Bounding Boxes and IoU

Intersection over union

Detectors describe objects with bounding boxes, usually as (x1, y1, x2, y2) corners or (centre x, centre y, width, height); always check which format a library uses. Intersection over Union (IoU) measures overlap: the area of the intersection divided by the area of the union, from 0 (no overlap) to 1 (identical). IoU decides whether a prediction matches a ground-truth object (commonly at 0.5 or higher), which predictions are duplicates, and how accurate localisation is.

Where and what

Detectors output boxes, labels and scores; IoU, NMS and average precision make them usable and measurable.

IoU for five predicted boxes, run

I ran this on CPU with Python 3, OpenCV 5.0.0, scikit-image 0.26.0, PyTorch 2.14.1 and torchvision 0.29.1, using scikit-image's bundled sample photos and torchvision's published pretrained weights. Against a 100 x 100 ground-truth box, a perfect prediction scores 1.000, a 20-pixel shift 0.667, a box 1.5 times too large 0.444, a half overlap 0.333 and a miss 0.000.

def iou(a, b):   # boxes as (x1, y1, x2, y2)
    ix1, iy1, ix2, iy2 = max(a[0], b[0]), max(a[1], b[1]), min(a[2], b[2]), min(a[3], b[3])
    inter = max(0, ix2 - ix1) * max(0, iy2 - iy1)
    area = lambda r: (r[2] - r[0]) * (r[3] - r[1])
    return inter / (area(a) + area(b) - inter)
truth = (50, 50, 150, 150)
for name, pred in [("perfect", (50, 50, 150, 150)), ("shifted 20px", (70, 50, 170, 150)),
                   ("too big", (25, 25, 175, 175)), ("half overlap", (100, 50, 200, 150)), ("miss", (200, 200, 260, 260))]:
    print(f"{name:<13} IoU {iou(truth, pred):.3f}")

Output:

perfect       IoU 1.000
shifted 20px  IoU 0.667
too big       IoU 0.444
half overlap  IoU 0.333
miss          IoU 0.000

Check the box format

Mixing (x, y, w, h) with (x1, y1, x2, y2) silently produces nonsense IoU values.

Quick check: A prediction shifted by 20 pixels on a 100-pixel box has IoU of about...

• 2.0
• 1.0
• 0.0
• 0.67