2nd/10_Wiki/Topics/AI_and_ML/Bounding-Box-Regression.md

---
id: wiki-2026-0508-bounding-box-regression
title: Bounding Box Regression
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [bbox regression, object detection, IoU, anchor box, NMS, DETR, YOLO, mAP]
duplicate_of: none
source_trust_level: A
confidence_score: 0.93
verification_status: applied
tags: [object-detection, bbox, computer-vision, iou, nms, yolo, detr, anchor-free, mAP]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: PyTorch / Ultralytics / Detectron2
---

# Bounding Box Regression

## 📌 한 줄 통찰
> **"매 image 의 정확한 주소"**. 매 (x, y, w, h) 의 4 number 의 predict + class. 매 object detection 의 core. 매 modern: 매 anchor-free + 매 DETR (transformer) 의 NMS-free.

## 📖 핵심

### 매 representation

#### (x, y, w, h)
- 매 center + size.

#### (x1, y1, x2, y2)
- 매 corner 좌표.

#### (cx, cy, w, h) normalized
- 매 image-relative (0-1).

#### Polar / RotatedBox
- 매 oriented (aerial, text).

### IoU (Intersection over Union)
$$IoU = \frac{|A \cap B|}{|A \cup B|}$$

- 매 0-1.
- 매 GT 와 predict 의 overlap.
- 매 NMS 의 base.
- 매 mAP 의 component.

### 매 loss

#### L1 / L2
- 매 simple.
- 매 scale-dependent.

#### IoU loss
- 매 (1 - IoU).
- 매 scale-invariant.

#### GIoU / DIoU / CIoU
- 매 IoU 의 변형.
- 매 non-overlap 의 case 도 gradient.
- 매 CIoU = 매 IoU + center distance + aspect ratio.

### 매 anchor

#### Anchor-based (Faster R-CNN, SSD, YOLOv3-v5)
- 매 미리 매 N 개 box 의 layout.
- 매 GT 와 closest anchor 의 match.
- 매 offset 의 regress.

#### Anchor-free (FCOS, YOLOX, CenterNet)
- 매 점 의 직접 regress.
- 매 hyperparameter ↓.
- 매 modern 의 trend.

### NMS (Non-Maximum Suppression)
- 매 highest score box 의 keep.
- 매 IoU > threshold 의 box 의 drop.
- 매 modern: Soft-NMS, Matrix NMS.

### 매 modern paradigm

#### YOLO (v8, v10, v11)
- 매 single-stage.
- 매 fast.
- 매 anchor-free + decoupled head.

#### DETR / Deformable DETR
- 매 transformer encoder-decoder.
- 매 set prediction (no NMS).
- 매 Hungarian matching loss.

#### DINO / Grounding DINO
- 매 DETR 변형 + open-vocab.

#### SAM (Segment Anything)
- 매 prompt-based segmentation.
- 매 bbox prompt → 매 mask.

### 매 응용
1. **Autonomous driving**: 매 vehicle / pedestrian.
2. **Surveillance**: 매 person / face.
3. **Retail**: 매 product detection.
4. **Medical**: 매 lesion / cell.
5. **Aerial**: 매 oriented bbox.
6. **Robotics**: 매 grasping.

### Metric
- **mAP** (mean Average Precision): 매 IoU threshold 별.
- **mAP@50**: 매 IoU 0.5 만.
- **mAP@50:95**: 매 0.5-0.95 의 average (COCO).
- **AR** (Average Recall).

## 💻 패턴

### IoU calculation
```python
def iou(box1, box2):
    """매 (x1, y1, x2, y2) format."""
    x1 = max(box1[0], box2[0])
    y1 = max(box1[1], box2[1])
    x2 = min(box1[2], box2[2])
    y2 = min(box1[3], box2[3])
    
    inter = max(0, x2 - x1) * max(0, y2 - y1)
    area1 = (box1[2] - box1[0]) * (box1[3] - box1[1])
    area2 = (box2[2] - box2[0]) * (box2[3] - box2[1])
    union = area1 + area2 - inter
    return inter / union if union > 0 else 0
```

### NMS
```python
def nms(boxes, scores, iou_threshold=0.5):
    indices = scores.argsort(descending=True)
    kept = []
    while len(indices) > 0:
        idx = indices[0]
        kept.append(idx.item())
        if len(indices) == 1: break
        rest = indices[1:]
        ious = torch.tensor([iou(boxes[idx], boxes[i]) for i in rest])
        indices = rest[ious <= iou_threshold]
    return kept
```

### CIoU loss
```python
import torch

def ciou_loss(pred, gt):
    iou_val = iou_tensor(pred, gt)
    
    # 매 center distance
    px, py = (pred[:, 0] + pred[:, 2]) / 2, (pred[:, 1] + pred[:, 3]) / 2
    gx, gy = (gt[:, 0] + gt[:, 2]) / 2, (gt[:, 1] + gt[:, 3]) / 2
    rho2 = (px - gx)**2 + (py - gy)**2
    
    # 매 enclosing box
    cx1 = torch.min(pred[:, 0], gt[:, 0])
    cy1 = torch.min(pred[:, 1], gt[:, 1])
    cx2 = torch.max(pred[:, 2], gt[:, 2])
    cy2 = torch.max(pred[:, 3], gt[:, 3])
    c2 = (cx2 - cx1)**2 + (cy2 - cy1)**2
    
    # 매 aspect ratio
    pw, ph = pred[:, 2] - pred[:, 0], pred[:, 3] - pred[:, 1]
    gw, gh = gt[:, 2] - gt[:, 0], gt[:, 3] - gt[:, 1]
    v = (4 / math.pi**2) * (torch.atan(gw / gh) - torch.atan(pw / ph))**2
    alpha = v / (1 - iou_val + v + 1e-7)
    
    return 1 - iou_val + rho2 / c2 + alpha * v
```

### YOLO inference (Ultralytics)
```python
from ultralytics import YOLO

model = YOLO('yolov8n.pt')
results = model('image.jpg', conf=0.25, iou=0.45)

for r in results:
    for box in r.boxes:
        xyxy = box.xyxy[0]  # (x1, y1, x2, y2)
        conf = box.conf[0]
        cls = int(box.cls[0])
        print(f'{model.names[cls]}: {conf:.2f} at {xyxy}')
```

### DETR (Hungarian matching)
```python
import torch
from scipy.optimize import linear_sum_assignment

def hungarian_matcher(pred_logits, pred_boxes, gt_labels, gt_boxes):
    """매 N pred ↔ M gt 의 optimal matching."""
    # 매 cost matrix: classification + bbox L1 + IoU
    cost_class = -pred_logits.softmax(-1)[:, gt_labels]
    cost_bbox = torch.cdist(pred_boxes, gt_boxes, p=1)
    cost_giou = -generalized_iou(pred_boxes, gt_boxes)
    
    cost = 1.0 * cost_class + 5.0 * cost_bbox + 2.0 * cost_giou
    
    indices = linear_sum_assignment(cost.cpu())
    return indices
```

### Custom training (Detectron2 / Ultralytics)
```python
from ultralytics import YOLO

model = YOLO('yolov8n.yaml')
model.train(
    data='coco.yaml',
    epochs=100,
    batch=16,
    imgsz=640,
    optimizer='AdamW',
    lr0=0.001,
    cos_lr=True,
)

# 매 export
model.export(format='onnx')
```

### mAP calculation
```python
from torchmetrics.detection import MeanAveragePrecision

metric = MeanAveragePrecision(box_format='xyxy', iou_type='bbox')
metric.update(preds=pred_boxes_list, target=gt_boxes_list)
result = metric.compute()
print(f"mAP@50:95: {result['map']:.4f}")
print(f"mAP@50: {result['map_50']:.4f}")
```

## 🤔 결정 기준
| 상황 | Model |
|---|---|
| Real-time | YOLOv8/10 |
| Accuracy | DINO / Co-DETR |
| Edge | YOLOv8n / NanoDet |
| Open-vocab | Grounding DINO |
| Aerial / oriented | RotatedBox + RoITrans |
| Crowd | DETR (no NMS) |
| Few-shot | Meta-learning + finetune |

**기본값**: YOLOv8 의 baseline. 매 SOTA 가 DETR family. 매 segmentation 의 SAM.

## 🔗 Graph
- 부모: [[Object-Detection]] · [[Computer Vision|Computer-Vision]]
- 변형: [[YOLO]] · [[Faster-R-CNN]] · [[DETR]] · [[SAM]]
- 응용: [[Autonomous Vehicles]]
- Loss: [[Focal-Loss]]
- Adjacent: [[Anchor-Box]] · [[NMS]] · [[mAP]]

## 🤖 LLM 활용
**언제**: 매 detection task. 매 model selection. 매 loss 의 design. 매 deployment optimization.
**언제 X**: 매 classification (no localization). 매 segmentation (use SAM/Mask R-CNN).

## ❌ 안티패턴
- **L2 loss only**: 매 scale-dependent.
- **NMS threshold 의 default**: 매 specific tuning 필요.
- **Anchor 의 default**: 매 dataset 의 statistics 의 reflect X.
- **mAP@50 만**: 매 strict (mAP@50:95) 의 hide.
- **Class imbalance 무시**: 매 minority class 의 fail.
- **Test set 의 augment**: 매 leakage.

## 🧪 검증 / 중복
- Verified (Faster R-CNN, YOLO papers, DETR, SAM).
- 신뢰도 A.
- Related: [[YOLO]] · [[DETR]] · [[Object-Detection]] · [[SAM]] · [[Autonomous Vehicles]].

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — IoU + NMS + DETR + 매 PyTorch / Ultralytics code |