IoU (Intersection over Union) - CNNs & Computer Vision

IoU (Intersection over Union)

What you'll build

The Intersection over Union of two axis-aligned bounding boxes.

Background

IoU is the basic overlap measure of object detection. It decides whether a prediction counts as a true positive (IoU >= 0.5 for PASCAL VOC, 0.5 to 0.95 for COCO mAP), which anchors are matched to ground truth during training, and which boxes NMS suppresses. It is scale invariant: two boxes overlapping by the same fraction score the same whatever their size.

Box format: xyxy

Each box is [x1, y1, x2, y2]: (x1, y1) is the top-left corner and (x2, y2) the bottom-right corner, with x2 >= x1 and y2 >= y1 (image coordinates, y grows downward). Coordinates are continuous, so a box's area is (x2 - x1) * (y2 - y1). Other formats exist: COCO stores xywh = [x, y, width, height] and YOLO stores cxcywh = [center_x, center_y, width, height]. Convert them to xyxy first.

Formula

ix1 = max(a_x1, b_x1)     iy1 = max(a_y1, b_y1)      # intersection top-left
ix2 = min(a_x2, b_x2)     iy2 = min(a_y2, b_y2)      # intersection bottom-right
intersection = max(0, ix2 - ix1) * max(0, iy2 - iy1)
union        = area_a + area_b - intersection
IoU          = intersection / union                   # in [0, 1]

Inputs

• box_a, box_b: length-4 arrays or lists [x1, y1, x2, y2] of ints or floats.

Expected return format

A Python float rounded to 4 decimal places.

Edge cases and conventions

• Disjoint boxes, or boxes that only touch along an edge, have IoU 0.0. Clamp the intersection width and height at 0 separately; a negative width times a negative height would otherwise look like a positive overlap.
• If the union is 0 (two zero-area boxes), return 0.0.
• No +1 pixel convention: areas use x2 - x1, not x2 - x1 + 1.

Constraints

Plain Python or NumPy.

Follow-up

• Vectorise it: compute an (N, M) IoU matrix between two sets of boxes with broadcasting.
• What do GIoU, DIoU and CIoU add, and why are they better regression losses than 1 - IoU?

Input: box_a = [0, 0, 2, 2], box_b = [1, 1, 3, 3]
Output: 0.1429

Input: box_a = [0, 0, 4, 4], box_b = [2, 0, 6, 4]
Output: 0.3333

Input: box_a = [0, 0, 1, 1], box_b = [2, 2, 3, 3]
Output: 0.0

import numpy as np

def iou(box_a, box_b):
    """
    Intersection over Union of two boxes in xyxy format.

    Args:
        box_a: [x1, y1, x2, y2], top-left (x1, y1) and bottom-right (x2, y2)
        box_b: [x1, y1, x2, y2]

    Returns:
        IoU as a Python float in [0, 1], rounded to 4 decimal places
        (0.0 when the union is 0)
    """
    # Your code here
    pass