.81% | +4.52% | +4.08% | +4.68% | +4.21% | +4.74% | +4.58% |
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| +2.41% | +2.04% | +2.39% | +2.52% | +2.50% | +2.37% | +2.58% | +2.46% |
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| +0.94% | +0.92% | −1.47% | −1.73% | −1.54% | −0.81% | −0.82% | −2.67% |
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| +2.57% | +1.06% | −2.61% | −1.95% | −1.99% | −2.12% | −1.80% | −1.53% |
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| +1.17% | +1.44% | −1.02% | −1.76% | −1.31% | −2.12% | −1.08% | −1.65% |
Performance of DA methods on . This table indicates the augment effect of different DA methods and parameters applied on when setting seed to 350. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy). The four DA methods with the best effect are still RandomRotation, Brightness, Contrast, and Shear. These four methods can obtain their best enhancement effect on with parameters 160°, 2, 5, and (−20°, 20°, −20°, 20°), respectively. The trend of the effect of different parameters is similar to that of , but with fewer increments for the average accuracy.
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| 1° | 2.64% | 0.1 | 2.86% | 0.1 | 2.27% | 0.1 | 1.72% | 0.1 | 2.76% | 0.1 | 1.90% |
| 2° | 3.37% | 0.2 | 2.82% | 0.2 | 2.10% | 0.2 | 2.73% | 0.2 | 2.31% | 0.2 | 2.10% |
| 3° | 3.40% | 0.3 | 3.57% | 0.3 | 3.17% | 0.3 | 2.70% | 0.3 | 2.52% | 0.3 | 1.89% |
| 4° | 3.37% | 0.4 | 3.34% | 0.4 | 2.70% | 0.4 | 2.32% | 0.4 | 2.83% | 0.4 | 2.45% |
| 5° | 3.34% | 0.5 | 4.02% | 0.5 | 3.23% | 0.5 | 2.41% | 0.5 | 1.98% | 0.5 | 2.11% |
| 6° | 3.79% | 0.6 | 4.22% | 0.6 | 4.02% | 0.6 | 2.92% | 0.6 | 2.52% | 0.6 | 2.17% |
| 7° | 3.13% | 0.7 | 4.43% | 0.7 | 3.46% | 0.7 | 2.00% | 0.7 | 2.37% | 0.7 | 2.24% |
| 8° | 3.73% | 0.8 | 4.03% | 0.8 | 3.51% | 0.8 | 2.75% | 0.8 | 2.07% | 0.8 | 2.44% |
| 9° | 2.96% | 0.9 | 4.11% | 0.9 | 4.84% | 0.9 | 3.15% | 0.9 | 2.21% | 0.9 | 1.54% |
| 10° | 2.98% | 1 | 4.65% | 1 | 4.45% | 1 | 3.16% | 1 | 1.14% | 1 | 0.09% |
| 20° | 3.66% | 1.1 | 4.69% | 1.3 | 4.33% | 1.5 | 3.68% | Shear | |||
| 30° | 4.06% | 1.2 | 4.17% | 1.5 | 4.54% | 2 | 2.97% | ||||
| 40° | 4.71% | 1.3 | 4.41% | 1.8 | 4.48% | 3 | 3.48% | 5° | 2.01% | ||
| 50° | 4.94% | 1.4 | 4.91% | 2 | 4.65% | 4 | 3.62% | 10° | 3.30% | ||
| 60° | 5.21% | 1.5 | 4.91% | 2.5 | 4.37% | 5 | 3.58% | 20° | 3.45% | ||
| 70° | 4.83% | 1.6 | 4.74% | 3 | 4.50% | 6 | 4.03% | 30° | 4.14% | ||
| 80° | 4.49% | 1.7 | 5.08% | 3.5 | 4.11% | 7 | 4.05% | 40° | 3.26% | ||
| 90° | 5.07% | 1.8 | 4.79% | 4 | 4.50% | 8 | 4.17% | (0°, 0°, −5°, 5°) | 2.91% | ||
| 100° | 5.00% | 1.9 | 4.38% | 4.5 | 4.88% | 9 | 3.39% | (0°, 0°, −10°, 10°) | 3.31% | ||
| 110° | 5.37% | 2 | 5.08% | 5 | 5.40% | 10 | 3.94% | (0°, 0°, −20°, 20°) | 3.37% | ||
| 120° | 4.72% | Hue | Translate | (0°, 0°, −30°, 30°) | 3.20% | ||||||
| 130° | 4.92% | (0°, 0°, −40°, 40°) | 4.27% | ||||||||
| 140° | 4.80% | 0.1 | 3.00% | (0.1, 0.1) | 3.23% | (−5°, 5°, −5°, 5°) | 2.77% | ||||
| 150° | 4.76% | 0.2 | 3.38% | (0.2, 0.2) | 3.06% | (−10°, 10°, −10°, 10°) | 3.81% | ||||
| 160° | 5.61% | 0.3 | 2.98% | (0.3, 0.3) | 2.16% | (−20°, 20°, −20°, 20°) | 4.54% | ||||
| 170° | 5.43% | 0.4 | 2.63% | (0.4, 0.4) | 2.19% | (−30°, 30°, −30°, 30°) | 4.03% | ||||
| 180° | 5.17% | 0.5 | 3.12% | (0.5, 0.5) | −0.17% | (−40°, 40°, −40°, 40°) | 4.45% | ||||
Performance of DA methods on . This heatmap shows the results when we increase the training set samples to 100 per class. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy). We can see that RandomRotation and RandomVerticalFlip have a negative impact. Saturation with a parameter of 9 and Brightness with a parameter of 1.7 are the two most effective DA methods and parameters.
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| 1° | 0.14% | 0.1 | 0.13% | 0.1 | 0.10% | 0.1 | 0.09% | 0.1 | −1.16% | 0.1 | 0.24% |
| 2° | 0.15% | 0.2 | 0.23% | 0.2 | 0.05% | 0.2 | 0.08% | 0.2 | −1.42% | 0.2 | 0.41% |
| 3° | 0.23% | 0.3 | 0.23% | 0.3 | 0.08% | 0.3 | 0.18% | 0.3 | −1.56% | 0.3 | 0.50% |
| 4° | 0.05% | 0.4 | 0.31% | 0.4 | 0.16% | 0.4 | 0.15% | 0.4 | −2.02% | 0.4 | 0.42% |
| 5° | 0.38% | 0.5 | 0.26% | 0.5 | 0.22% | 0.5 | 0.26% | 0.5 | −1.95% | 0.5 | 0.50% |
| 6° | 0.51% | 0.6 | 0.27% | 0.6 | 0.25% | 0.6 | 0.07% | 0.6 | −2.13% | 0.6 | 0.47% |
| 7° | 0.50% | 0.7 | −0.08% | 0.7 | −0.23% | 0.7 | 0.08% | 0.7 | −2.53% | 0.7 | 0.34% |
| 8° | 0.65% | 0.8 | 0.03% | 0.8 | −1.36% | 0.8 | 0.30% | 0.8 | −2.43% | 0.8 | 0.20% |
| 9° | 0.55% | 0.9 | 0.60% | 0.9 | 0.13% | 0.9 | 0.21% | 0.9 | −2.10% | 0.9 | 0.24% |
| 10° | −0.01% | 1 | 0.66% | 1 | 0.19% | 1 | 0.24% | 1 | −7.55% | 1 | 0.27% |
| 20° | −0.01% | 1.1 | 0.88% | 1.3 | 0.41% | 1.5 | 0.37% | Shear | |||
| 30° | −0.17% | 1.2 | 0.71% | 1.5 | 0.50% | 2 | 0.53% | ||||
| 40° | −0.20% | 1.3 | 0.45% | 1.8 | 0.45% | 3 | 0.63% | 5° | 0.36% | ||
| 50° | 0.10% | 1.4 | 0.29% | 2 | 0.62% | 4 | 1.02% | 10° | 0.44% | ||
| 60° | −0.45% | 1.5 | 0.75% | 2.5 | 0.70% | 5 | 1.27% | 20° | 0.11% | ||
| 70° | −0.56% | 1.6 | 0.70% | 3 | 0.52% | 6 | 1.14% | 30° | −0.03% | ||
| 80° | −3.18% | 1.7 | 0.95% | 3.5 | −0.31% | 7 | 1.24% | 40° | 0.01% | ||
| 90° | −2.44% | 1.8 | 0.57% | 4 | 0.31% | 8 | 1.30% | (0°, 0°, −5°, 5°) | 0.29% | ||
| 100° | −2.68% | 1.9 | 0.58% | 4.5 | 0.83% | 9 | 1.41% | (0°, 0°, −10°, 10°) | 0.33% | ||
| 110° | −2.11% | 2 | 0.32% | 5 | −0.36% | 10 | 1.35% | (0°, 0°, −20°, 20°) | 0.28% | ||
| 120° | −2.34% | Hue | Translate | (0°, 0°, −30°, 30°) | 0.48% | ||||||
| 130° | −1.83% | (0°, 0°, −40°, 40°) | 0.56% | ||||||||
| 140° | −3.11% | 0.1 | 0.50% | (0.1, 0.1) | −0.16% | (−5°, 5°, −5°, 5°) | 0.53% | ||||
| 150° | −3.36% | 0.2 | 0.57% | (0.2, 0.2) | −0.44% | (−10°, 10°, −10°, 10°) | 0.37% | ||||
| 160° | −3.38% | 0.3 | 0.69% | (0.3, 0.3) | −0.34% | (−20°, 20°, −20°, 20°) | 0.50% | ||||
| 170° | −3.22% | 0.4 | 0.52% | (0.4, 0.4) | −2.34% | (−30°, 30°, −30°, 30°) | 0.35% | ||||
| 180° | −3.12% | 0.5 | 0.52% | (0.5, 0.5) | −2.76% | (−40°, 40°, −40°, 40°) | −0.21% | ||||
Performance of DA methods on with setting seed to 3500. This heatmap shows the effect of different DA methods and parameters on the average accuracy improvement of when setting seed to 3500. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy). DA methods show a similar trend to that at seed is 350.
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| 1° | 3.26% | 0.1 | 1.76% | 0.1 | 1.06% | 0.1 | 0.75% | 0.1 | 2.26% | 0.1 | 1.60% |
| 2° | 4.34% | 0.2 | 2.57% | 0.2 | 1.52% | 0.2 | 0.88% | 0.2 | 2.64% | 0.2 | 1.75% |
| 3° | 4.96% | 0.3 | 3.19% | 0.3 | 2.12% | 0.3 | 1.32% | 0.3 | 2.87% | 0.3 | 2.00% |
| 4° | 5.21% | 0.4 | 3.16% | 0.4 | 1.24% | 0.4 | 1.63% | 0.4 | 2.91% | 0.4 | 2.08% |
| 5° | 5.45% | 0.5 | 3.59% | 0.5 | 2.98% | 0.5 | 1.63% | 0.5 | 2.99% | 0.5 | 1.97% |
| 6° | 5.58% | 0.6 | 3.94% | 0.6 | 3.29% | 0.6 | 1.94% | 0.6 | 2.79% | 0.6 | 1.93% |
| 7° | 5.65% | 0.7 | 4.16% | 0.7 | 3.61% | 0.7 | 2.16% | 0.7 | 2.72% | 0.7 | 1.88% |
| 8° | 5.68% | 0.8 | 4.70% | 0.8 | 4.01% | 0.8 | 2.11% | 0.8 | 2.74% | 0.8 | 1.67% |
| 9° | 5.75% | 0.9 | 5.30% | 0.9 | 4.43% | 0.9 | 2.51% | 0.9 | 2.55% | 0.9 | 1.21% |
| 10° | 5.58% | 1 | 5.76% | 1 | 4.84% | 1 | 2.48% | 1 | −0.51% | 1 | −0.36% |
| 20° | 5.61% | 1.1 | 5.34% | 1.3 | 4.83% | 1.5 | 2.69% | Shear | |||
| 30° | 5.81% | 1.2 | 5.34% | 1.5 | 4.83% | 2 | 3.00% | ||||
| 40° | 6.10% | 1.3 | 6.17% | 1.8 | 4.77% | 3 | 3.17% | 5° | 3.36% | ||
| 50° | 6.25% | 1.4 | 5.97% | 2 | 5.12% | 4 | 3.50% | 10° | 3.68% | ||
| 60° | 6.25% | 1.5 | 6.10% | 2.5 | 5.78% | 5 | 4.02% | 20° | 4.30% | ||
| 70° | 6.71% | 1.6 | 5.92% | 3 | 5.49% | 6 | 4.20% | 30° | 5.79% | ||
| 80° | 7.21% | 1.7 | 6.06% | 3.5 | 5.80% | 7 | 4.25% | 40° | 5.65% | ||
| 90° | 7.31% | 1.8 | 5.66% | 4 | 5.75% | 8 | 4.22% | (0°, 0°, −5°, 5°) | 4.17% | ||
| 100° | 7.59% | 1.9 | 6.13% | 4.5 | 5.12% | 9 | 4.48% | (0°, 0°, −10°, 10°) | 4.60% | ||
| 110° | 7.45% | 2 | 6.34% | 5 | 6.70% | 10 | 4.53% | (0°, 0°, −20°, 20°) | 4.98% | ||
| 120° | 7.21% | Hue | Translate | (0°, 0°, −30°, 30°) | 5.59% | ||||||
| 130° | 7.24% | (0°, 0°, −40°, 40°) | 5.98% | ||||||||
| 140° | 7.10% | 0.1 | 3.01% | (0.1, 0.1) | 5.50% | (−5°, 5°, −5°, 5°) | 5.32% | ||||
| 150° | 7.53% | 0.2 | 3.91% | (0.2, 0.2) | 4.20% | (−10°, 10°, −10°, 10°) | 5.07% | ||||
| 160° | 7.28% | 0.3 | 3.83% | (0.3, 0.3) | 3.31% | (−20°, 20°, −20°, 20°) | 5.52% | ||||
| 170° | 7.42% | 0.4 | 3.75% | (0.4, 0.4) | 1.54% | (−30°, 30°, −30°, 30°) | 6.32% | ||||
| 180° | 6.94% | 0.5 | 3.47% | (0.5, 0.5) | −3.24% | (−40°, 40°, −40°, 40°) | 5.41% | ||||
Performance of DA methods on with setting seed to 3500. The displayed percentage values describe the increase/decrease of in percent. The value is color-coded from blue (increase in accuracy) over white (no effect) to orange (decrease in accuracy). This heatmap shows the effect of different DA methods and different parameters on the average accuracy improvement of when setting seed to 3500. As with the experimental results on , the performance of DA is similar under different seeds.
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| 1° | 4.14% | 0.1 | 2.76% | 0.1 | 2.45% | 0.1 | 1.51% | 0.1 | 3.61% | 0.1 | 2.72% |
| 2° | 4.11% | 0.2 | 3.18% | 0.2 | 3.23% | 0.2 | 1.62% | 0.2 | 3.20% | 0.2 | 3.02% |
| 3° | 4.60% | 0.3 | 4.03% | 0.3 | 3.23% | 0.3 | 1.21% | 0.3 | 3.23% | 0.3 | 3.10% |
| 4° | 4.56% | 0.4 | 4.08% | 0.4 | 3.93% | 0.4 | 2.08% | 0.4 | 3.10% | 0.4 | 3.28% |
| 5° | 4.53% | 0.5 | 4.49% | 0.5 | 4.25% | 0.5 | 2.10% | 0.5 | 3.14% | 0.5 | 3.04% |
| 6° | 4.51% | 0.6 | 4.75% | 0.6 | 4.42% | 0.6 | 2.12% | 0.6 | 3.11% | 0.6 | 3.12% |
| 7° | 4.43% | 0.7 | 4.35% | 0.7 | 4.59% | 0.7 | 2.34% | 0.7 | 2.90% | 0.7 | 3.23% |
| 8° | 4.69% | 0.8 | 4.47% | 0.8 | 4.66% | 0.8 | 2.00% | 0.8 | 2.57% | 0.8 | 3.10% |
| 9° | 4.97% | 0.9 | 4.86% | 0.9 | 4.79% | 0.9 | 2.11% | 0.9 | 2.32% | 0.9 | 2.81% |
| 10° | 4.61% | 1 | 4.58% | 1 | 3.44% | 1 | 2.22% | 1 | −1.51% | 1 | 0.16% |
| 20° | 5.28% | 1.1 | 4.45% | 1.3 | 5.09% | 1.5 | 2.73% | Shear | |||
| 30° | 5.16% | 1.2 | 4.83% | 1.5 | 4.50% | 2 | 2.71% | ||||
| 40° | 5.22% | 1.3 | 5.08% | 1.8 | 4.85% | 3 | 2.83% | 5° | 4.18% | ||
| 50° | 5.44% | 1.4 | 4.86% | 2 | 5.29% | 4 | 2.93% | 10° | 4.38% | ||
| 60° | 5.58% | 1.5 | 5.33% | 2.5 | 5.64% | 5 | 2.93% | 20° | 4.56% | ||
| 70° | 5.76% | 1.6 | 5.20% | 3 | 5.75% | 6 | 3.09% | 30° | 4.95% | ||
| 80° | 5.50% | 1.7 | 4.93% | 3.5 | 5.21% | 7 | 2.78% | 40° | 5.21% | ||
| 90° | 6.19% | 1.8 | 4.86% | 4 | 5.82% | 8 | 2.52% | (0°, 0°, −5°, 5°) | 4.13% | ||
| 100° | 6.31% | 1.9 | 4.89% | 4.5 | 5.38% | 9 | 2.60% | (0°, 0°, −10°, 10°) | 4.49% | ||
| 110° | 6.27% | 2 | 4.81% | 5 | 5.48% | 10 | 2.41% | (0°, 0°, −20°, 20°) | 4.22% | ||
| 120° | 5.73% | Hue | Translate | (0°, 0°, −30°, 30°) | 5.00% | ||||||
| 130° | 5.82% | (0°, 0°, −40°, 40°) | 4.77% | ||||||||
| 140° | 6.08% | 0.1 | 2.59% | (0.1, 0.1) | 4.30% | (−5°, 5°, −5°, 5°) | 4.98% | ||||
| 150° | 5.97% | 0.2 | 2.77% | (0.2, 0.2) | 4.07% | (−10°, 10°, −10°, 10°) | 4.97% | ||||
| 160° | 6.07% | 0.3 | 2.79% | (0.3, 0.3) | 3.54% | (−20°, 20°, −20°, 20°) | 5.29% | ||||
| 170° | 5.98% | 0.4 | 3.35% | (0.4, 0.4) | 1.94% | (−30°, 30°, −30°, 30°) | 4.84% | ||||
| 180° | 6.22% | 0.5 | 3.12% | (0.5, 0.5) | −1.62% | (−40°, 40°, −40°, 40°) | 4.72% | ||||