[目标检测]IoU

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IoU(Intersection over union, 交集并集比)是目标检测领域常用的评价标准，通过比较真值边界框（the ground-truth bounding box，手动标记）和预测边界框（the predicted bounding box）的重合度来判定算法检测性能

原理解析

在上图中，绿色边框是真值边界框，红色边框是算法检测得到的预测边界框，IoU需要计算两个边界框的重叠面积和并集面积的比率

\[ IoU = \frac {Area\ of\ Overlap}{Area\ of\ Union} \]

更多情况下，分母计算的是由预测边界框和真值边界框所包围的区域

IoU的取值范围在[0,1]之间，当IoU>0.5时通常认为是好的预测

python实现

分别使用numpy和pytorch计算两个边界框的IoU，分为3种情况：

  1. 完全重叠
  2. 部分重叠
  3. 没有重叠
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# -*- coding: utf-8 -*-

"""
@author: zj
@file:   iou-compute.py
@time:   2020-01-19
"""

import numpy as np
import torch
import cv2


def numpy_iou(target_boxes, pred_boxes):
    """
    target_boxes和pred_boxes大小相同:[N, 4]，其中N表示边框数目，4表示保存的是[xmin, ymin, xmax, ymax]
    """
    xA = np.maximum(target_boxes[:, 0], pred_boxes[:, 0])
    yA = np.maximum(target_boxes[:, 1], pred_boxes[:, 1])
    xB = np.minimum(target_boxes[:, 2], pred_boxes[:, 2])
    yB = np.minimum(target_boxes[:, 3], pred_boxes[:, 3])
    # 计算交集面积
    intersection = np.maximum(0.0, xB - xA) * np.maximum(0.0, yB - yA)
    # 计算两个边界框面积
    boxAArea = (target_boxes[:, 2] - target_boxes[:, 0]) * (target_boxes[:, 3] - target_boxes[:, 1])
    boxBArea = (pred_boxes[:, 2] - pred_boxes[:, 0]) * (pred_boxes[:, 3] - pred_boxes[:, 1])

    iou = intersection / (boxAArea + boxBArea - intersection)
    return iou


def pytorch_iou(target_boxes, pred_boxes):
    x_min = torch.max(target_boxes[:, 0], pred_boxes[:, 0])
    y_min = torch.max(target_boxes[:, 1], pred_boxes[:, 1])
    x_max = torch.min(target_boxes[:, 2], pred_boxes[:, 2])
    y_max = torch.min(target_boxes[:, 3], pred_boxes[:, 3])
    # 计算交集面积
    intersection = torch.max(torch.zeros(x_max.shape), x_max - x_min) \
                   * torch.max(torch.zeros(y_max.shape), y_max - y_min)

    # 计算两个边界框面积
    boxAArea = (target_boxes[:, 2] - target_boxes[:, 0]) * (target_boxes[:, 3] - target_boxes[:, 1])
    boxBArea = (pred_boxes[:, 2] - pred_boxes[:, 0]) * (pred_boxes[:, 3] - pred_boxes[:, 1])

    iou = intersection / (boxAArea + boxBArea - intersection)
    return iou


if __name__ == '__main__':
    target_boxes = np.array([[10, 10, 50, 50], [40, 270, 100, 380], [450, 300, 500, 500]])
    pred_boxes = np.array([[20, 20, 40, 40], [30, 280, 200, 300], [400, 200, 450, 250]])

    iou1 = numpy_iou(target_boxes, pred_boxes)
    iou2 = pytorch_iou(torch.Tensor(target_boxes), torch.Tensor(pred_boxes))

    print('numpy:', iou1)
    print('pytorch:', iou2)

    img = np.ones((650, 650, 3)) * 255
    for item in target_boxes:
        xmin, ymin, xmax, ymax = item
        cv2.rectangle(img, (xmin, ymin), (xmax, ymax), (0, 0, 255), thickness=2)
    for item in pred_boxes:
        xmin, ymin, xmax, ymax = item
        cv2.rectangle(img, (xmin, ymin), (xmax, ymax), (0, 255, 0), thickness=2)

    cv2.imshow('img', img)
    cv2.waitKey(0)

计算结果如下：

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2
numpy: [0.25       0.13636364 0.        ]
pytorch: tensor([0.2500, 0.1364, 0.0000])

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