Python code to compute the intersection of two boundingboxes

iou.py

from typing import Tuple


def intersection_over_union(boxA: Tuple[float, float, float, float], boxB: Tuple[float, float, float, float]) -> float:
    """Calculates the intersection of union between two rectangles/bounding boxes.

    See https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/ for more information about IOU.

    Args:
        boxA: First bounding box with coordinates in the format [xmin, ymin, xmax, ymax].
        boxB: Second bounding box with coordinates in the format [xmin, ymin, xmax, ymax].

    Returns:
        IOU in the range [0, 1] = [no intersection, complete intersection].
    """

    xminA, yminA, xmaxA, ymaxA = boxA
    xminB, yminB, xmaxB, ymaxB = boxB

    # Fix possible missordering
    if xminA > xmaxA:
        xminA, xmaxA = xmaxA, xminA
    if yminA > ymaxA:
        yminA, ymaxA = ymaxA, yminA
    if xminB > xmaxB:
        xminB, xmaxB = xmaxB, xminB
    if yminB > ymaxB:
        yminB, ymaxB = ymaxB, yminB
    
    # Determine the (x, y)-coordinates of the intersection rectangle
    xA = max(xminA, xminB)
    yA = max(yminA, yminB)
    xB = min(xmaxA, xmaxB)
    yB = min(ymaxA, ymaxB)

    # Compute the area of intersection rectangle
    interArea = abs(max((xB - xA, 0)) * max((yB - yA), 0))
    if interArea == 0:
        return 0
    # Compute the area of both the prediction and ground-truth rectangles
    boxAArea = abs((xmaxA - xminA) * (ymaxA - yminA))
    boxBArea = abs((xmaxB - xminB) * (ymaxB - yminB))

    # Compute the intersection over union by taking the intersection area and dividing it by the sum of prediction + ground-truth areas - the interesection area
    iou = interArea / float(boxAArea + boxBArea - interArea)

    return iou


if __name__ == '__main__':
    # Pointing out a wrong IoU implementation in https://www.pyimagesearch.com/2016/11/07/intersection-over-union-iou-for-object-detection/
    boxA = [0., 0., 10., 10.]
    boxB = [1., 1., 11., 11.]

    correct = intersection_over_union(boxA, boxB)
    print('Correct solution - also analytical: {0}\n'
          'Solution by published function: {1}\n'
          'Solution by correction (ptyshevs): {2}'.format(correct, '0.704225352113', '0.680672268908'))

    print('Normalizing coordinates in a 100x100 coordinate system')
    boxA = [a / 100. for a in boxA]
    boxB = [b / 100. for b in boxB]

    correct = intersection_over_union(boxA, boxB)

    print('Correct solution - also analytical: {0}\n'
          'Solution by published function: {1}\n'
          'Solution by correction: {2}'.format(correct, '0.964445166004', '0.680672268908'))
    
    print('Two boxes with no overlap')
    boxA = [0., 0., 10., 10.]
    boxB = [12., 12., 22., 22.]
    correct = intersection_over_union(boxA, boxB)

    print('Correct solution - also analytical: {0}\n'
          'Solution by published function: {1}\n'
          'Solution by correction (ptyshevs): {2}'.format(correct, '0.0', '0.0204081632653'))


    print('Example in the comments from ptyshevs')
    boxA = [0., 0., 2., 2.]
    boxB = [1., 1., 3., 3.]
    correct = intersection_over_union(boxA, boxB)

    print('Correct solution - also analytical: {0}\n'
          'Solution by published function: {1}\n'
          'Solution by correction (ptyshevs): {2}'.format(correct, '0.285714285714', '0.142857142857'))