The DOI matches its Crossref record; 34 of the 36 references it cites were found in a registry or an index; none of the 27 sources its claims cite is checked for support yet.
Weighted boxes fusion: Ensembling boxes from different object detection models
Open accessOverview
AI snapshot
Written from the paper’s full text.
TL;DR
Weighted Boxes Fusion (WBF) ensembles object detection boxes by fusing all predictions using confidence-weighted coordinates and rescaling confidence by cluster size and model count. It outperformed NMS, soft-NMS, and NMW on COCO and Open Images ensembles, reaching 56.1 mAP on COCO validation and 56.4 mAP on COCO test.
Key findings
- On a two-model COCO ensemble (EfficientDetB6 + EfficientDetB7), WBF achieved mAP(0.5..0.95) = 0.5344, mAP@0.5 = 0.7244, and mAP@0.75 = 0.5824, compared with NMS 0.5269/0.7156/0.5737, soft-NMS 0.5239/0.7121/0.5677, and NMW 0.5285/0.7171/0.5743.
- For test-time augmentation with EfficientDetB7, WBF reached mAP(0.5..0.95) = 0.5262, versus NMS 0.5233, soft-NMS 0.5210, and NMW 0.5250.
- On a many-model COCO ensemble, WBF gave 56.1 mAP on validation and 56.4 mAP on test, described as the top third result on the MS COCO leaderboard as of 07/08/2020.
- On Open Images, WBF reached 0.5665 mAP@0.5 for a RetinaNet ensemble (vs NMS 0.5442 and soft-NMS 0.5428) and 0.5982 mAP@0.5 for an ensemble of fairly different models (vs NMW 0.5667, NMS 0.5642, soft-NMS 0.5616), helping achieve 7th out of 558 in the challenge.
Methods
- WBF collects all predicted boxes, sorts them by confidence, clusters boxes with IoU > THR (THR = 0.55 was close to optimal in experiments), fuses coordinates as confidence-weighted sums, sets fused confidence as the average confidence, then rescales confidence by the number of boxes in the cluster divided by the number of models.
- Evaluation used Open Images V5 (about 16M boxes, 600 classes, 1.9M images; training 1,743,042 images, validation 41,620, test 99,999; mAP@0.5) and MS COCO (over 200,000 images, 80 categories; train2017 118k, val2017 5k, test 20k; mAP over IoU 0.5 to 0.95).
- Models included RetinaNet, EfficientDet, DetectoRS, YOLOv5, Faster R-CNN, Mask R-CNN, and Cascade R-CNN; WBF was compared against NMS, soft-NMS, and NMW, with grid search for optimal parameters.
Limitations
- The paper states WBF is slower than NMS and soft-NMS, on average around three times slower than standard NMS.
- The paper reports that replacing NMS at the output of an individual model with WBF degraded performance: RetinaNet ResNet152 on Open Images gave raw boxes 0.1718 mAP, NMS default 0.4902, NMS optimal 0.4906, and WBF optimal 0.4532; the authors attribute this to excessive low-scored wrong predictions, noting WBF works better for ensembles of fairly accurate models.
- Evident from the text: WBF performance depends on tuned parameters such as IoU threshold and model weights, which were optimized by grid search in the reported experiments.
Model-written summary. Check it against the paper before relying on it.
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16 Not checked yet · 15 Own result · 8 Own interpretation · 5 No basis given · 3 Own method
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This method significantly improves the quality of the combined predicted rectangles.”
- Also stated in: § 6.2. An ensemble of two different models · p. 4 · boosted
“Even for the ensemble of only two models, the WBF method outperformed significantly other methods.”
boosteddirect- Asserted: passes — The authors put it forward as true.
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- Also stated in: § 6.2. An ensemble of two different models · p. 4 · boosted
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the WBF method demonstrated the best results.”
boosted- Asserted: passes — The authors put it forward as true.
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In the paper
“The third top entry represents the results described in this paper.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“The WBF method outperformed by far the other algorithms (see Table 5)”
boosteddirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Combining predictions from several detectors with different backbones yields better performance”
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In the paper
“The technique was evaluated in the context of the Open Images Object Detection Challenge and helped achieving one of the top results in the challenge [3].”
- Also stated in: § Abstract · p. 1 · plain
“We tested method on several datasets and evaluated it in the context of the Open Images and COCO Object Detection tracks, achieving top results in these challenges.”
What the sources say
- Not checked yetcites [3]
plaindirect- Asserted: passes — The authors put it forward as true.
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- Also stated in: § Abstract · p. 1 · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“NMS with default IoU threshold = 0.5 (e.g. standard model output) - mAP: 0.4902”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Raw boxes (no NMS/WBF) - mAP: 0.1718”
plainSingle case- Asserted: passes — The authors put it forward as true.
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In the paper
“The method was expanded on the 3D boxes fusion as well.”
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In the paper
“WBFwith optimal parameters - mAP: 0.4532 (the optimized parameters: IoU threshold = 0.43, skip threshold = 0.21)”
plaincorrelationalSingle case- Asserted: passes — The authors put it forward as true.
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- It may state two separate claims as one. 13
- Probably not a substantial claim. 15
- The quote only partly states this claim. 3
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The WBF method for combining predictions of detection models gave 56.1 mAP for the validation data set and 56.4 mAP for the test set.”
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“the top performance for the COCO Detection Challenge (( 56.1 mAP for validation data set and 56.4 mAP for the test-dev set).”
plain- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Note: in our experiments, THR = 0 . 55 was close to an optimal threshold.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Even for the ensemble of only two models, the WBF method outperformed significantly other methods.”
boosteddirect- Asserted: passes — The authors put it forward as true.
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The quote only partly states this claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“the WBF algorithm, on average, is around three times slower than the standard NMS.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“| NMS | 0.5233 | 0.7129 | 0.5656 |”
- Also stated in: § 6.3. Test-time-augmentation ensemble · p. 5 · plain
“| Soft-NMS | 0.5210 | 0.7092 | 0.5633 |”
- Also stated in: § 6.3. Test-time-augmentation ensemble · p. 5 · plain
“| NMW | 0.5250 | 0.7138 | 0.5691 |”
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one. The quote only partly states this claim.
- Also stated in: § 6.3. Test-time-augmentation ensemble · p. 5 · plain
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In the paper
“In practice, the outcome for both variants did not differ significantly, with the first being slightly better.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
In the paper
“It is a considerable improvement compared to the performance of individual models and gives the top third result on the MS COCO official leaderboard [6] (as of 07/08/2020).”
What the sources say
- Not checked yetcites [6]
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“the winners from the first place of 3D Detection and Domain Adaptation track [13] and the second place from the 2D Object Detection track [11] used this method for combining predictions.”
What the sources say
- Not checked yetcites [13]
- Not checked yetcites [11]
- Not checked yetcites [19]
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
None of the sources cited for this claim have been checked yet.
In the paper
“The soft-NMS method was proposed in [9] to reduce this problem. Instead of completely removing the detection proposals with high IoU and high confidence, it reduces the confidences of the proposals proportional to IoU value.”
- Also stated in: § 2.2. Soft-NMS · p. 2 · boosted
“Soft-NMS demonstrated noticeable improvements over traditional NMS on standard benchmark datasets, like PASCALVOCandMSCOCO[5]. It has shown to improve performance for single models [9].”
What the sources say
- Not checked yetcites [9]
- Not checked yetcites [5]
boosteddirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: unclear — It is unclear whether the paper’s conclusions depend on it.
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It may state two separate claims as one.
- Also stated in: § 2.2. Soft-NMS · p. 2 · boosted
None of the sources cited for this claim have been checked yet.
In the paper
“Microsoft COCO [5, 23], one of the most popular benchmark datasets for object detection.”
What the sources say
- Not checked yetcites [5]
- Not checked yetcites [23]
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Both NMS and soft-NMS exclude some boxes, while WBF uses all boxes. Thus, it can fix cases where all boxes are predicted inaccurately by all models. This case is illustrated in Figure3. NMS/soft-NMS will leave only one inaccurate box, while WBF will fuse it using all predicted boxes.”
plaindirect- Asserted: passes — The authors put it forward as true.
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What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“As the test set labels are not available, we performed the ablation study on the validation set.”
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
- Rests on an assumption: The test set labels are not available.
In the paper
“It was also reported that the WBF method gives the best results on the Wheat detection dataset for boxes ensemble comparing to other methods [32].”
What the sources say
- Not checked yetcites [32]
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“The first place winners from Lyft 3D Object Detection for Autonomous Vehicles [19] reported that WBF gives better score for their ensemble (0.222 vs 0.220) [48].”
What the sources say
- Not checked yetcites [48]
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“These results can be reproduced using a benchmark published on GitHub [46].”
What the sources say
- Not checked yetcites [46]
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
In the paper
“Combining predictions from different models generalizes better and usually yields more accurate results compared to a single model [27].”
What the sources say
- Not checked yetcites [27]
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Such methods work well on a single model. However, they only select the boxes and can not produce averaged localization of predictions combined from various models effectively.”
- Also stated in: § 2.2. Soft-NMS · p. 2 · plain
“However, both NMS and soft-NMS discard redundant boxes, and thus can not produce averaged localization predictions from different models effectively.”
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It may state two separate claims as one.
- Also stated in: § 2.2. Soft-NMS · p. 2 · plain
In the paper
“These models have recently shown top results on the COCO database [36].”
What the sources say
- Not checked yetcites [36]
plain- Asserted: passes — The authors put it forward as true.
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- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We think it is due to the excessive number of low scored wrong predictions given by the model output.”
hedgeddirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim.
- Rests on an assumption: Most neural networks for Object Detection use NMS or Soft-NMS output to filter predicted boxes.
None of the sources cited for this claim have been checked yet.
In the paper
“The non-maximum weighted (NMW) method proposed in [49, 26] has a similar idea. However, the NMW method does not change confidence scores; it uses IoU value to weight the boxes. NMW uses a box with the highest confidence to compare with, while WBF updates a fused box at each step, and uses it to check the overlap with the next predicted boxes.”
What the sources say
- Not checked yetcites [49]
- Not checked yetcites [26]
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
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It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“We used a grid search to find the optimal parameters for each of the four methods, which allowed achieving the best mAP for the given method.”
- Also stated in: § 6.3. Test-time-augmentation ensemble · p. 4 · plain
“Then, we perform a grid search to find optimal parameters for all four ensemble methods.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
- Also stated in: § 6.3. Test-time-augmentation ensemble · p. 4 · plain
None of the sources cited for this claim have been checked yet.
In the paper
“The ensemble methods often get top places in machine learning competitions, for example, see [12, 15, 34, 33, 42, 7].”
What the sources say
- Not checked yetcites [12]
- Not checked yetcites [15]
- Not checked yetcites [34]
- Not checked yetcites [33]
- Not checked yetcites [42]
- Not checked yetcites [7]
plaincorrelational- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“Also, NMW does not use information about how many models predict a given box in a cluster and, therefore, does not produce the best results for models' ensemble.”
What the sources say
- Not checked yetcites [49]
- Not checked yetcites [26]
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The NMS or soft-NMS produces more efficient filtering for those predictions”
plaindirectSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
The quote only partly states this claim.
- Rests on an assumption: Most neural networks for Object Detection use NMS or Soft-NMS output to filter predicted boxes.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“when it comes to a large number of overlapping boxes with different confidence scores, WBF gives worse results than NMS.”
plaindirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: fails — The paper may give no reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.
- Rests on an assumption: Most neural networks for Object Detection use NMS or Soft-NMS output to filter predicted boxes.
In the paper
“Such errors reduce the precision of the model.”
What the sources say
- Not checked yetcites [25]
plainconditional- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
It may state two separate claims as one.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“The weights in the final ensemble and IoU threshold for the WBF methods were optimized using the validation set.”
plain- Asserted: passes — The authors put it forward as true.
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- Load-bearing: passes — The paper’s conclusions depend on it.
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Probably not a substantial claim.
In the paper
“These results can be reproduced using benchmark published on GitHub [46].”
What the sources say
- Not checked yetcites [46]
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: fails — The paper’s conclusions may not depend on it.
- Based: passes — The paper gives a reason why it holds.
Probably not a substantial claim. The paper’s conclusions may not depend on it.
The paper relies on this without support.
The 3D version of boxes fusion was successfully applied by the winning teams of Waymo Open Dataset and Lyft 3D Object Detection for Autonomous Vehicles challenges.
“The 3D version of boxes fusion was successfully applied by the winning teams of Waymo Open Dataset and Lyft 3D Object Detection for Autonomous Vehicles challenges.”
The paper relies on this without support.
The Open Images dataset is the largest labeled dataset with object detection annotations to date.
“We used the Open Images data set [20], the largest data set with object detection annotations to date”
“To date, it is the largest labeled dataset with object detection annotations.”
The paper relies on this without support.
The test set labels are not available.
“As the test set labels are not available, we performed the ablation study on the validation set.”
The paper relies on this without support.
Most neural networks for Object Detection use NMS or Soft-NMS output to filter predicted boxes.
“Most neural networks for Object Detection use NMS or Soft-NMS output to filter predicted boxes.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The advantage of this type of method is that it takes full consideration of object relationships and their spatial layout [118, 119].”
From Object Detection in 20 Years: A Survey (2023) · cites this paper as [118]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ 3. Weighted Boxes Fusion · p. 3
“This case is illustrated in Figure3. NMS/soft-NMS will leave only one inaccurate box, while WBF will fuse it using all predicted boxes.”
§ 6.4.2 Ensemble of RetinaNet models for Open Images Dataset · p. 6
“Figure 3: The official leader boards of COCO Detection Challenge (Bounding Box) as of 07/08/20.”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ 6.3. Test-time-augmentation ensemble · p. 5
“| Model | mAP(0.5..0.95) | mAP(@0.5 IoU) | mAP(@0.5 IoU) |”
§ 6.3. Test-time-augmentation ensemble · p. 5
“| Method | mAP(0.5..0.95) | mAP(0.5) | mAP(0.75) |”
Citations
Cites
Deep Residual Learning for Image Recognition
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Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks
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TPH-YOLOv5-Air: Airport Confusing Object Detection via Adaptively Spatial Feature Fusion
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Gaussian Synthesis for High-Precision Location in Oriented Object Detection
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ICDAR 2023 Competition on Detection and Recognition of Greek Letters on Papyri
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Enhanced Non-Maximum Suppression for the Detection of Steel Surface Defects
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Cow-YOLO: Automatic cow mounting detection based on non-local CSPDarknet53 and multiscale neck
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Integrating AI and edge computing for advanced safety at railroad grade crossings
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Highly adaptable deep-learning platform for automated detection and analysis of vesicle exocytosis
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ICDAR 2021 Competition on Mathematical Formula Detection
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FEMFER: feature enhancement for multi-faces expression recognition in classroom images
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MoDAR: Using Motion Forecasting for 3D Object Detection in Point Cloud Sequences
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YOLO-RDS: An efficient algorithm for monitoring the uprightness of seedling transplantation
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Road Object Detection Robust to Distorted Objects at the Edge Regions of Images
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Improving small intestinal stromal tumor detection using 3D context and auxiliary priori cues
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Exploring Model Learning Heterogeneity for Boosting Ensemble Robustness
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Universal lesion detection in CT scans using neural network ensembles
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A face detection method via ensemble of four versions of YOLOs
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ARSD: An Adaptive Region Selection Object Detection Framework for UAV Images
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Metadata
- Authors
- Solovyev, R., Wang, W., & Gabruseva, T.
- Affiliations
- Russian Academy of Sciences (RU)
- National University of Singapore (SG)
- Cork University Hospital (IE)
- Corresponding author
- Solovyev, Roman
- Venue
- Image and Vision Computing
- Publisher
- Elsevier BV
- Published
- 2021-03
- Volume
- 107
- Pages
- 104117
- ISSN
- 0262-8856 (ISSN-L)
- OpenAlex
- W3127743092
- Semantic Scholar
- 2765484bdd3e5d8674917efc98145daa1a71e9fa
- Cited by
- 543
- References
- 36
- Citations by year
- 2026: 108 · 2025: 98 · 2024: 92 · 2023: 130 · 2022: 76 · 2021: 36
- FWCI
- 30.03
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Image and Vision Computing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image and Video Retrieval Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Visual Attention and Saliency Detection
- Keywords
- object detection, model ensembling, confidence scores, 3D object detection, autonomous driving, Waymo Open Dataset
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
A language model drew the claims from the paper on 2026-10-07, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).
A second model labelled each claim on 2026-10-07 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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