#encoding:GBK
"""
Created on 2019/09/23 16:19:11
@author: Sirius_xuan
"""
'''
基于PCA的图像降维及重构
'''
import numpy as np
import cv2 as cv
def Z(dataMat):
rows,cols=dataMat.shape
meanVal = np.mean(dataMat, axis=0) # 按列求均值，即求各个特征的均值
meanVal = np.tile(meanVal,(rows,1))
stdVal = np.std(dataMat, axis=0) # 按列求标准差，即求各个特征的标准差
stdVal = np.tile(stdVal,(rows,1))
newdata = (dataMat-meanVal) / stdVal
return newdata, meanVal
#数据中心化
def Z_centered(dataMat):
rows,cols=dataMat.shape
meanVal = np.mean(dataMat, axis=0) # 按列求均值，即求各个特征的均值
meanVal = np.tile(meanVal,(rows,1))
'''
stdVal = np.std(dataMat, axis=0) # 按列求标准差，即求各个特征的标准差
stdVal = np.tile(stdVal,(rows,1))
newdata = (dataMat-meanVal) / stdVal
'''
newdata = dataMat-meanVal
return newdata, meanVal
#协方差矩阵
def Cov(dataMat):
meanVal = np.mean(data,0) #压缩行，返回1*cols矩阵，对各列求均值
meanVal = np.tile(meanVal, (rows,1)) #返回rows行的均值矩阵
Z = dataMat - meanVal
Zcov = (1/(rows-1))*Z.T * Z
return Zcov
#最小化降维造成的损失，确定k
def Percentage2n(eigVals, percentage):
sortArray = np.sort(eigVals) # 升序
sortArray = sortArray[-1::-1] # 逆转，即降序
arraySum = sum(sortArray)
tmpSum = 0
num = 0
for i in sortArray:
tmpSum += i
num += 1
if tmpSum >= arraySum * percentage:
return num
#得到最大的k个特征值和特征向量
def EigDV(covMat, p):
D, V = np.linalg.eig(covMat) # 得到特征值和特征向量
k = Percentage2n(D, p) # 确定k值
print("保留99%信息，降维后的特征个数："+str(k)+"\n")
eigenvalue = np.argsort(D)
K_eigenValue = eigenvalue[-1:-(k+1):-1]
K_eigenVector = V[:,K_eigenValue]
return K_eigenValue, K_eigenVector
#得到降维后的数据
def getlowDataMat(DataMat, K_eigenVector):
return DataMat * K_eigenVector
#重构数据
def Reconstruction(lowDataMat, K_eigenVector, meanVal):
reconDataMat = lowDataMat * K_eigenVector.T + meanVal
return reconDataMat
#PCA算法
def PCA(data, p):
dataMat = np.float32(np.mat(data))
#数据中心化
dataMat, meanVal = Z_centered(dataMat)
#计算协方差矩阵
#covMat = Cov(dataMat)
covMat = np.cov(dataMat, rowvar=0)
#得到最大的k个特征值和特征向量
D, V = EigDV(covMat, p)
#得到降维后的数据
lowDataMat = getlowDataMat(dataMat, V)
#重构数据
reconDataMat = Reconstruction(lowDataMat, V, meanVal)
return reconDataMat
def main():
imagePath = 'D:/desktop/banana.jpg'
image = cv.imread(imagePath)
image=cv.cvtColor(image,cv.COLOR_BGR2GRAY)
rows,cols=image.shape
print("降维前的特征个数："+str(cols)+"\n")
print(image)
print('----------------------------------------')
reconImage = PCA(image, 0.99)
reconImage = reconImage.astype(np.uint8)
print(reconImage)
cv.imshow('test',reconImage)
cv.waitKey(0)
cv.destroyAllWindows()
if __name__=='__main__':
main()
