文章作者：Tyan
博客：noahsnail.com  |  CSDN  |  简书

1. 什么是非极大值抑制

非极大值抑制，简称为NMS算法，英文为Non-Maximum Suppression。其思想是搜素局部最大值，抑制极大值。NMS算法在不同应用中的具体实现不太一样，但思想是一样的。非极大值抑制，在计算机视觉任务中得到了广泛的应用，例如边缘检测、人脸检测、目标检测（DPM，YOLO，SSD，Faster R-CNN）等。

2. 为什么要用非极大值抑制

以目标检测为例：目标检测的过程中在同一目标的位置上会产生大量的候选框，这些候选框相互之间可能会有重叠，此时我们需要利用非极大值抑制找到最佳的目标边界框，消除冗余的边界框。Demo如下图：

左图是人脸检测的候选框结果，每个边界框有一个置信度得分(confidence score)，如果不使用非极大值抑制，就会有多个候选框出现。右图是使用非极大值抑制之后的结果，符合我们人脸检测的预期结果。

3. 如何使用非极大值抑制

前提：目标边界框列表及其对应的置信度得分列表，设定阈值，阈值用来删除重叠较大的边界框。
IoU：intersection-over-union，即两个边界框的交集部分除以它们的并集。

非极大值抑制的流程如下：

• 根据置信度得分进行排序
• 选择置信度最高的比边界框添加到最终输出列表中，将其从边界框列表中删除
• 计算所有边界框的面积
• 计算置信度最高的边界框与其它候选框的IoU。
• 删除IoU大于阈值的边界框
• 重复上述过程，直至边界框列表为空。

Python代码如下：

#!/usr/bin/env python# _*_ coding: utf-8 _*_  import cv2import numpy as np  """    Non-max Suppression Algorithm    @param list  Object candidate bounding boxes    @param list  Confidence score of bounding boxes    @param float IoU threshold    @return Rest boxes after nms operation"""def nms(bounding_boxes, confidence_score, threshold):    # If no bounding boxes, return empty list    if len(bounding_boxes) == 0:        return [], []     # Bounding boxes    boxes = np.array(bounding_boxes)     # coordinates of bounding boxes    start_x = boxes[:, 0]    start_y = boxes[:, 1]    end_x = boxes[:, 2]    end_y = boxes[:, 3]     # Confidence scores of bounding boxes    score = np.array(confidence_score)     # Picked bounding boxes    picked_boxes = []    picked_score = []     # Compute areas of bounding boxes    areas = (end_x - start_x + 1) * (end_y - start_y + 1)     # Sort by confidence score of bounding boxes    order = np.argsort(score)     # Iterate bounding boxes    while order.size > 0:        # The index of largest confidence score        index = order[-1]         # Pick the bounding box with largest confidence score        picked_boxes.append(bounding_boxes[index])        picked_score.append(confidence_score[index])         # Compute ordinates of intersection-over-union(IOU)        x1 = np.maximum(start_x[index], start_x[order[:-1]])        x2 = np.minimum(end_x[index], end_x[order[:-1]])        y1 = np.maximum(start_y[index], start_y[order[:-1]])        y2 = np.minimum(end_y[index], end_y[order[:-1]])         # Compute areas of intersection-over-union        w = np.maximum(0.0, x2 - x1 + 1)        h = np.maximum(0.0, y2 - y1 + 1)        intersection = w * h         # Compute the ratio between intersection and union        ratio = intersection / (areas[index] + areas[order[:-1]] - intersection)         left = np.where(ratio < threshold)        order = order[left]     return picked_boxes, picked_score  # Image nameimage_name = 'nms.jpg' # Bounding boxesbounding_boxes = [(187, 82, 337, 317), (150, 67, 305, 282), (246, 121, 368, 304)]confidence_score = [0.9, 0.75, 0.8] # Read imageimage = cv2.imread(image_name) # Copy image as originalorg = image.copy() # Draw parametersfont = cv2.FONT_HERSHEY_SIMPLEXfont_scale = 1thickness = 2 # IoU thresholdthreshold = 0.4 # Draw bounding boxes and confidence scorefor (start_x, start_y, end_x, end_y), confidence in zip(bounding_boxes, confidence_score):    (w, h), baseline = cv2.getTextSize(str(confidence), font, font_scale, thickness)    cv2.rectangle(org, (start_x, start_y - (2 * baseline + 5)), (start_x + w, start_y), (0, 255, 255), -1)    cv2.rectangle(org, (start_x, start_y), (end_x, end_y), (0, 255, 255), 2)    cv2.putText(org, str(confidence), (start_x, start_y), font, font_scale, (0, 0, 0), thickness) # Run non-max suppression algorithmpicked_boxes, picked_score = nms(bounding_boxes, confidence_score, threshold) # Draw bounding boxes and confidence score after non-maximum supressionfor (start_x, start_y, end_x, end_y), confidence in zip(picked_boxes, picked_score):    (w, h), baseline = cv2.getTextSize(str(confidence), font, font_scale, thickness)    cv2.rectangle(image, (start_x, start_y - (2 * baseline + 5)), (start_x + w, start_y), (0, 255, 255), -1)    cv2.rectangle(image, (start_x, start_y), (end_x, end_y), (0, 255, 255), 2)    cv2.putText(image, str(confidence), (start_x, start_y), font, font_scale, (0, 0, 0), thickness) # Show imagecv2.imshow('Original', org)cv2.imshow('NMS', image)cv2.waitKey(0)

源码下载地址：https://github.com/SnailTyan/deep-learning-tools/blob/master/nms.py
记得给个Star。Demo原图在README.md里。

实验结果：

• 阈值为0.6

• 阈值为0.5
  
• 阈值为0.4
  

4. 参考资料

1. https://www.pyimagesearch.com/2014/11/17/non-maximum-suppression-object-detection-python/
2. http://cs.brown.edu/~pff/papers/lsvm-pami.pdf
3. http://blog.csdn.net/shuzfan/article/details/52711706
4. http://www.cnblogs.com/liekkas0626/p/5219244.html
5. http://www.tk4479.net/yzhang6_10/article/details/50886747
6. http://blog.csdn.net/qq_14845119/article/details/52064928