cv：：阈值分割OTUS原理+代码

opencv库的阈值分割分为全局分割和局部分割

全局分割：普通分割

ret1,th1 = cv2.threshold(img,127, 255, cv2.THRESH_BINARY)
#127为阈值
#cv2.THRESH_BINARY |cv2.THRESH_BINARY_INV | cv2.THRESH_TRUNC|cv2.THRESH_TOZERO|cv2.THRESH_TOZERO_INV

局部分割：自适应分割,阈值自计算

th2=cv2.adaptiveThreshold(img,255,cv2.ADAPTIVE_THRESH_MEAN_C，cv2.THRESH_BINARY,11,2)
#阈值变为
#均值：cv2.ADAPTIVE_THRESH_MEAN_C，
#高斯加权：cv2.ADAPTIVE_THRESH_GAUSSIAN_C
#窗口大小：11
#c：均值-常数

特殊:OTUS 大津法,最大类间方差

ret2,th2 = cv2.threshold(img,0, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU)

原理:

使用于双峰图像,将灰度直方图分为两部分,使得两部分类间方差最大,试了一下两部分类内方差最小也行,效果差不多,opencv的api用的是最大类间方差.

步骤:

1. 灰度图片计算灰度直方图，并归一化

2. 类间方差计算：其实就是求灰度的方差

1. 假设当前灰度阈值为i，将[0,256]分为h1=[0,i-1]和h2=[i,256]两部分

2. 求每一部分的灰度个数s = sum（h[i]），求s1，s2

3. 求每一部分的灰度均值，mean = sum(h1[i]*i)/s求m1,m2,mg(总积分)

4. 求每一个类间的方差，[s1*（m1-mg）*(m1-mg)+s2*(m2-mg)*(m2-mg)]/(s1+s2)

d.(1)，类内方差v = sum((i-m)*(i-m)*h[i]/s),最小类内方差也行

3. i 取值[0,256],求使得类间方差最大的i就是阈值

import cv2
import numpy as np
import matplotlib.pyplot as pltimg = cv2.imread("otsu.jpg",0)hist = cv2.calcHist([img],[0],None,[256],[0,256])
histnorm = (hist-hist.min())/(hist.max()-hist.min())
bins = np.arange(256)# plt.plot(histnorm)
# plt.xlim([0,256])
# plt.show()fnmin = 99999
tmp = 0
fnmax = 0
tm = 0
p = hist/sum(hist)
histnorm = np.squeeze(histnorm)
for i in range(1,256):s1 = np.sum(histnorm[:i])s2 = np.sum(histnorm[i:])q1 = histnorm[i:]*bins[i:]m1 = np.sum(histnorm[:i] * bins[:i])/s1m2 = np.sum(histnorm[i:] * bins[i:])/s2mg = np.sum(histnorm* bins)/(s1+s2)#最大类间方差fm = (s1*(m1-mg)*(m1-mg)+ s2*(m2-mg)*(m2-mg))/(s1+s2)if fm>fnmax:fnmax = fmtm = i#最小类内方差v1 = np.sum((bins[:i] - m1)*(bins[:i] - m1)*(histnorm[:i])/s1)v2 = np.sum((bins[i:] - m2)*(bins[i:] - m2)*(histnorm[i:])/s2)fn = v1+v2if fn<fnmin:fnmin = fntmp = iret1,th1 = cv2.threshold(img,tm, 255, cv2.THRESH_BINARY)
print(tm,ret1)
ret2,th2 = cv2.threshold(img,tmp, 255, cv2.THRESH_BINARY)
print(tmp,ret2)
ret3,th3 = cv2.threshold(img,0, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU)
print(ret3)cv2.imshow("th1",th1)
cv2.imshow("th2",th2)
cv2.imshow("th3",th3)
cv2.waitKey(0)

图片：从别博客里面保存的

结果：最大类间方差和cv2.THRESH_OTSU计算出来的阈值一样，最小类间方差要小一点