Otsu源码复现---python

Otsu简介

即最大类间方差法，是一种图像二值化的算法，利用阈值将原图像分成前景，背景两个图象。当取最佳阈值时，背景应该与前景差别最大，关键在于如何选择衡量差别的标准，而在otsu算法中这个衡量差别的标准就是最大类间方差。

具体公式推导参考：https://www.cnblogs.com/xiaomanon/p/4110006.html

 

python源码

# -*- coding: utf-8 -*-
"""
Created on Mon Apr  8 18:31:35 2019

@author: lenovo
"""

import cv2 as cv
import numpy as np
import matplotlib.pyplot as plt


def OTSU(gray): 
    hist = cv.calcHist([gray],[0],None,[256],[0,256])#255*1的灰度直方图的数组
    gray_size = gray.size#图像像素数
    k = 0#初始化灰度阈值
    best_k = 0#最佳阈值
    best_M = 0#衡量阈值性
    
    p = []#灰度出现概率
    
    
    #for k in range(30,150):
    for i in range(len(hist)):
        p.insert(i,hist[i][0]/gray_size) #灰度集概率分布

    for k in range(30,150):
        u = 0#从1到k的累计出现概率的平均灰度级
        u_t = 0#从1到256的累计出现概率的平均灰度级
        σ2_0 = 0#类内方差
        σ2_1 = 0#类内方差 
        σ2_t = 0#灰度级的总方差
        sum_0 = np.sum(hist[0:k+1:], axis=0)
        sum_1 = np.sum(hist[k+1:256:], axis=0)
        
        w_0 = np.sum(p[0:k+1:])
        w_1 = np.sum(p[k+1:256:])#各类的概率
        
        for i in range(k+1):
            u = i*p[i]+u
        
        for i in range(len(hist)):
            u_t = i*p[i]+u_t
        
        u0 = u/w_0
        u1 = (u_t - u)/w_1#各类的平均灰度级
        
        
        for i in range(k+1):
            σ2_0 = (p[i]/w_0)*np.square(i-u0) + σ2_0
        for i in range(k+1,256):
            σ2_1 = (p[i]/w_1)*np.square(i-u1) + σ2_1#两类的类内方差
        for i in range(256):
            σ2_t = p[i]*np.square(i-u_t) + σ2_t#总方差
            
        σ2_w = w_0*σ2_0+w_1*σ2_1#类内方差
        σ2_b = w_0*w_1*np.square(u1-u0)#类间方差
    
        M = σ2_b/σ2_t#衡量阈值k的好坏
        if M>best_M:
            best_M = M;
            best_k= k;
    return best_M,best_k


if __name__ == "__main__":
    img = cv.imread('flower.jpg')#读取图像（BGR）
    gray = cv.cvtColor(img, cv.COLOR_BGR2GRAY) #转灰度图像
    M,k = OTSU(gray)
    print(M,k)
    ret,thresh1=cv.threshold(gray,k,255,cv.THRESH_BINARY)
    cv.imshow("histogram", thresh1)

分析

            

灰度直方图：

        

 

          

 

总结

Otsu算法在处理目标和背景大小相差不大时（灰度直方图具有典型双峰性）效果还好，否则二值化效果不理想。