ES156-JPEG - Student Version

!apt update !apt-get install ffmpeg libsm6 libxext6 -y !pip install opencv-python from PIL import Image import matplotlib.pyplot as plt import numpy as np import math from scipy import ndimage import cv2 import copy import warnings from scipy import fftpack from scipy.fftpack import fft2, ifft2 import utils

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Requirement already satisfied: opencv-python in /root/venv/lib/python3.7/site-packages (4.5.1.48)
Requirement already satisfied: numpy>=1.14.5 in /shared-libs/python3.7/py/lib/python3.7/site-packages (from opencv-python) (1.19.5)
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Traceback (most recent call last):
  File "/root/venv/bin/pip", line 8, in <module>
    sys.exit(main())
  File "/root/venv/lib/python3.7/site-packages/pip/_internal/cli/main.py", line 73, in main
    return command.main(cmd_args)
  File "/root/venv/lib/python3.7/site-packages/pip/_internal/cli/base_command.py", line 111, in main
    return self._main(args)
  File "/root/venv/lib/python3.7/site-packages/pip/_internal/cli/base_command.py", line 226, in _main
    self.handle_pip_version_check(options)
  File "/root/venv/lib/python3.7/site-packages/pip/_internal/cli/req_command.py", line 151, in handle_pip_version_check
    pip_self_version_check(session, options)
  File "/root/venv/lib/python3.7/site-packages/pip/_internal/self_outdated_check.py", line 120, in pip_self_version_check
    installed_version = get_installed_version("pip")
  File "/root/venv/lib/python3.7/site-packages/pip/_internal/utils/misc.py", line 644, in get_installed_version
    working_set = pkg_resources.WorkingSet()
  File "/root/venv/lib/python3.7/site-packages/pip/_vendor/pkg_resources/__init__.py", line 567, in __init__
    self.add_entry(entry)
  File "/root/venv/lib/python3.7/site-packages/pip/_vendor/pkg_resources/__init__.py", line 623, in add_entry
    for dist in find_distributions(entry, True):
  File "/root/venv/lib/python3.7/site-packages/pip/_vendor/pkg_resources/__init__.py", line 2065, in find_on_path
    for dist in factory(fullpath):
  File "/root/venv/lib/python3.7/site-packages/pip/_vendor/pkg_resources/__init__.py", line 2127, in distributions_from_metadata
    if len(os.listdir(path)) == 0:
KeyboardInterrupt

# Height and width of our images in parts 1 and 2 M = 512 N = 512

im_original = cv2.imread("images/puppy1.png", 0) im_noisy = utils.noise_image(im_original, 6.0, N, M)

def denoise(img): #Hint: check out the "filter image" function in utils # Denoise the image with specified method p = np.asarray(img, dtype=np.uint8) + np.zeros((int(M/2),int(N/2)), dtype=np.uint8) for i in range(1, int(M/2)-1): for j in range(1, int(N/2)-1): neighbors = np.asarray([p[i-1, j], p[i+1, j], p[i, j-1],p[i, j+1], p[i+1, j+1], p[i-1, j+1], p[i+1, j-1], p[i+1, j-1]]) mindist = min(abs(p[i,j] - n) for n in neighbors) std = np.std(neighbors) if mindist > std: p[i, j] = np.mean(neighbors) return p

plt.imshow(denoise(im_noisy), cmap = 'gray') plt.show()

def compute_MSE(img, img_new): for i in range(1, int(N/2)-1): for j in range(1, int(M/2)-1): inner = np.sum(np.square(np.subtract(img_new[i,j], img[i,j]))) # including the 1/M and 1/N cause the error curve to become too flat # in comparison to the goal curve # ... but maybe that is what we want? Less error is good... MSE = (1/M)*(1/N)*inner return MSE

noise_amounts = np.linspace(0,16,8, dtype=np.float64) errors = [] for i in noise_amounts: noisy_im = utils.noise_image(im_original, i, M, N) filtered_im = denoise(noisy_im) errors.append(compute_MSE(im_original, filtered_im)) goal_curve = [90, 95, 100, 120, 170, 250, 375, 550] plt.plot(noise_amounts, errors, 'bo--', label='errors') plt.plot(noise_amounts, goal_curve, 'gs--', label='goal') plt.legend() plt.xlabel('Gaussian Noise Added') plt.ylabel('Reconstruction Error') plt.show()

im1 = cv2.imread("images/kitten1.png",0) plt.imshow(im1, cmap='gray') plt.show()

# Keeping track of function documentaion for reference... # https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.fft2.html # https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html#numpy.linalg.norm def get_coeffs(X): # Compute discrete (2D) fourier for the image series = fft2(X) for n in range (0, int(N/2) -1) cfts = (1/N)*np.sum(series*(math.e^(-j*k*n*((2*math.pi)/N)))) # Compute the magnitudes of the coefficients mgs = np.linalg.norm(cfts) return cfts, mgs

IndentationError: unexpected indent (<ipython-input-61-b153cf121475>, line 9)

coefficients, mags = get_coeffs(im1)

NameError: name 'get_coeffs' is not defined

# Pick 2 values for alpha to show the difference in quality of reconstruction alpha1 = .99 alpha2 = .01 coeffs1 = utils.get_alpha_coeffs(coefficients, mags, alpha1, N, M) coeffs2 = utils.get_alpha_coeffs(coefficients, mags, alpha2, N, M)

NameError: name 'coefficients' is not defined

# Keeping track of function documentaion for reference... # https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.ifft2.html#scipy.fft.ifft2 def inverse_ft(cfs): # Get the IDFT invert = ifft2(cfs) for n in range (0, int(N/2) -1) inv = (1/N)*np.sum(invert*(math.e^(-j*k*n*((2*math.pi)/N)))) # Get the magnitudes inv_mags = np.linalg.norm(inv) return inv, inv_mags

IndentationError: unexpected indent (<ipython-input-10-c7d6b266272f>, line 7)

inverse1, inverse_mags1 = inverse_ft(coeffs1) inverse2, inverse_mags2 = inverse_ft(coeffs2)

NameError: name 'inverse_ft' is not defined

f = plt.figure(figsize=(12,12)) plt.subplot(131),plt.imshow(im1, cmap = 'gray') plt.xlabel('Orginal', fontsize=8), plt.xticks([]), plt.yticks([]) plt.subplot(132),plt.imshow(inverse_mags1, cmap = 'gray') plt.xlabel("alpha = " + str(alpha1), fontsize=8), plt.xticks([]), plt.yticks([]) plt.subplot(133),plt.imshow(inverse_mags2, cmap = 'gray') plt.xlabel("alpha = " + str(alpha2), fontsize=8), plt.xticks([]), plt.yticks([]) plt.show()

NameError: name 'inverse_mags1' is not defined

# Computes reconstruction error def compute_error(img, img_new): error = compute_MSE(img,img_new) return error

alphas = np.linspace(.01,.99,25, dtype=np.float64) errors = np.zeros(len(alphas)) for a in range(len(alphas)): cfs = utils.get_alpha_coeffs(coefficients, mags, alphas[a], N, M) icfs = cv2.idft(cfs) imags = cv2.magnitude(icfs[:,:,0],icfs[:,:,1])/(M*N) errors[a] = compute_error(im1,imags) plt.plot(alphas, errors, 'o') plt.xlabel('alpha') plt.ylabel('Reconstruction Error') plt.title('FT Compression/Distortion Trade-Off') plt.show()

# Redefine image dimensions for part 3.1 N = 35

# Comments reference SciPy Reference guide -> # https://docs.scipy.org/doc/scipy/reference/generated/scipy.fft.dct.html def compute_dct(X): # Set empty array for dct coefficients dct = np.zeros((N, N), dtype=np.float64) # Iterate through and compute values for all coefficients for k in range(N): for l in range(N): # from scipy DCT type 2 dct = 2*np.sum(X) # For norm='ortho' both directions are scaled by the same factor of 1/sqrt(N) dct = 2*dct/np.sqrt(N**2) return dct

IndentationError: expected an indented block (<ipython-input-78-21f7f10ba0d7>, line 13)

img = cv2.imread("images/dct_sample1.png", 0) dct = compute_dct(img) dct2 = fftpack.dct(fftpack.dct(img.T, type=2, norm='ortho').T, type=2, norm='ortho') # Plot the image next to the transform and the scipy transform f = plt.figure(figsize=(12,12)) plt.subplot(131),plt.imshow(img, cmap = 'gray') plt.xlabel('', fontsize=8), plt.xticks([]), plt.yticks([]) plt.title('Original Image') plt.subplot(132),plt.imshow(dct, cmap = 'gray') plt.xlabel('', fontsize=8), plt.xticks([]), plt.yticks([]) plt.title('Results of DCT Function') plt.subplot(133),plt.imshow(dct2, cmap = 'gray') plt.xlabel('', fontsize=8), plt.xticks([]), plt.yticks([]) plt.title('Scipys DCT Function') plt.show()

NameError: name 'compute_dct' is not defined

# Redefine image dimensions for part 3.1 N = 256

im1 = cv2.imread("images/puppy3_small.png",0) plt.imshow(im1, cmap='gray') plt.show()

# Number of patches prange = N/8

def partition_img(img): return

def partitioned_dct(ppatches, K): # Set empty array of sizes K^2 per patch return dct_patches

patches = partition_img(im1) for i in range(8): for j in range(8): plt.subplot(8,8,int(1+j+i*8)), plt.imshow(patches[i][j], cmap="gray") plt.xticks([]) plt.yticks([]) plt.show()

partitioned_img = partition_img(im1) dct4 = partitioned_dct(partitioned_img, 2) dct16 = partitioned_dct(partitioned_img, 4) dct36 = partitioned_dct(partitioned_img, 6) dct64 = partitioned_dct(partitioned_img, 8) plt.subplot(141),plt.imshow(dct4[0][0], cmap='gray'), plt.xticks([]),plt.yticks([]) plt.subplot(142),plt.imshow(dct16[0][0],cmap='gray'), plt.xticks([]),plt.yticks([]) plt.subplot(143),plt.imshow(dct36[0][0],cmap='gray'), plt.xticks([]),plt.yticks([]) plt.subplot(144),plt.imshow(dct64[0][0],cmap='gray'), plt.xticks([]),plt.yticks([]) plt.show()

# Compute the quantized version of the specified transform (DCT or DFT) def quantize(dct_patches): # Initialize the quantization matrix Qmtrx = np.zeros((8,8)) Qmtrx[0,:] = [16, 11, 10, 16, 24, 40, 51, 61] Qmtrx[1,:] = [12, 12, 14, 19, 26, 58, 60, 55] Qmtrx[2,:] = [14, 13, 16, 24, 40, 57, 69, 56] Qmtrx[3,:] = [14, 17, 22, 29, 51, 87, 80, 62] Qmtrx[4,:] = [18, 22, 37, 56, 68, 109, 103, 77] Qmtrx[5,:] = [24, 36, 55, 64, 81, 104, 113, 92] Qmtrx[6,:] = [49, 64, 78, 87, 103, 121, 120, 101] Qmtrx[7,:] = [72, 92, 95, 98, 112, 100, 103, 99] # Store dimensions of DCT coefficient matrix patches for iteration # Initialize an empty matrix to store the quantized coefficients # Compute and store the quantized coefficients return q_dct

qdct4 = quantize(dct4) qdct16 = quantize(dct16) qdct36 = quantize(dct36) qdct64 = quantize(dct64) plt.subplot(141),plt.imshow(qdct4[0][0], cmap='gray'), plt.xticks([]),plt.yticks([]) plt.subplot(142),plt.imshow(qdct16[0][0],cmap='gray'), plt.xticks([]),plt.yticks([]) plt.subplot(143),plt.imshow(qdct36[0][0],cmap='gray'), plt.xticks([]),plt.yticks([]) plt.subplot(144),plt.imshow(qdct64[0][0],cmap='gray'), plt.xticks([]),plt.yticks([]) plt.show()

def unquantize(qdct_patches): # Initialize the quantization matrix Qmtrx = np.zeros((8,8)) Qmtrx[0,:] = [16, 11, 10, 16, 24, 40, 51, 61] Qmtrx[1,:] = [12, 12, 14, 19, 26, 58, 60, 55] Qmtrx[2,:] = [14, 13, 16, 24, 40, 57, 69, 56] Qmtrx[3,:] = [14, 17, 22, 29, 51, 87, 80, 62] Qmtrx[4,:] = [18, 22, 37, 56, 68, 109, 103, 77] Qmtrx[5,:] = [24, 36, 55, 64, 81, 104, 113, 92] Qmtrx[6,:] = [49, 64, 78, 87, 103, 121, 120, 101] Qmtrx[7,:] = [72, 92, 95, 98, 112, 100, 103, 99] # Store dimensions of DCT coefficient matrix patches for iteration # Initialize an empty matrix to store the quantized coefficients # Compute and store the quantized coefficients return iq_dct

# Computes iDCTs for patches def inverse_dct(patches): # Set empty array for recovered set of patches image i_patches = np.zeros((prange,prange, 8, 8), dtype=np.float64) return i_patches

def stitch(patches): recovered = np.zeros((N,N), dtype=np.float64) return recovered

recovered4 = stitch(inverse_dct(unquantize(qdct4))) recovered16 = stitch(inverse_dct(unquantize(qdct16))) recovered36 = stitch(inverse_dct(unquantize(qdct16))) recovered64 = stitch(inverse_dct(unquantize(qdct64))) plt.subplot(141),plt.imshow(recovered4,cmap='gray'), plt.title('K^2=4',fontsize=8), plt.xticks([]), plt.yticks([]) plt.subplot(142),plt.imshow(recovered16, cmap='gray'), plt.title('K^2 = 16',fontsize=8), plt.xticks([]),plt.yticks([]) plt.subplot(143),plt.imshow(recovered36,cmap='gray'), plt.title('K^2 = 36',fontsize=8), plt.xticks([]),plt.yticks([]) plt.subplot(144),plt.imshow(recovered64, cmap='gray'), plt.title('K^2 = 64',fontsize=8), plt.xticks([]),plt.yticks([]) plt.show()

# Computes reconstruction error def compute_error(img, img_new): error = compute_MSE(img,img_new) return error

dcq_errors = [compute_error(im1, q) for q in [recovered4, recovered16, recovered36, recovered64]] K2list = [4,16,36,64] jpeg1 = cv2.imread("images/puppy3_small1.jpg", 0) j1 = compute_error(im1, jpeg1) j1 = [j1, j1, j1, j1] jpeg2 = cv2.imread("images/puppy3_small2.jpg", 0) j2 = compute_error(im1, jpeg2) j2 = [j2, j2, j2, j2] jpeg3 = cv2.imread("images/puppy3_small3.jpg", 0) j3 = compute_error(im1, jpeg3) j3 = [j3, j3, j3, j3] jpeg4 = cv2.imread("images/puppy3_small4.jpg", 0) j4 = compute_error(im1, jpeg4) j4 = [j4, j4, j4, j4] # Plot the MSE Reconstruction Errors against the Jpeg standard plt.plot(K2list, dcq_errors, 'k-s', label='Quantized DCT') plt.plot(K2list, j1, 'r--', label='JPEG Low Standard') plt.plot(K2list, j2, 'y--', label='JPEG Medium Standard') plt.plot(K2list, j3, 'g--', label='JPEG High Standard') plt.plot(K2list, j4, 'b--', label='JPEG Max Standard') plt.legend() plt.xlabel('K^2') plt.ylabel('Reconstruction Error') plt.title('DFT and DCT Reconstruction Error for Varying K^2') plt.savefig('JPEG_standard_plot.png') plt.show()