def box_area(boxes):
    """
    Computes the area of a set of bounding boxes, which are specified by its
    (x1, y1, x2, y2) coordinates.

    Arguments:
        boxes (Tensor[N, 4]): boxes for which the area will be computed. They
            are expected to be in (x1, y1, x2, y2) format

    Returns:
        area (Tensor[N]): area for each box
    """
    return (boxes[:, 2] - boxes[:, 0]) * (boxes[:, 3] - boxes[:, 1])


# implementation from https://github.com/kuangliu/torchcv/blob/master/torchcv/utils/box.py
# with slight modifications
def box_iou(boxes1, boxes2):
    """
    Return intersection-over-union (Jaccard index) of boxes.

    Both sets of boxes are expected to be in (x1, y1, x2, y2) format.

    Arguments:
        boxes1 (Tensor[N, 4])
        boxes2 (Tensor[M, 4])

    Returns:
        iou (Tensor[N, M]): the NxM matrix containing the pairwise
            IoU values for every element in boxes1 and boxes2
    """
    area1 = box_area(boxes1)
    area2 = box_area(boxes2)

    lt = torch.max(boxes1[:, None, :2], boxes2[:, :2])  # [N,M,2]
    rb = torch.min(boxes1[:, None, 2:], boxes2[:, 2:])  # [N,M,2]

    wh = (rb - lt).clamp(min=0)  # [N,M,2]
    inter = wh[:, :, 0] * wh[:, :, 1]  # [N,M]

    iou = inter / (area1[:, None] + area2 - inter)
    return iou

用numpy实现

import numpy as np

def box_area(boxes):
    return (boxes[:, 2] - boxes[:, 0]) * (boxes[:, 3] - boxes[:, 1])

def box_iou(boxes1, boxes2):
    area1 = box_area(boxes1)
    area2 = box_area(boxes2)
    lt = np.maximum(boxes1[:, np.newaxis, :2], boxes2[:, :2])
    rb = np.minimum(boxes1[:, np.newaxis, 2:], boxes2[:, 2:])
    
    wh = (rb - lt).clip(0)
    inter = wh[:, :, 0] * wh[:, :, 1]
    iou = inter / (area1[:, np.newaxis] + area2 - inter)
    return iou