Object Detection Frameworks

# Object Detection Frameworks

## Introduction & Motivation

Object detection: localize and classify objects. YOLO, R-CNN, SSD. Applications: surveillance, autonomous driving.

Motivation: Find objects in images with bounding boxes.

Applications: Real-time detection, traffic monitoring.

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## Core Concepts & Theory

### Region-Based Detection

R-CNN family approaches.

### Single-Shot Detection

YOLO, SSD one-stage methods.

### Anchor Boxes

Pre-defined bounding box templates.

### Non-Maximum Suppression

Remove duplicate detections.

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## Mathematical Formulation

Bounding Box Regression:
$$\Delta x = (x - x_a) / w_a, \quad \Delta y = (y - y_a) / h_a$$
$$\Delta w = \log(w / w_a), \quad \Delta h = \log(h / h_a)$$

IoU:
$$ ext{IoU} = \frac{ ext{Area}_{ ext{intersection}}}{ ext{Area}_{ ext{union}}}$$

NMS:
$$ ext{suppress if } ext{IoU} > ext{threshold}$$

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## Advanced Theory & Extensions

### Focal Loss

Address class imbalance.

### Feature Pyramid Networks

Multi-scale feature extraction.

### Cascade Detection

Progressive refinement.

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## Computational Considerations

Region proposal: O(H·W·K).

Classification: O(N·K·C).

NMS: O(N²).

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## Practical Implementation Strategies

### Anchor Generation

Multi-scale anchor boxes.

### Hard Negative Mining

Focus on difficult negatives.

### Data Augmentation

Geometric and photometric transforms.

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## Benchmark Datasets & Evaluation

COCO: 80 object categories, complex scenes.

Pascal VOC: 20 classes, 16k images.

Open Images: Large-scale diverse dataset.

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## Key Challenges & Limitations

### Scale Variation

Objects at different sizes.

### Occlusion

Partially visible objects.

### Small Object Detection

Limited pixel information.

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## Hyperparameter Tuning

Anchor scales: 32, 64, 128, 256, 512.

Aspect ratios: 0.5, 1.0, 2.0.

NMS threshold: 0.5-0.7.

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## Real-World Applications & Case Studies

Traffic Monitoring: Vehicle and pedestrian detection.

Autonomous Driving: Real-time obstacle detection.

Security: Threat detection in surveillance.

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## Integration with Other Methods

Detection + tracking for video; + segmentation for instance masks.

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## Summary & Key Takeaways

Object detection localizes and classifies objects in images.

Principles:
1. Region proposal: Candidate generation.
2. Classification: Object identification.
3. Regression: Bounding box refinement.
4. NMS: Duplicate removal.
5. Multi-scale: Hierarchical detection.

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## Appendix: Practical Labs

### Lab 1: Bounding Box Encoding

import numpy as np

def encode_bbox(gt_box, anchor_box):
 """Encode ground truth to anchor relative coords"""
 xa, ya, wa, ha = anchor_box
 xg, yg, wg, hg = gt_box
 
 dx = (xg - xa) / wa
 dy = (yg - ya) / ha
 dw = np.log(wg / wa)
 dh = np.log(hg / ha)
 
 return np.array([dx, dy, dw, dh])

anchor = [100, 100, 50, 50]
gt = [110, 105, 60, 45]
encoded = encode_bbox(gt, anchor)
assert encoded.shape == (4,), "Correct encoding shape"
print("✓ Bounding box encoding working")

### Lab 2: IoU Calculation

import numpy as np

def compute_iou(box1, box2):
 """Compute intersection over union"""
 x1_min, y1_min, x1_max, y1_max = box1
 x2_min, y2_min, x2_max, y2_max = box2
 
 inter_xmin = max(x1_min, x2_min)
 inter_ymin = max(y1_min, y2_min)
 inter_xmax = min(x1_max, x2_max)
 inter_ymax = min(y1_max, y2_max)
 
 inter_area = max(0, inter_xmax - inter_xmin) * max(0, inter_ymax - inter_ymin)
 
 box1_area = (x1_max - x1_min) * (y1_max - y1_min)
 box2_area = (x2_max - x2_min) * (y2_max - y2_min)
 
 union_area = box1_area + box2_area - inter_area
 
 iou = inter_area / union_area if union_area > 0 else 0
 return iou

box1 = [0, 0, 10, 10]
box2 = [5, 5, 15, 15]
iou = compute_iou(box1, box2)
assert 0 <= iou <= 1, "Valid IoU"
print(f"✓ IoU calculation working: {iou:.4f}")

### Lab 3: Non-Maximum Suppression

import numpy as np

def non_maximum_suppression(detections, iou_threshold=0.5):
 """Suppress overlapping detections"""
 if len(detections) == 0:
 return []
 
 detections = sorted(detections, key=lambda x: x[4], reverse=True)
 keep = []
 
 while len(detections) > 0:
 keep.append(detections[0])
 
 if len(detections) == 1:
 break
 
 remaining = []
 for det in detections[1:]:
 iou = compute_iou(detections[0][:4], det[:4])
 if iou < iou_threshold:
 remaining.append(det)
 
 detections = remaining
 
 return keep

def compute_iou(box1, box2):
 x1_min, y1_min, x1_max, y1_max = box1
 x2_min, y2_min, x2_max, y2_max = box2
 inter_area = max(0, min(x1_max, x2_max) - max(x1_min, x2_min)) * max(0, min(y1_max, y2_max) - max(y1_min, y2_min))
 union_area = (x1_max - x1_min) * (y1_max - y1_min) + (x2_max - x2_min) * (y2_max - y2_min) - inter_area
 return inter_area / union_area if union_area > 0 else 0

detections = [
 [0, 0, 10, 10, 0.9],
 [1, 1, 11, 11, 0.8],
 [20, 20, 30, 30, 0.7]
]
kept = non_maximum_suppression(detections)
assert len(kept) <= len(detections), "NMS reduces detections"
print("✓ Non-maximum suppression working")

### Lab 4: Anchor Generation

import numpy as np

def generate_anchors(image_size, feature_size, scales=[32, 64], ratios=[0.5, 1, 2]):
 """Generate anchor boxes for feature map"""
 stride = image_size // feature_size
 anchors = []
 
 for i in range(feature_size):
 for j in range(feature_size):
 cx = (j + 0.5) * stride
 cy = (i + 0.5) * stride
 
 for scale in scales:
 for ratio in ratios:
 w = scale * np.sqrt(1 / ratio)
 h = scale * np.sqrt(ratio)
 
 anchors.append([cx - w/2, cy - h/2, cx + w/2, cy + h/2])
 
 return np.array(anchors)

anchors = generate_anchors(image_size=224, feature_size=7)
assert anchors.shape[1] == 4, "Correct anchor format"
print(f"✓ Generated {len(anchors)} anchors")

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