基于anchor的目标检测算法中，会产生很多候选矩形框冗余。会出现多个矩形框指向同一个目标的情况，为了将最能代表位置的矩形框留下，将其他矩形框剔除，提出了非极大值抑制算法。

非极大值抑制（Non-Maximum Suppression）算法简称NMS算法。

原理
IoU(Intersection over Union)为交并比，如图1所示，IoU相当于两个区域交叉的部分除以两个区域的并集部分得出的结果。图2是IoU为各个取值时的情况展示，一般来说，这个score ＞ 0.5 就可以被认为一个不错的结果了。

经典NMS最初第一次应用到目标检测中是在RCNN算法中，其实现严格按照搜索局部极大值，抑制非极大值元素的思想来实现的，具体的实现步骤如下：
中文：
（1）设定目标框的置信度阈值，常用的阈值是0.5左右
（2）根据置信度降序排列候选框列表
（3）选取置信度最高的框A添加到输出列表，并将其从候选框列表中删除
（4）计算A与候选框列表中的所有框的IoU值，删除大于阈值的候选框
（5）重复上述过程，直到候选框列表为空，返回输出列表
英文：
1. choose the highest score element a_1 in set B, add a_1 to the keep set C
2. compute the IOU between the chosen element(such as a_1) and others elements in set B
3. only keep the nums at set B whose IOU value is less than thresholds (can be set as >=0.5), delete the nums similiar
to a_1(the higher IOU it is , the more interseciton between a_1 and it will have)
4. choose the highest score value a_2 left at set B and add a_2 to set C
5. repeat the 2-4 until there is nothing in set B, while set C is the NMS value set

相关代码

#!/usr/bin/env python3# -*- coding: utf-8 -*-"""NMS function（Non-Maximum Suppression，抑制不是极大值的元素）psedocode:1. choose the highest score elementa_1in set B, add a_1 to the keep set C2. compute the IOU between the chosen element(such as a_1) and others elements in set B3. only keep the numsat set B whose IOU value is less than thresholds (can be set as >=0.5), delete the nums similiarto a_1(the higher IOU it is , the more interseciton between a_1 and it will have)4. choose the highest score value a_2 left at set Band add a_2 to set C5. repeat the 2-4 untilthere is nothing in set B, while set C is the NMS value set"""import numpy as np# boxes表示人脸框的xywh4点坐标+相关置信度boxes = np.array([[100, 100, 210, 210, 0.72],[250, 250, 420, 420, 0.8],[220, 220, 320, 330, 0.92],[100, 100, 210, 210, 0.72],[230, 240, 325, 330, 0.81],[220, 230, 315, 340, 0.9]])def py_cpu_nms(dets, thresh):# dets:(m,5)thresh:scalerx1 = dets[:, 0]y1 = dets[:, 1]x2 = dets[:, 2]y2 = dets[:, 3]areas = (y2 - y1 + 1) * (x2 - x1 + 1)scores = dets[:, 4]keep = []# index表示按照scores从高到底的相关box的序列号index = scores.argsort()[::-1]while index.size > 0:print("sorted index of boxes according to scores", index)# 选择得分最高的score直接加入keep列表中i = index[0]keep.append(i)# 计算score最高的box和其他box分别的相关交集坐标x11 = np.maximum(x1[i], x1[index[1:]])y11 = np.maximum(y1[i], y1[index[1:]])x22 = np.minimum(x2[i], x2[index[1:]])y22 = np.minimum(y2[i], y2[index[1:]])print("x1 values by original order:", x1)print("x1 value by scores:", x1[index[:]])print("x11 value meansreplacing the less value compared"\" with the value by the largest score :" , x11)# 计算交集面积w = np.maximum(0, x22 - x11 + 1)# the weights of overlaph = np.maximum(0, y22 - y11 + 1)# the height of overlapoverlaps = w * h# 计算相关IOU值（交集面积/并集面积，表示边框重合程度，越大表示越相似，越该删除）ious = overlaps / (areas[i] + areas[index[1:]] - overlaps)# 只保留iou小于阈值的索引号，重复上步idx = np.where(ious <= thresh)[0]# 因为第一步index[0]已经被划走，所以需要原来的索引号需要多加一index = index[idx + 1]return keepimport matplotlib.pyplot as pltdef plot_bbox(dets, c='k', title_name="title"):x1 = dets[:, 0]y1 = dets[:, 1]x2 = dets[:, 2]y2 = dets[:, 3]plt.plot([x1, x2], [y1, y1], c)plt.plot([x1, x1], [y1, y2], c)plt.plot([x1, x2], [y2, y2], c)plt.plot([x2, x2], [y1, y2], c)plt.title(title_name)if __name__ == '__main__':plot_bbox(boxes, 'k', title_name="before nms")# before nmsplt.show()keep = py_cpu_nms(boxes, thresh=0.7)plot_bbox(boxes[keep], 'r', title_name="after_nme")# after nmsplt.show()

运行结果：