目标检测中的mAP计算

一、经典NMS
非极大值抑制（Non-Maximum Suppression，NMS）的思想是搜索局部极大值，抑制非极大值元素。

经典NMS最初第一次应用到目标检测中是在R-CNN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：

先假设有6个输出的矩形框(即proposal_clip_box)，根据分类器类别分类概率做排序，从小到大分别属于车辆的概率(scores)分别为A、B、C、D、E、F。
(1) 从最大概率矩形框F开始，分别判断A~E与F的重叠度IOU是否大于某个设定的阈值;
(2) 假设B、D与F的重叠度超过阈值，那么就扔掉B、D；并标记第一个矩形框F，是我们保留下来的。
(3) 从剩下的矩形框A、C、E中，选择概率最大的E，然后判断E与A、C的重叠度，重叠度大于一定的阈值，那么就扔掉；并标记E是我们保留下来的第二个矩形框。
就这样一直重复，找到所有被保留下来的矩形框。

如上图F与BD重合度较大，可以去除BD。AE重合度较大，我们删除A,保留scores较大的E。C和其他重叠都小保留C。最终留下了C、E、F三个。

# -*- coding: utf-8 -*-
"""
Created on Fri Sep  4 15:35:06 2020

@author: zqq
"""

import numpy as np

boxes=np.array([[100,100,210,210,0.72],
        [250,250,420,420,0.8],
        [220,220,320,330,0.92],
        [100,100,190,200,0.71],
        [230,240,325,330,0.81],
        [220,230,315,340,0.9]]) 
 
 
def py_cpu_nms(dets, thresh):
    "Pure Python NMS baseline"
    # x1、y1、x2、y2以及score赋值
    x1 = dets[:,0]
    y1 = dets[:,1]
    x2 = dets[:,2]
    y2 = dets[:,3]
    scores = dets[:, 4]

    # 每一个检测框的面积
    areas = (y2-y1+1) * (x2-x1+1)
    print(areas)
    # 按照score置信度降序排序
    order = scores.argsort()[::-1]

    keep = [] # 保留的结果框集合
    while order.size >0:
        i = order[0]       # every time the first is the biggst, and add it directly
        keep.append(i) # 保留该类剩余box中得分最高的一个
        # 得到相交区域,左上及右下
        xx1 = np.maximum(x1[i], x1[order[1:]])
        yy1 = np.maximum(y1[i], y1[order[1:]])
        xx2 = np.minimum(x2[i], x2[order[1:]])
        yy2 = np.minimum(y2[i], y2[order[1:]])

        # 计算相交的面积,不重叠时面积为0
        w = np.maximum(0, xx2-xx1+1)    # the weights of overlap
        h = np.maximum(0, yy2-yy1+1)    # the height of overlap
        inter = w*h
        # 计算IoU：重叠面积 /（面积1+面积2-重叠面积）
        ovr = inter / (areas[i]+areas[order[1:]] - inter)
        # 保留IoU小于阈值的box
        indx = np.where(ovr<=thresh)[0]
        order = order[indx+1]   # 因为ovr数组的长度比order数组少一个,所以这里要将所有下标后移一位

    return keep
        
 
import matplotlib.pyplot as plt
def plot_bbox(dets, c='k'):
    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(" nms")
    #plt.show()

plt.figure(1)
ax1 = plt.subplot(1,2,1)
ax1.set_title('before nms')
ax2 = plt.subplot(1,2,2)
ax2.set_title('after nms')
 
plt.sca(ax1)
plot_bbox(boxes,'k')   # before nms

keep = py_cpu_nms(boxes, thresh=0.7)
plt.sca(ax2)
plot_bbox(boxes[keep], 'b')# after nms
plt.show()

二、Soft-NMS

soft NMS提出尤其对密集物体检测的检测效果有一定的提升作用．

绝大部分目标检测方法，最后都要用到 NMS-非极大值抑制进行后处理。 通常的做法是将检测框按得分排序，然后保留得分最高的框，同时删除与该框重叠面积大于一定比例的其它框。

这种贪心式方法存在如下图所示的问题： 红色框和绿色框是当前的检测结果，二者的得分分别是0.95和0.80。如果按照传统的NMS进行处理，首先选中得分最高的红色框，然后绿色框就会因为与之重叠面积过大而被删掉。

思路：不要粗鲁地删除所有IOU大于阈值的框，而是降低其置信度。

soft NMS算法的大致思路为：M为当前得分最高框，bi 为待处理框，bi 和M的IOU越大，bi 的得分si 就下降的越厉害。

算法结构如图所示：

NMS中：

Soft-NMS中：

（１）线性加权：

（２）高斯加权：

soft NMS仍然有问题：其阈值仍然需要手工设定

Soft-NMS代码：

# coding:utf-8
import numpy as np
def soft_nms(boxes, sigma=0.5, Nt=0.1, threshold=0.001, method=1):
    N = boxes.shape[0]
    pos = 0
    maxscore = 0
    maxpos = 0

    for i in range(N):
        maxscore = boxes[i, 4]
        maxpos = i

        tx1 = boxes[i,0]
        ty1 = boxes[i,1]
        tx2 = boxes[i,2]
        ty2 = boxes[i,3]
        ts = boxes[i,4]

        pos = i + 1
    # get max box
        while pos < N:
            if maxscore < boxes[pos, 4]:
                maxscore = boxes[pos, 4]
                maxpos = pos
            pos = pos + 1

    # add max box as a detection
        boxes[i,0] = boxes[maxpos,0]
        boxes[i,1] = boxes[maxpos,1]
        boxes[i,2] = boxes[maxpos,2]
        boxes[i,3] = boxes[maxpos,3]
        boxes[i,4] = boxes[maxpos,4]

    # swap ith box with position of max box
        boxes[maxpos,0] = tx1
        boxes[maxpos,1] = ty1
        boxes[maxpos,2] = tx2
        boxes[maxpos,3] = ty2
        boxes[maxpos,4] = ts

        tx1 = boxes[i,0]
        ty1 = boxes[i,1]
        tx2 = boxes[i,2]
        ty2 = boxes[i,3]
        ts = boxes[i,4]

        pos = i + 1
    # NMS iterations, note that N changes if detection boxes fall below threshold
        while pos < N:
            x1 = boxes[pos, 0]
            y1 = boxes[pos, 1]
            x2 = boxes[pos, 2]
            y2 = boxes[pos, 3]
            s = boxes[pos, 4]

            area = (x2 - x1 + 1) * (y2 - y1 + 1)
            iw = (min(tx2, x2) - max(tx1, x1) + 1)
            if iw > 0:
                ih = (min(ty2, y2) - max(ty1, y1) + 1)
                if ih > 0:
                    ua = float((tx2 - tx1 + 1) * (ty2 - ty1 + 1) + area - iw * ih)
                    ov = iw * ih / ua #iou between max box and detection box

                    if method == 1: # linear
                        if ov > Nt:
                            weight = 1 - ov
                        else:
                            weight = 1
                    elif method == 2: # gaussian
                        weight = np.exp(-(ov * ov)/sigma)
                    else: # original NMS
                        if ov > Nt:
                            weight = 0
                        else:
                            weight = 1

                    boxes[pos, 4] = weight*boxes[pos, 4]
                    print(boxes[:, 4])

            # if box score falls below threshold, discard the box by swapping with last box
            # update N
                    if boxes[pos, 4] < threshold:
                        boxes[pos,0] = boxes[N-1, 0]
                        boxes[pos,1] = boxes[N-1, 1]
                        boxes[pos,2] = boxes[N-1, 2]
                        boxes[pos,3] = boxes[N-1, 3]
                        boxes[pos,4] = boxes[N-1, 4]
                        N = N - 1
                        pos = pos - 1

            pos = pos + 1
    keep = [i for i in range(N)]
    return keep
boxes = np.array([[100, 100, 150, 168, 0.63],[166, 70, 312, 190, 0.55],[221, 250, 389, 500, 0.79],[12, 190, 300, 399, 0.9],[28, 130, 134, 302, 0.3]])
keep = soft_nms(boxes)
print(keep)