Object Detection

Definition

The task of predicting axis-aligned bounding boxes and class labels for all instances of target object categories in an image; requires solving localization and classification jointly.

Intuition

Unlike classification (one label per image), detection must find where each object is. YOLO-style models predict boxes directly from grid cells; anchor boxes provide shape priors; IoU measures localization quality; NMS removes duplicate detections.

Formal Description

Bounding box parameterization: $(b_x,b_y,b_w,b_h)$ = center + width/height, normalized to image or grid cell dimensions.

Intersection over Union (IoU):

$\text{IoU}(B_1,B_2)=\frac{\text{area}(B_1\cap B_2)}{\text{area}(B_1\cup B_2)}\in [0,1]$

Threshold typically 0.5 for “correct” detection; used in loss and NMS.

Anchor boxes: predefined box shapes (aspect ratios) at each grid cell position; each grid cell predicts multiple boxes (one per anchor); box prediction is a delta from the anchor shape; improves detection of elongated objects (cars, pedestrians).

YOLO (You Only Look Once): divide image into $S\times S$ grid; each cell predicts $B$ boxes (one per anchor), each box has $(b_x,b_y,b_w,b_h,p_{\text{obj}})$ + $C$ class probabilities; output tensor: $S\times S\times B\times (5+C)$; single forward pass — fast enough for real-time.

Non-Maximum Suppression (NMS):

1. Discard boxes with $p_{\text{obj}}<\text{threshold}$
2. For each class, sort remaining by confidence
3. Greedily keep the highest-confidence box
4. Remove all remaining boxes with IoU ≥ threshold against the kept box
5. Repeat

Loss function (YOLO-style): sum of localization loss (MSE on box coordinates), confidence loss (BCE on objectness), classification loss (BCE or CE).

Applications

Autonomous driving (pedestrian/vehicle detection), surveillance, medical imaging (lesion detection), retail (inventory counting).

Trade-offs

• YOLO trades accuracy for speed vs. two-stage detectors (Faster R-CNN)
• NMS is sequential and hard to parallelize
• Anchor box design is domain-specific (sizes must match typical object scales)
• Recent anchor-free methods (FCOS, DETR) avoid anchor design

Links

• convolution
• cnn_architecture
• face_recognition