'''
1.样本设置 橘子-1 背景-0 苹果-2
2.求Sb 每类均值向量,所有样本均值向量
3.求Sw 三类样本协方差之和
4.求解Sw 和Sb 的特征值
5.求取 W 取 K 个特征向量组成 W 矩阵
6.读入图像,进行RGB变换,变换成3行1 列向量(参考二类分类)
7.y = W(T) x
# 计算三类样本中心的位置
# 求f(x),得到2行1列的判断向量
# Fisher判断类别
'''
import numpy as np
import cv2
import math
from copy import deepcopy
# 设置样本,为了进行对比,与Bayes三类分类使用相同的样本
def Dataset():
# 共35个样本数据 橘子10 背景10 苹果15
samples_data = [[199,114,34], [199,113,36], [188,93,11],
[196,101,17], [193,97,13], [85,37,23],
[192,99,19], [178,83,3], [87,38,24],
[87,37,26], [126,137,143], [125,136,142],
[131,142,148], [130,141,147], [129,140,146],
[181,197,210], [183,201,213], [182,200,212],
[180,198,210], [181,199,209], [166,108,94],
[167,108,94], [165,107,93], [159,99,89],
[156,96,86], [154,94,84], [149,81,78],
[155,87,84], [157,82,86], [156,81,85],
[156,84,85], [130,58,62], [166,110,93],
[150,83,77], [130,58,62]]
class_lable = [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]
# 橘子--1 背景--0 苹果--2
return samples_data,class_lable
# 求每类样本均值向量 和 总体均值向量
def Get_Junzhi(samples_data,class_lable):
L = len(samples_data)
m = 0 # 水果
n = 0 # 背景
k = 0 # 苹果
r1 = 0
g1 = 0
b1 = 0
r0 = 0
g0 = 0
b0 = 0
r2 = 0
g2 = 0
b2 = 0
mv = [0]
mean_vector1 = [mv]*3
mean_vector0 = [mv]*3
mean_vector2 = [mv]*3
for i in range(L):
if class_lable[i] == 1:
m += 1
elif class_lable[i] == 0:
n += 1
else:
k += 1
for i in range(L):
if i < m:
r1 += samples_data[i][0]
g1 += samples_data[i][1]
b1 += samples_data[i][2]
elif i >= m+n:
r2 += samples_data[i][0]
g2 += samples_data[i][1]
b2 += samples_data[i][2]
else:
r0 += samples_data[i][0]
g0 += samples_data[i][1]
b0 += samples_data[i][2]
mean_vector1 = [[int(r1/m)],[int(g1/m)],[int(b1/m)]] # 三维均值向量
mean_vector0 = [[int(r0/n)],[int(g0/n)],[int(b0/n)]]
mean_vector2 = [[int(r2/k)],[int(g2/k)],[int(b2/k)]]
mean_all = [[int((r0+r1+r2)/L)],[int((g0+g1+g2)/L)],[int((b0+b1+b2)/L)]]
# print(mean_vector1)
# print(mean_vector0)
# print(mean_vector2)
# print(mean_all)
return mean_vector1, mean_vector0, mean_vector2, mean_all
# 求Sb
def Get_Sb(mean_vector1,mean_vector0,mean_vector2,mean_all):
# 求u-ui
# #求u-ui的转置
mean1 = [[0], [0], [0]]
mean0 = [[0], [0], [0]]
mean2 = [[0], [0], [0]]
t1 = [[0,0,0]]
t0 = [[0,0,0]]
t2 = [[0,0,0]]
Sb = [[0,0,0],[0,0,0],[0,0,0]]
for i in range(3):
for j in range(1):
mean1[i][j] = mean_vector1[i][j] - mean_all[i][j]
mean0[i][j] = mean_vector0[i][j] - mean_all[i][j]
mean2[i][j] = mean_vector2[i][j] - mean_all[i][j]
t1[j][i] = mean1[i][j]
t0[j][i] = mean0[i][j]
t2[j][i] = mean2[i][j]
# m1 = np.dot(10,np.dot(mean1,t1))
# m0 = np.dot(10,np.dot(mean0,t0)) # 疑似错误用法
# m2 = np.dot(15, np.dot(mean2, t2))
m_1 = np.dot(mean1,t1)
m1 = np.dot(10,m_1)
m_0 = np.dot(mean0,t0)
m0 = np.dot(10,m_0)
m_2 = np.dot(mean2,t2)
m2 = np.dot(15,m_2)
for i in range(len(m1)):
for j in range(len(m0)):
Sb[i][j] = m_1[i][j] + m_0[i][j] + m_2[i][j]
#print(Sb)
# 求Sb
return Sb
# 求协方差之和 Sw
def Get_Cov(samples_data,mean_vector1,mean_vector0,mean_vector2):
L= len(samples_data)
m = 10
n = 10
k = 15
cov = [0]*3
Cov_1 = [cov]*3
Cov_0 = [cov]*3
Cov_2 = [cov]*3
cov_bb1 = 0
cov_gb1 = 0
cov_gg1 = 0
cov_rb1 = 0
cov_rg1 = 0
cov_rr1 = 0
cov_bb0 = 0
cov_gb0 = 0
cov_gg0 = 0
cov_rb0 = 0
cov_rg0 = 0
cov_rr0 = 0
cov_bb2 = 0
cov_gb2 = 0
cov_gg2 = 0
cov_rb2 = 0
cov_rg2 = 0
cov_rr2 = 0
Sw = []
ve = [0,0,0]
for i in range(L):
if i < m:
cov_rr1 += (samples_data[i][0]-mean_vector1[0][0])*(samples_data[i][0]-mean_vector1[0][0])
cov_rg1 += (samples_data[i][0]-mean_vector1[0][0])*(samples_data[i][1]-mean_vector1[1][0])
cov_rb1 += (samples_data[i][0]-mean_vector1[0][0])*(samples_data[i][2]-mean_vector1[2][0])
cov_gg1 += (samples_data[i][1]-mean_vector1[1][0])*(samples_data[i][1]-mean_vector1[1][0])
cov_gb1 += (samples_data[i][1]-mean_vector1[1][0])*(samples_data[i][2]-mean_vector1[2][0])
cov_bb1 += (samples_data[i][2]-mean_vector1[2][0])*(samples_data[i][2]-mean_vector1[2][0])
elif i >= m+n:
cov_rr2 += (samples_data[i][0] - mean_vector2[0][0]) * (samples_data[i][0] - mean_vector2[0][0])
cov_rg2 += (samples_data[i][0] - mean_vector2[0][0]) * (samples_data[i][1] - mean_vector2[1][0])
cov_rb2 += (samples_data[i][0] - mean_vector2[0][0]) * (samples_data[i][2] - mean_vector2[2][0])
cov_gg2 += (samples_data[i][1] - mean_vector2[1][0]) * (samples_data[i][1] - mean_vector2[1][0])
cov_gb2 += (samples_data[i][1] - mean_vector2[1][0]) * (samples_data[i][2] - mean_vector2[2][0])
cov_bb2 += (samples_data[i][2] - mean_vector2[2][0]) * (samples_data[i][2] - mean_vector2[2][0])
else:
cov_rr0 += (samples_data[i][0] - mean_vector0[0][0]) * (samples_data[i][0] - mean_vector0[0][0])
cov_rg0 += (samples_data[i][0] - mean_vector0[0][0]) * (samples_data[i][1] - mean_vector0[1][0])
cov_rb0 += (samples_data[i][0] - mean_vector0[0][0]) * (samples_data[i][2] - mean_vector0[2][0])
cov_gg0 += (samples_data[i][1] - mean_vector0[1][0]) * (samples_data[i][1] - mean_vector0[1][0])
cov_gb0 += (samples_data[i][1] - mean_vector0[1][0]) * (samples_data[i][2] - mean_vector0[2][0])
cov_bb0 += (samples_data[i][2] - mean_vector0[2][0]) * (samples_data[i][2] - mean_vector0[2][0])
a = m-1
b = n-1
c = k-1
Cov_1 = [[cov_rr1/a,cov_rg1/a,cov_rb1/a],[cov_rg1/a,cov_gg1/a,cov_gb1/a],[cov_rb1/a,cov_gb1/a,cov_bb1/a]]
Cov_0 = [[cov_rr0/b,cov_rg0/b,cov_rb0/b],[cov_rg0/b,cov_gg0/b,cov_gb0/b],[cov_rb0/b,cov_gb0/b,cov_bb0/b]]
Cov_2 = [[cov_rr2/c,cov_rg2/c,cov_rb2/c],[cov_rg2/c,cov_gg2/c,cov_gb2/c],[cov_rb2/c,cov_gb2/c,cov_bb2/c]]
for i in range(3):
for j in range(1):
a = Cov_1[i][j] + Cov_0[i][j] + Cov_2[i][j]
b = Cov_1[i][j+1] + Cov_0[i][j+1] + Cov_2[i][j+1]
c = Cov_1[i][j+2] + Cov_0[i][j+2] + Cov_2[i][j+2]
ve= [a,b,c]
V = deepcopy(ve)
Sw.append(V)
# print(Sw)
return Sw
# 求Sw的逆和Sb的乘积的特征值和 特征向量 W以及 W的转置
# 返回 W_T
def Get_tezhengzhi(Sb,Sw):
Inv_Sw = np.linalg.inv(Sw)
Sw_Sb = np.dot(Inv_Sw,Sb)
a, W = np.linalg.eig(Sw_Sb) # a--特征值 W--特征向量
# 取前最大的2(投影向量的个数)个特征向量组成W矩阵即可,这里取w2,w3
W_T = [[0, 0, 0], [0, 0, 0]]
for i in range(3):
for j in range(1,3):
W_T[j-1][i] = W[i][j]
return W_T
# 计算三类样本中心的位置
def Get_Center_XY(mean_vector1,mean_vector0,mean_vector2,W_T):
XY_1 = np.dot(W_T,mean_vector1)
XY_0 = np.dot(W_T, mean_vector0)
XY_2 = np.dot(W_T, mean_vector2)
XY_center = [XY_1,XY_0,XY_2]
return XY_center
# 求f(x),得到2行1列的判断向量
# Fisher判断类别
def Get_F(data,W_T,XY_center):
XY_data = np.dot(W_T,data)
Cla = [0,0,0]
for i in range(3):
x = XY_data[0][0] - XY_center[i][0]
y = XY_data[1][0] - XY_center[i][1]
Cla[i] = x*x + y*y
F_classify = min(Cla)
if F_classify == Cla[0]:
F = 1
elif F_classify == Cla[1]:
F = 0
elif F_classify == Cla[2]:
F = 2
return F
# RGB 变换
# 改变图像RGB存储形式
# 编成3行1列形式
def Get_RGB(image):
w = image.shape[0]
h = image.shape[1]
data = []
ve = [[0] for i in range(3)]
new_data = [ve for i in range(w*h)]
for i in range(w):
for j in range(h):
for k in range(1): # B G 调换
a = image[i,j,k+0]
image[i,j,k+0] = image[i,j,k+2]
image[i,j,k+2] = a
# print(image)
for i in range(w):
for j in range(h):
new_data[i*h+j][0][0] = image[i][j][0]
new_data[i*h+j][1][0] = image[i][j][1]
new_data[i*h+j][2][0] = image[i][j][2]
V = deepcopy(ve)
data.append(V)
return data
#实现费歇尔三类分类
# 把图片的RGB传进来对每一个像素做分类 橘子赋值 [255,128,0] ,背景赋值 255， 苹果赋值 [255,0,0]
def Get_Cla_Image(test_data, image,W_T,XY_Center):
w = image.shape[0]
h = image.shape[1]
L = len(test_data)
for i in range(w):
for j in range(h):
a = [test_data[i*h+j]]
F_X = Get_F(a,W_T,XY_center)
if F_X == 1:
image[i][j][0] = 0 # 这里图片是RGB形式 橘子
image[i][j][1] = 128 # 赋值时需要注意
image[i][j][2] = 255
elif F_X == 0: # 背景
image[i][j] = 255
elif F_X == 2:
image[i][j][0] = 0 # 74,114,216 这里图片是RGB形式 苹果
image[i][j][1] = 0 # 赋值时需要注意
image[i][j][2] = 255
return image
test_data, test_lable = Dataset()
m1, m0, m2, mall = Get_Junzhi(test_data,test_lable)
Sb = Get_Sb(m1,m0,m2,mall)
Sw = Get_Cov(test_data,m1,m0,m2)
W_T = Get_tezhengzhi(Sb,Sw)
XY_center = Get_Center_XY(m1,m0,m2,W_T)
image = cv2.imread('JP3.jpg')
test_data = Get_RGB(image)
Fisher_Image = Get_Cla_Image(test_data,image,W_T,XY_center)
cv2.imshow('Fisher_three', Fisher_Image)
cv2.waitKey(0)
cv2.destroyAllWindows()
'''
data = [[72],[61],[69]]
test_data, test_lable = Dataset()
m1, m0, m2, mall = Get_Junzhi(test_data,test_lable)
Sb = Get_Sb(m1,m0,m2,mall)
Sw = Get_Cov(test_data,m1,m0,m2)
W_T = Get_tezhengzhi(Sb,Sw)
XY_center = Get_Center_XY(m1,m0,m2,W_T)
F = Get_F(data,W_T,XY_center)
'''
'''
print(cov1)
print(cov0)
print(cov2)
print(Sb)
'''
