Intersection over Union (Jaccard index)

jaccard.py

from typing import Tuple

def jaccard(a: Tuple[int, int, int, int], b: Tuple[int, int, int, int]) -> float:
    ax, ay, aw, ah = a
    bx, by, bw, bh = b
    left_i = max(ax, bx)
    top_i = max(ay, by)
    right_i = min(ax + aw, bx + bw)
    bottom_i = min(ay + ah, by + bh)
    
    # If the boxes don't overlap, the smallest right/bottom coordinate
    # will be less than the biggest left/top one.
    if right_i < left_i or bottom_i < top_i:
        return 0
    
    # Intersection and box areas
    intersection_area = (right_i - left_i) * (bottom_i - top_i)
    area_a = ah * aw
    area_b = bh * bw
    
    # If the boxes still have a zero intersection (e.g. because they overlap,
    # but their area is zero), we return zero.
    if intersection_area < 1e-6:
        return 0
    
    union_area = area_a + area_b - intersection_area
    return intersection_area / union_area