二维熵

import cv2
import matplotlib.pyplot as plt
import numpy as np
import math
def calc_2D_Entropy():
    '''
    邻域 3*3的小格子
     __ __ __
    |__|__|__|
    |__||||__|
    |__|__|__|
    角点
     __ __
    ||||__|
    |__|__|
    边
     __ __
    |  |__|
    ||||__|
    |__|__|
    '''
    img=cv2.imread('C:/Users/xpp/Desktop/Lena.png',0)#读取图像
    N=1
    S=img.shape
    IJ=[]
    #计算j
    for row in range(S[0]):
        for col in range(S[1]):
            Left_x=np.max([0,col-N])
            Right_x=np.min([S[1],col+N+1])
            up_y=np.max([0,row-N])
            down_y=np.min([S[0],row+N+1])
            region=img[up_y:down_y,Left_x:Right_x] # 九宫格区域
            j=(np.sum(region)-img[row][col])/((2*N+1)**2-1)
            IJ.append([img[row][col],j])
    print(IJ)
    F=[]#计算F(i,j)
    arr=[list(i) for i in set(tuple(j) for j in IJ)]#去重
    for i in range(len(arr)):
        F.append(IJ.count(arr[i]))
    print(F)
    P=np.array(F)/len(F)#计算pij
    E=np.sum([p*np.log2(1/p) for p in P])#二维熵
    print(E)
calc_2D_Entropy()

[1, 75, 98, 59, 42, 73, 30, 37, 49, 5, 4, 11, 7, 4, 6, 2, 3, 5, 1, 1, 4, 2, 1, 1, 1, 3, 4, 5, 6, 2, 7, 1, 1, 2, 1, 1, 1, 1, 2, 1, 5, 2, 1, 4, 8, 8, 9, 4, 12, 7, 5, 1, 1, 1, 1, 1, 31, 27, 26, 31, 39, 40, 22, 31, 24, 34, 17, 17, 25, 11, 1, 1, 1, 1, 3, 4, 2, 2, 1, 2, 1, 1, 3, 2, 3, 3, 2, 1, 1, 1, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 4, 2, 1, 2, 3, 2, 6, 10, 7, 4, 5, 1, 4, 3, 1, 3, 1, 1, 1, 1, 2, 1, 3, 3, 1, 1, 2, 19, 13, 9, 9, 10, 8, 6, 2, 2, 1, 1, 2, 10, 7, 10, 13, 18, 10, 8, 6, 1, 4, 2, 2, 11, 9, 11, 8, 12, 10, 10, 4, 1, 4, 1, 2, 6, 1, 2, 1, 5, 5, 11, 7, 11, 11, 12, 3, 2, 4, 3, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 18, 30, 13, 17, 19, 6, 1, 2, 1, 3, 1, 1, 2, 1, 1, 2, 2, 1, 16, 15, 20, 13, 16, 17, 15, 8, 4, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 23, 30, 8, 13, 13, 12, 20, 11, 4, 3, 15, 8, 2, 1, 1, 2, 2, 3, 1, 1, 1, 5, 2, 4, 2, 2, 2, 2, 1, 3, 2, 4, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 7, 2, 2, 2, 2, 2, 1, 1, 1, 4, 2, 3, 6, 7, 2, 1, 1, 1, 1, 1, 1, 2, 3, 1, 2, 2, 2, 22, 20, 21, 16, 10, 16, 20, 11, 1, 1, 1, 1, 2, 3, 2, 2, 1, 1, 2, 2, 1, 1, 18, 16, 13, 21, 12, 20, 40, 28, 33, 25, 34, 28, 29, 22, 1, 1, 2, 1, 3, 97, 61, 60, 71, 83, 50, 68, 44, 1, 1, 1, 1, 1, 1, 3, 92, 57, 68, 71, 51, 96, 39, 40, 1, 1, 1, 1, 2, 1, 1, 1, 1, 24, 16, 20, 25, 27, 19, 20, 22, 2, 2, 1, 1, 1, 2, 5, 2, 2, 1, 2, 2, 4, 1, 1, 1, 2, 4, 1, 5, 4, 8, 7, 3, 3, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 5, 2, 5, 3, 8, 6, 3, 5, 3, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 1, 2, 1,...... 2, 2, 2, 1, 2, 2, 1, 3, 5, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 2, 2, 3, 1, 2, 1, 1, 1, 40, 42, 44, 32, 28, 29, 41, 31, 3, 2, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 1, 2, 2, 1, 3, 9, 3, 7, 5, 4, 7, 4, 136, 125, 39, 123, 17, 33, 21, 29, 2, 4, 1, 1, 1, 1, 29, 24, 22, 17, 16, 22, 16, 22, 15, 24, 1, 1, 2, 1, 1, 1, 3, 2, 3, 3, 3, 2, 2, 3, 2, 2, 1, 1, 13, 13, 17, 18, 15, 9, 12, 10, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 33, 26, 33, 36, 27, 24, 20, 30, 1, 1, 1, 1, 7, 5, 15, 2, 1, 5, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 3, 1, 6, 8, 8, 6, 7, 1, 1, 4, 2, 2, 2, 3, 1, 1, 2, 1, 2, 3, 4, 3, 1, 1, 1, 6, 8, 3, 9, 3, 3, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 7, 9, 2, 3, 5, 15, 12, 5, 9, 10, 11, 8, 5, 1, 2, 2, 1, 2, 2, 1, 3, 1, 6, 3, 1, 6, 4, 7, 5, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 4, 2, 6, 2, 3, 4, 7, 2, 55, 55, 52, 53, 1, 1, 2, 44, 2, 1, 1, 177, 173, 181, 1, 83, 53, 101, 37, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 2, 1, 8, 15, 14, 5, 7, 12, 18, 14] 79.43241144310961

算法：二维熵是在一维熵的基础上引入能够反映灰度分布空间特征的特征量来组成图像的二维熵。这表征灰度信息的空间特征，引入图像的像素点与该点的邻域信息，表示邻域灰度均值(0≤j≤255)。

其中，pij表示某像素位置上的灰度值与其周围像素的灰度分布的综合特征，f(i,j)表示特征二元组(i,j)出现的次数W,H为图像尺寸。