import numpy as np from sklearn.linear_model import LogisticRegression import matplotlib.pyplot as plt from PIL import Image, ImageOps import matplotlib.pyplot as plt

# Download original, full data-set or pre-sampled data # !wget https://storage.googleapis.com/am_205_bucket/img_align_celeba.zip -P ./ # !unzip -q ./img_align_celeba.zip -d ./ !wget https://storage.googleapis.com/am_205_bucket/celeb_sample.zip -P ./ !unzip -q ./celeb_sample.zip -d ./celeb_sample

# Code for random sampling of celeba dataset sample_size = 1000 # vals = np.random.choice(list(range(200000)), size=sample_size, replace=False) # img_lst = [Image.open('./img_align_celeba/{}.jpg'.format( str(i).zfill(6) )) for i in vals] # X = np.array([np.array(img) for img in img_lst]) # !mkdir celeb_sample # [img.save('celeb_sample/{}.jpg'.format(i)) for i, img in enumerate(img_lst)] # Loading pre-sampled celeb images img_lst = [Image.open('./celeb_sample/{}.jpg'.format(i)) for i in range(sample_size)] X = np.array([np.array(img) for img in img_lst]) / 255 im_shape = X[0].shape X.shape

# Visualize some samples from the training dataset fig, ax = plt.subplots(2, 5, figsize=(15, 7)) for i in range(5): ax[0, i].imshow(X[i]) ax[1, i].imshow(X[i+5]) ax[0, i].axis("off") ax[1, i].axis("off") fig.suptitle('Sample CelebA Data') plt.show()

# Compute SVD Compression and Decompression of an image # rank-k approximation and rank-r reconstruction def svd_compression(im, k, r): m,n,p = im.shape S = np.vstack([im[:,:,0], im[:,:,1], im[:,:,2]]) # compute the mean of each row to obtain a mean column. Sm = np.mean(S, axis=1, keepdims=True) # compute the centered matrix A. A = S - Sm def rank_approx(A, k): L = [] U, s, Vt = np.linalg.svd(A, full_matrices=False) for i in range(k): L.append(np.dot(s[i], np.dot(U[:, i].reshape(-1, 1), Vt[i].reshape(1, -1)))) return L, U[:, :k], s[:k], Vt[:k] def reconstruct(L, r, Sbar): if r > len(L): print("Error: r must be less than the length of L.") return m = len(Sbar)//3 # the leading dimension of a single channel # Reconstruct the original image up to rank j. Ar = np.sum(L[:(r-1)], axis=0) # Add back the mean and reshape into m by n by p. Ar += Sbar.reshape(-1,1) imr = np.stack([Ar[:m,:],Ar[m:2*m,:],Ar[2*m:,:]], axis=2) # truncate values and return the reconstructed image. imr[imr<0] = 0; imr[imr>1] = 1 return imr return rank_approx(A, k), reconstruct(rank_approx(A, k)[0], r, Sm) # Run a test: test_vals = [2, 4, 8, 16, 32, 64]

# compute SVD compression and decompression for a list of images and ranks def test_SVD(ims, test_vals=test_vals): res_mean = [] err_mean = [] for val in test_vals: sizes = [] errs = [] for im in ims: res, imr = svd_compression(im, val, val) L, U, s, Vt = res U = np.array(U) s = np.array(s) Vt = np.array(Vt) L = np.array(L) errs.append(np.mean((np.linalg.norm(im-imr, axis=2))**2)) res_mean.append((U.shape[0] * U.shape[1] + s.shape[0] + Vt.shape[0]) / (im_shape[0] * im_shape[1] * im_shape[2]) ) err_mean.append(np.mean(errs)) return res_mean, err_mean size_svd, err_svd = test_SVD(X)

# Plot values of size and MSE accross test values plt.scatter(test_vals, 100 * np.array(size_svd)) plt.plot(test_vals, 100 * np.array(size_svd)) plt.title('Rank vs. Size of Compression') plt.xlabel('Rank Value') plt.ylabel('Image Size (as % of original') plt.show() plt.scatter(test_vals, err_svd) plt.plot(test_vals, err_svd) plt.title('Rank vs. MSE') plt.xlabel('Rank Value') plt.ylabel('Image MSE') plt.show()

# Plot SVD of different ranks accross test images fig, ax = plt.subplots(len(test_vals) + 1, 5, figsize=(15, 21)) for j, val in enumerate(test_vals[::-1]): for i in range(5): if j == 0: ax[j][i].imshow(X[i]) ax[j][i].axis('off') ax[j][i].set_title(f'Image {i}') res, imr = svd_compression(X[i], val, val) L, U, s, Vt = res U = np.array(U) s = np.array(s) Vt = np.array(Vt) L = np.array(L) ax[j+1][i].imshow(imr) ax[j+1][i].axis('off') ax[j+1][i].set_title(f'Image {i}, rank: {val}\n {round(100 * (U.shape[0] * U.shape[1] + s.shape[0] + Vt.shape[0]) / (im_shape[0] * im_shape[1] * im_shape[2]),4)}% of image size') fig.tight_layout(pad=3)

# import and define helper functions for DCT from scipy.fftpack import dct, idct def dct3d(img): return dct(dct(dct(img, norm='ortho', axis=0), norm='ortho', axis=1), norm='ortho', axis=2) def idct3d(img): return idct(idct(idct(img, norm='ortho', axis=0), norm='ortho', axis=1), norm='ortho', axis=2) # run DCT accross variety of images and threshold values def test_dct(ims, test_thresholds): res_mean = [] err_mean = [] size_all = [] for val in test_thresholds: sizes = [] errs = [] for im in ims: im_red = dct3d(im) im_comp = im_red * (abs(im_red) > val) imr = idct3d(im_comp) errs.append(np.mean((np.linalg.norm(im-imr, axis=2))**2)) sizes.append(300*np.mean(im_comp != 0)) size_all.append(sizes) res_mean.append(np.mean(sizes)) err_mean.append(np.mean(errs)) return res_mean, err_mean, size_all test_thresholds = [0.05, 0.1, 0.175, 0.25, 0.5, 0.75]

size_dct, err_dct, size_all = test_dct(X, test_thresholds)

# Plot relevant metrics of size and error accross threshold values plt.scatter(test_thresholds, size_dct) plt.plot(test_thresholds, size_dct) plt.title('Test Threshold vs. Size of Compression') plt.xlabel('Threshold Value') plt.ylabel('% Size of Original Image') plt.show() plt.scatter(test_thresholds, err_dct) plt.plot(test_thresholds, err_dct) plt.title('Test Threshold vs. MSE') plt.xlabel('Threshold Value') plt.ylabel('Image MSE') plt.show()

# Plot distribution of image sizes accross threshold values fig, ax = plt.subplots(3, 2, figsize=(10, 15)) for i in range(6): ax[i // 2][i % 2].hist(size_all[i]) ax[i // 2][i % 2].set_title(f'% Size of Original Image\nThreshold: {test_thresholds[i]} | Average Size: {round(np.mean(size_all[i]), 2)}%') ax[i // 2][i % 2].set_xlabel('% Size of Original Image') ax[i // 2][i % 2].set_ylabel('Frequency') fig.tight_layout(pad=3) plt.show()

# Plot DCT for sample of images accross threshold values fig, ax = plt.subplots(len(test_thresholds) + 1, 5, figsize=(15, 21)) for i in range(5): im_red = dct3d(X[i]) for j, val in enumerate(test_thresholds): if j == 0: ax[j][i].imshow(X[i]) ax[j][i].axis('off') ax[j][i].set_title(f'Image {i}') im_comp = im_red * (abs(im_red) > val) imr = idct3d(im_red * (abs(im_red) > val)) ax[j+1][i].imshow(imr) ax[j+1][i].axis('off') ax[j+1][i].set_title(f'Image {i}, threshold: {val}\n{ round(100*(1 - np.mean(im_comp == 0)) * 3,4)}% Of Image Size') fig.tight_layout(pad=3)

print("DCT:", err_dct[::-1]) print("SVD:", err_svd)