{"notes":[{"id":"object-detection/fcos","category":"object-detection","legacyPath":"object-detection/1904-fcos","legacySlug":"1904-fcos","legacyPaths":[],"title":"FCOS","subtitle":"A World Without Anchors","author":"Z. 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Yuan","paperDate":"2020-06-08","publishedOn":"2025-08-23","paperTitle":"Generalized Focal Loss: Learning Qualified and Distributed Bounding Boxes for Dense Object Detection","paperUrl":"https://arxiv.org/abs/2006.04388","bibliography":{"title":"Generalized Focal Loss: Learning Qualified and Distributed Bounding Boxes for Dense Object Detection","authors":["Xiang Li","Wenhai Wang","Lijun Wu","Shuo Chen","Xiaolin Hu","Jun Li","Jinhui Tang","Jian Yang"],"url":"https://arxiv.org/abs/2006.04388","pdfUrl":"https://proceedings.neurips.cc/paper_files/paper/2020/file/f0bda020d2470f2e74990a07a607ebd9-Paper.pdf","codeUrl":"https://github.com/implus/GFocal","preprint":{"id":"2006.04388","submittedOn":"2020-06-08","url":"https://arxiv.org/abs/2006.04388"},"publication":{"venue":"NeurIPS","year":2020,"kind":"conference","url":"https://papers.nips.cc/paper_files/paper/2020/hash/f0bda020d2470f2e74990a07a607ebd9-Abstract.html"},"citation":"@misc{objectdetectiongfl2020,\n  title = {{Generalized Focal Loss: Learning Qualified and Distributed Bounding Boxes for Dense Object Detection}},\n  author = {Xiang Li and Wenhai Wang and Lijun Wu and Shuo Chen and Xiaolin Hu and Jun Li and Jinhui Tang and Jian Yang},\n  year = {2020},\n  eprint = {2006.04388},\n  archivePrefix = {arXiv},\n  url = {https://arxiv.org/abs/2006.04388}\n}\n","citationPath":"/content/papers/citations/object-detection/gfl.71fabce4b963.bib"},"thumbnail":{"src":"/content/papers/assets/b23270560323cea28f3b1fe736d861dd3365d20c4fb99278dcc3ce306df890dc.jpg","width":1224,"height":380},"locale":"en","path":"/content/papers/en/object-detection/gfl.b9fa7b27fd1a.md","headings":[{"id":"problem-definition","text":"Problem Definition","depth":2},{"id":"solution","text":"Solution","depth":2},{"id":"focal-loss","text":"Focal Loss","depth":3},{"id":"quality-focal-loss","text":"Quality Focal Loss","depth":3},{"id":"distribution-focal-loss","text":"Distribution Focal Loss","depth":3},{"id":"generalized-focal-loss","text":"Generalized Focal Loss","depth":3},{"id":"discussion","text":"Discussion","depth":2},{"id":"is-qfl-effective","text":"Is QFL Effective?","depth":3},{"id":"is-dfl-effective","text":"Is DFL Effective?","depth":3},{"id":"conclusion","text":"Conclusion","depth":2}],"anchorAliases":{"解決問題":"solution","qfl-put-quality-into-the-class-score":"quality-focal-loss","dfl-turn-one-distance-into-a-distribution":"distribution-focal-loss","one-general-form-two-uses":"generalized-focal-loss","experimental-results-and-discussion":"discussion","qfl-does-the-score-improve-ranking":"is-qfl-effective","dfl-what-does-the-box-distribution-add":"is-dfl-effective"},"guide":null,"relatedReading":[{"id":"object-detection/fcos","relation":"comparison","topic":"Aligning classification and localization quality"},{"id":"object-detection/tood","relation":"comparison","topic":"Aligning classification and localization quality"}]}],"text":"At the time of the author's note, this paper had already drawn more than seven thousand citations.\n\nA classic paper that we must take a look at.\n\n## Problem Definition\n\nFor a long time, mainstream object detection methods have been dominated by **anchor-based** designs.\n\nFrom Faster R-CNN, SSD to YOLOv2/v3, everyone has centered their designs around anchors: laying out a huge number of candidate boxes and then deciding which are positive and which are negative samples.\n\nWhile practical, this design brings several concerns:\n\n1. **Numerous hyperparameters**: Anchor size, aspect ratio, count, and IoU thresholds need tuning. The FCOS paper cites a RetinaNet ablation where anchor configuration changes COCO AP by up to about four points.\n2. **Poor generalization**: Fixed anchor shapes can make objects of very different sizes or unusual shapes difficult to cover, and a new detection task may require redesigning them.\n3. **Imbalance of positive and negative samples**: To ensure recall, thousands of anchors must be tiled across the image. The vast majority become negative samples, leading to extremely imbalanced training.\n4. **Complex computation**: From IoU calculations to matching rules, anchors introduce additional computation and complexity.\n\nAlthough anchor-free is not a new concept, previous methods each had obvious flaws.\n\nFor example, YOLOv1 predicts boxes from grid locations near object centers and has limited recall; CornerNet pairs detected corners but needs extra grouping work; DenseBox regresses from positions directly, yet varying object sizes and overlapping boxes made generic detection difficult. The latter family was mainly used for specialized tasks such as text or face detection.\n\nThere are many more examples.\n\nAnchor-free architectures have always been a step behind in overall performance—in the field already ruled by anchor-based methods, they had no real foothold.\n\n**Does object detection really depend on anchors?**\n\nThe authors aim to break this deadlock: like semantic segmentation, the detector could predict at each sampled feature-map location, without anchors or their IoU matching rules. FCOS still needs rules for assigning positive locations and scales.\n\nObject detection, in their view, should return to the clean paradigm of **fully convolutional per-pixel prediction**.\n\n## Solution\n\nThe core idea of FCOS is to reframe object detection as a **per-pixel prediction** problem. Instead of matching a grid of candidate anchors with ground truth, it treats sampled feature-map locations mapped to the image as training samples.\n\nSuppose at the $i$-th layer of the backbone, we obtain a feature map $F_i \\in \\mathbb{R}^{H \\times W \\times C}$ with stride $s$.\n\nThe ground-truth bounding box for an input image is denoted as\n\n$$\nB_i = (x^{(i)}_0, y^{(i)}_0, x^{(i)}_1, y^{(i)}_1, c^{(i)}) \\in \\mathbb{R}^4 \\times \\{1,2,\\dots,C\\},\n$$\n\nwhere $(x^{(i)}_0, y^{(i)}_0)$ and $(x^{(i)}_1, y^{(i)}_1)$ are the coordinates of the top-left and bottom-right corners, and $c^{(i)}$ is the class label.\n\nFor a location $(x,y)$ on the feature map, write its corresponding **input-image** coordinates as $(X,Y)$:\n\n$$\n(X,Y)=(\\lfloor \\tfrac{s}{2} \\rfloor + xs, \\; \\lfloor \\tfrac{s}{2} \\rfloor + ys).\n$$\n\nIf this image position falls within a ground-truth box $B_i$, it is a positive sample with class label $c^*=c^{(i)}$; otherwise, it is background ($c^*=0$).\n\nBesides classification, each location must regress a 4D vector:\n\n$$\nt^* = (l^*, t^*, r^*, b^*),\n$$\n\nwhich represents the distances from that position to the left, top, right, and bottom edges of the box, as illustrated below:\n\n\n\n![bounding box](/content/papers/assets/3a3080a9d661cc13b2dc595c01e4807b9e8b854d7c8d6b40328ceca1e5ca7026.jpg)\n\n\n\n$$\nl^* = X - x^{(i)}_0, \\quad\nt^* = Y - y^{(i)}_0, \\quad\nr^* = x^{(i)}_1 - X, \\quad\nb^* = y^{(i)}_1 - Y\n$$\n\nIf a position falls within multiple boxes, the box with the smallest area is chosen as the regression target to reduce ambiguity.\n\nIn this way, **each sampled location directly outputs “what is here” and “where is the box,”** without relying on anchors.\n\nAt the network output, the last layer outputs both a classification branch $p \\in \\mathbb{R}^C$ and a regression branch $t = (l, t, r, b)$.\n\nSince regression distances must be positive, the authors use $\\exp(x)$ to map any real number to $(0,\\infty)$. When the regression head is shared across FPN levels, they use a learned scale $s_i$ for each level and output $\\exp(s_i x)$.\n\nCompared with a RetinaNet-like detector using nine anchors at each location, this design needs roughly one ninth as many class and box output variables per location. That is a comparison with that nine-anchor setup, not a general ninefold speedup.\n\nThe overall loss is defined as:\n\n$$\nL(\\{p_{x,y}\\}, \\{t_{x,y}\\}) =\n\\frac{1}{N_{\\text{pos}}} \\sum_{x,y} L_{\\text{cls}}(p_{x,y}, c^*_{x,y}) \\; + \\;\n\\frac{\\lambda}{N_{\\text{pos}}} \\sum_{x,y} \\mathbf{1}_{\\{c^*_{x,y}>0\\}} \\, L_{\\text{reg}}(t_{x,y}, t^*_{x,y})\n$$\n\nHere $L_{\\text{cls}}$ uses **Focal Loss** across locations, while the indicator restricts **IoU regression loss** $L_{\\text{reg}}$ to positives. $N_{\\text{pos}}$ is the number of positive samples and $\\lambda=1$. Once center-ness is added, its BCE loss is trained separately.\n\nDuring inference, for each location $(x, y)$, we obtain its classification score $p_{x,y}$ and regression result $t_{x,y}$. As long as $p_{x,y} > 0.05$, it is treated as a candidate box and mapped back to image coordinates by inverse transformation.\n\nAt this point, the core idea of FCOS is clear: remove anchors and let each sampled location predict directly.\n\nHowever, this design immediately faces two challenges:\n\n1. The stride of the feature map may be too large, causing small objects to be missed and recall to drop;\n2. Overlapping boxes cause ambiguity—which box should a pixel regress to?\n\nThe authors' solution is **multi-level prediction via FPN**, as shown below:\n\n\n\n![model_arch](/content/papers/assets/23edca5ceca50cfcadbf6fd9cb8e8720100daff3135c951a4554454e3b9c69e7.jpg)\n\n\n\nThe authors use five levels ($\\{P_3,P_4,P_5,P_6,P_7\\}$) with strides of 8, 16, 32, 64, and 128.\n\nThe authors assign a positive location to a level according to the **maximum of its four side distances** to the ground-truth box: for example, $P_3$ covers the 0–64-pixel regression range and $P_4$ the 64–128-pixel range. This is not a direct threshold on box area. Objects of different sizes therefore often land on different levels, reducing overlap ambiguity.\n\nEven so, there remains a final issue: pixels far from the center often produce low-quality boxes.\n\nTo address this, the authors introduce a lightweight **center-ness branch** to measure how far a location deviates from the object center.\n\nFor position $(x, y)$, the target is defined as:\n\n$$\n\\text{centerness}^* = \\sqrt{\\frac{\\min(l^*, r^*)}{\\max(l^*, r^*)} \\times \\frac{\\min(t^*, b^*)}{\\max(t^*, b^*)}}\n$$\n\nThis value lies in $[0, 1]$, approaching 1 near the object center.\n\nBCE loss supervises this branch during training. At inference, its score is **multiplied by the classification score**, lowering the rank of edge-location predictions so that poor boxes are more likely to be removed during subsequent NMS.\n\nUltimately, FCOS, with its simplest per-pixel design, together with multi-level assignment via FPN and centerness for quality control, completely abandons anchors—yet demonstrates performance comparable to, and even surpassing, mainstream anchor-based methods.\n\n## Discussion\n\nThe authors validate FCOS on the **MS COCO** benchmark, following standard practice: **trainval35k (115K)** is used for training, **minival (5K)** for ablation, and main results are submitted to **test-dev (20K)**.\n\nUnless otherwise specified, the backbone is **ResNet-50**, and the optimizer and hyperparameters follow the **RetinaNet** settings: SGD, 90K iterations, batch size 16, initial learning rate 0.01, which drops by a factor of 10 at both 60K and 80K iterations, weight decay 0.0001, momentum 0.9, input image short side 800, and long side no more than 1333.\n\nInference also adopts RetinaNet's post-processing and hyperparameters, with candidate location threshold $p_{x,y}>0.05$; further performance gains are possible if parameters are specifically tuned for FCOS.\n\nBefore the rest of the analysis, let us clarify **Best Possible Recall (BPR)** so that the tables are easier to read:\n\n$$\n\\text{BPR} \\;=\\; \\frac{\\#\\{\\text{GT boxes assigned to at least one sample during training}\\}}{\\#\\{\\text{all GT boxes}\\}} .\n$$\n\n### Multi-Level FPN and Recall Upper Bound\n\n\n\n![fpn](/content/papers/assets/3303496b90e961b6a0e1248980e0805ecaa1d27dd219636afbde4aa0af01915f.jpg)\n\n\n\nFirst, the authors consider that FCN-style detectors may suffer from insufficient recall due to larger stride, so they test with a single **P4 (stride 16)** layer: with only this layer, FCOS still achieves **BPR = 95.55%**, which is significantly higher than the official Detectron version of **RetinaNet** (low-quality matching, IoU≥0.4), which achieves **90.92%**.\n\nWith **FPN (P3–P7)**, FCOS reaches **98.40% BPR**, **0.83 percentage points below** RetinaNet's **99.23%** when all low-quality matches are allowed.\n\nBPR is assignment-based recall coverage, not the detector's measured recall. FCOS's **AR** is higher than RetinaNet's in the controlled comparison below, so these experiments do not show the BPR gap becoming the main performance bottleneck.\n\n### Ambiguous Samples Caused by Overlaps\n\n\n\n![overlap](/content/papers/assets/271981e0a84bc568c57b8d0b109ff3222d1349daa36ab70b5eb4c9ee197d2bf8.jpg)\n\n\n\nWhen multiple GT boxes overlap in space, per-pixel assignment may cause ambiguity as to \"which box a given location should regress to.\"\n\nWith only **P4**, ambiguous samples on minival account for **23.16%** of all positive samples; after introducing **FPN**, because objects of different sizes are assigned to different levels, ambiguity drops sharply to **7.14%**. Excluding \"same-class overlaps\" (which do not affect classification accuracy), the cross-class ambiguity rate drops from **17.84%** to **3.75%**.\n\nAt inference time, only **2.3%** of detected boxes originate from ambiguous locations, and for cross-class ambiguities, this drops to **1.5%**.\n\nThus **multi-level assignment plus the smallest-area rule** substantially reduce ambiguity. These rates and the subsequent AP results support the method.\n\n### The Necessity and Effectiveness of Center-ness\n\n\n\n![centerness](/content/papers/assets/91cfdfe50bcdade13a480ebaf36b082666dfac2444ce9c17bc0c35e3ef054258.jpg)\n\n\n\nEven with FPN, pixels far from the object center still easily generate low-quality boxes.\n\nTo address this, FCOS adds a single-layer **center-ness** branch alongside the classification branch, predicting the normalized offset from center:\n\n$$\n\\text{centerness}^* \\;=\\; \\sqrt{\\frac{\\min(l^*,r^*)}{\\max(l^*,r^*)}\\cdot\\frac{\\min(t^*,b^*)}{\\max(t^*,b^*)}}\n$$\n\nThis is supervised with **BCE** during training. At inference, $\\text{score}=\\text{cls}\\times\\text{centerness}$ lowers edge predictions in the ranking, making poor candidates more likely to be filtered by subsequent NMS.\n\nIn this minival ablation, a predicted center-ness branch raises **AP from 33.5% to 37.1%**. Computing center-ness directly from regressed sides instead leaves AP at 33.5%. This supports a separate learned branch in this setup.\n\n### Fair Comparison With Anchor-based Methods\n\n\n\n![comparison](/content/papers/assets/313f3b5c10e28a4c787956017fa2dcfc07fa11733e89ce6c607161d15f803de8.jpg)\n\n\n\nTo rule out implementation differences, the authors adjust FCOS to settings nearly identical to **RetinaNet**: removing **GroupNorm** (using gradient clipping for stability instead), generating **P6/P7** from **C5** rather than **P5**.\n\nIn this minival comparison, FCOS has **36.3% AP versus RetinaNet's 35.9%**, but its AP50 is **54.8% versus 56.0%**. Learning rate, NMS threshold, and other hyperparameters follow RetinaNet. The result supports FCOS as an anchor-free alternative; it cannot by itself isolate the contribution of a simpler architecture or of assignment rules. The authors also suggest FCOS may improve with dedicated tuning.\n\n### Overall Comparison With Contemporary SOTA\n\n\n\n![compare with sota](/content/papers/assets/5707aba72f44c416510e8c6b9c519a26c82f3bb8131fb0ad03e4a86bf5a2eb7f.jpg)\n\n\n\nOn test-dev, FCOS with **ResNet-101-FPN** reaches **41.5 AP** versus **39.1 AP** for a same-backbone RetinaNet row, a 2.4-AP cross-method gap whose training conditions are not fully controlled. With a **ResNeXt-101-64×4d-FPN** backbone, FCOS reaches **43.2 AP**, above anchor-free **CornerNet's 40.5 AP**, while avoiding its corner pairing and embedding aggregation.\n\nWith center-ness branch placement, center sampling, GIoU, and regression-target normalization added, the single-model, single-scale result reaches **44.7 AP**. This improved system is a separate row from the 43.2-AP FCOS result; the extra changes should remain visible when comparing them.\n\n## Conclusion\n\nFCOS brings object detection back to the simple **per-pixel** paradigm: no proposals, no predefined anchors. Each sampled location learns both “what is here” and “where is the box.” FPN assignment reduces size and overlap ambiguity, and a lightweight **center-ness** branch helps rank box quality.\n\nThe influence of FCOS is reflected on three main levels.\n\nFirst, **sample assignment and task alignment** became active lines of work. [ATSS](https://arxiv.org/abs/1912.02424) studies statistical assignment; [PAA](https://arxiv.org/abs/2007.08103), [OTA](https://arxiv.org/abs/2103.14259), and [YOLOX's SimOTA](https://arxiv.org/abs/2107.08430) explore other dynamic or optimization-based assignments; [TOOD](https://arxiv.org/abs/2108.07755) works on classification-localization alignment. They tackle related questions about which locations should learn from which objects, although these works should not all be presented as direct descendants of FCOS.\n\nSecond, **quality-aware scoring and box regression** took several paths. [GFL's QFL/DFL](https://arxiv.org/abs/2006.04388) links classification scores to localization quality and uses distributional box regression. [VarifocalNet](https://arxiv.org/abs/2008.13367) uses IoU-aware scores and star-shaped box features. These are related ways to reflect box quality; their mechanisms are not interchangeable with FCOS center-ness or with each other.\n\nThird, the **Transformer line**, starting with [DETR](https://arxiv.org/abs/2005.12872) and followed by Deformable DETR, DINO, and RT-DETR, offers another route using set matching that can avoid anchors and NMS. In **real-time and edge settings**, lightweight convolutional heads like FCOS remain useful baselines. Later anchor-free YOLO designs also address assignment and quality scoring.\n\nIn summary, FCOS's contribution is not just \"removing anchors,\" but reframing the detection problem: **let each location make its own decision, and use correct assignment and scoring so that good boxes naturally emerge**.\n\nAnchor-based methods did not disappear. FCOS left a clearer way to ask how locations are assigned and how good boxes are scored.\n","imageSizes":{"/content/papers/assets/3a3080a9d661cc13b2dc595c01e4807b9e8b854d7c8d6b40328ceca1e5ca7026.jpg":{"width":896,"height":512},"/content/papers/assets/23edca5ceca50cfcadbf6fd9cb8e8720100daff3135c951a4554454e3b9c69e7.jpg":{"width":1508,"height":668},"/content/papers/assets/3303496b90e961b6a0e1248980e0805ecaa1d27dd219636afbde4aa0af01915f.jpg":{"width":852,"height":260},"/content/papers/assets/271981e0a84bc568c57b8d0b109ff3222d1349daa36ab70b5eb4c9ee197d2bf8.jpg":{"width":844,"height":128},"/content/papers/assets/91cfdfe50bcdade13a480ebaf36b082666dfac2444ce9c17bc0c35e3ef054258.jpg":{"width":876,"height":176},"/content/papers/assets/313f3b5c10e28a4c787956017fa2dcfc07fa11733e89ce6c607161d15f803de8.jpg":{"width":1836,"height":480},"/content/papers/assets/5707aba72f44c416510e8c6b9c519a26c82f3bb8131fb0ad03e4a86bf5a2eb7f.jpg":{"width":1140,"height":516}}}