import cv2 from sklearn.preprocessing import StandardScaler import numpy as np import pandas as pd from PIL import Image import matplotlib.pyplot as plt

def openImage(imagePath): A = plt.imread(imagePath) X = np.mean(A,-1) #img = plt.imshow(X) #img.set_cmap('gray') #plt.axis('off') #plt.show() return X arr = openImage('The-Lena-face-Test-Image.ppm') print(arr.shape)

def svd(k,arr): A = np.dot(arr.T,arr) rank = np.linalg.matrix_rank(A) val2,vec2 = np.linalg.eig(A) idx = val2.argsort()[::-1] val2 = val2[idx] vec2 = vec2[:,idx] sigma = np.zeros(arr.shape) sqrt_eval = np.sqrt(np.round_(val2.real,2)) for i in range(min(arr.shape)): sigma[i][i] = sqrt_eval[i] u = np.zeros((arr.shape[0], arr.shape[0])) i =0 while sqrt_eval[i]>0: temp = (np.dot(arr,vec2[:,i]))/sqrt_eval[i] u[:,i] = temp.real i +=1 re_construct = u[:,:k] @ sigma[0:k,:k] @ vec2.T[:k, :] print(u.shape,sigma.shape,vec.T.shape) return re_construct

def pca(k,img): cov_mat = np.cov(img , rowvar = False) eigen_values, eigen_vectors = np.linalg.eigh(cov_mat) idx = np.argsort(eigen_values)[::-1] eigenvalues = eigen_values[idx] eigenvectors = eigen_vectors[:,idx] eigenvector_subset = eigenvectors[:,0:k] imgreduced = np.dot(eigenvector_subset.T , img.T ).T imgreconstr = np.dot(imgreduced,eigenvector_subset.T) img = scaler.inverse_transform(img) imgreconstr = scaler.inverse_transform(imgreconstr) return imgreconstr

def plot(k,img,arr): pca_img = pca(k,img) svd_img = svd(k,arr) pca_img = pca_img/255 fig = plt.figure(figsize = (10, 5)) s = 'K : ' + str(k) + ' Frobenius norm :' + str(np.linalg.norm(svd_img - pca_img,'fro')) fig.suptitle(s) fig.add_subplot(121) plt.text(15, -0.01,"PCA Image") plt.imshow(pca_img, cmap='gray') plt.axis('off') fig.add_subplot(122) plt.text(15, -0.01,"SVD Image") plt.imshow(svd_img, cmap='gray') plt.axis("off") plt.show()

import cv2 from sklearn.preprocessing import StandardScaler import numpy as np import pandas as pd from PIL import Image import matplotlib.pyplot as plt def openImage(imagePath): A = plt.imread(imagePath) X = np.mean(A,-1) #img = plt.imshow(X) #img.set_cmap('gray') #plt.axis('off') #plt.show() return XA arr = openImage('The-Lena-face-Test-Image.ppm') def svd(k,arr): A = np.dot(arr.T,arr) rank = np.linalg.matrix_rank(A) val2,vec2 = np.linalg.eig(A) idx = val2.argsort()[::-1] val2 = val2[idx] vec2 = vec2[:,idx] sigma = np.zeros(arr.shape) sqrt_eval = np.sqrt(np.round_(val2.real,2)) for i in range(min(arr.shape)): sigma[i][i] = sqrt_eval[i] u = np.zeros((arr.shape[0], arr.shape[0])) i =0 while sqrt_eval[i]>0: temp = (np.dot(arr,vec2[:,i]))/sqrt_eval[i] u[:,i] = temp.real i +=1 re_construct = u[:,:k] @ sigma[0:k,:k] @ vec2.T[:k, :] #print(u.shape,sigma.shape,vec.T.shape) return re_construct img = cv2.imread("The-Lena-face-Test-Image.ppm") img = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY) scaler = StandardScaler() scaler.fit(img) img = scaler.transform(img) def pca(k,img): cov_mat = np.cov(img , rowvar = False) eigen_values, eigen_vectors = np.linalg.eigh(cov_mat) idx = np.argsort(eigen_values)[::-1] eigenvalues = eigen_values[idx] eigenvectors = eigen_vectors[:,idx] eigenvector_subset = eigenvectors[:,0:k] imgreduced = np.dot(eigenvector_subset.T , img.T ).T imgreconstr = np.dot(imgreduced,eigenvector_subset.T) img = scaler.inverse_transform(img) imgreconstr = scaler.inverse_transform(imgreconstr) return imgreconstr def plot(k,img,arr): pca_img = pca(k,img) svd_img = svd(k,arr) pca_img = pca_img/255 fig = plt.figure(figsize = (10, 5)) s = 'K : ' + str(k) + ' Frobenius norm :' + str(np.linalg.norm(svd_img - pca_img,'fro')) fig.suptitle(s) fig.add_subplot(121) plt.text(15, -0.01,"PCA Image") plt.imshow(pca_img, cmap='gray') plt.axis('off') fig.add_subplot(122) plt.text(15, -0.01,"SVD Image") plt.imshow(svd_img, cmap='gray') plt.axis("off") plt.show() k = [20,40,60,80,100,150,200] for i in k: plot(i,img,arr)