IoU of bounding boxes

Background

Intersection over Union (IoU) measures how well two boxes overlap and is the workhorse metric of object detection. For a predicted box and a ground-truth box, IoU is the area of their intersection divided by the area of their union. A value of 1 means a perfect match; 0 means no overlap. Detectors use IoU thresholds to decide true positives and to suppress duplicate boxes (NMS).

Problem statement

Implement iou(box1, box2) for two axis-aligned boxes in [x1, y1, x2, y2] format (top-left and bottom-right corners):

$$\text{IoU} = \frac{\text{area}(\text{intersection})}{\text{area}(\text{box1}) + \text{area}(\text{box2}) - \text{area}(\text{intersection})}$$

If the boxes do not overlap, the intersection area is 0. If the union area is 0, return 0.0.

Input

• box1, box2 — sequences [x1, y1, x2, y2] with x2 >= x1 and y2 >= y1.

Output

A float IoU in $[0, 1]$.

Examples

Example 1

Input:  box1 = [0, 0, 2, 2], box2 = [1, 1, 3, 3]
Output: 0.142857...   (= 1/7)

Explanation: both boxes have area 4. They overlap in the unit square $[1,2]\times[1,2]$, so intersection $=1$ and union $=4+4-1=7$, giving $1/7$.

Constraints

• Intersection width/height are clamped at 0: max(0, ix2 - ix1) and max(0, iy2 - iy1).
• union = area1 + area2 - intersection.
• Guard against division by zero (return 0.0 when union is 0).

Notes

• Clamping the overlap dimensions to 0 is what makes non-overlapping (or edge-touching) boxes correctly score 0.
• IoU is scale-invariant: scaling both boxes by the same factor leaves the ratio unchanged.