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compress.py
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compress.py
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##
#
# @author: Zimehr Abbasi
# @date: 2021
# A basic compressor which uses singular value decomposition to compress image files
#
##
from PIL import Image
import numpy as np
from numpy import linalg as LA
from matplotlib import pyplot as plt
from matplotlib.image import imsave
class LinearPress:
def __init__(self, image_dir, eigenvalues_to_keep=None):
self.image_dir = image_dir # Image Directory
self.image = None # Stores the image file as ann array
self.eigenvalues_to_keep = eigenvalues_to_keep # number of eigenvalues to keep
# array with the average of the RGB values instead of the tuple
self.single_val_array = None
self.rotate = False # for functionality of the rotation
self.final = None # Compressed image
'''
This function takes in as parameters 2 vectors and calculates the projection of the first vector on the second vector
v1: numpy array
v2: numpy array
'''
def calc_projection(self, v1, v2):
# Return 0 if the length is 0
if(np.dot(v2, v2) == 0):
return 0
# Calculate the projection
w = np.dot(v1, v2)/np.dot(v2, v2) * v2
# return the projection
return w
'''
This function takes in as a parameter a single vector and returns the norm of the vector
vector: numpy array
'''
def norm(self, vector):
# return if the norm is 0
if len(vector) == 0:
return 0
# Calculate the square of the norm of the inputted vector
running_sum = 0
for x in range(len(vector)):
running_sum += vector[x]**2
# return norm of the vector
return np.sqrt(running_sum)
'''
This fucntion takes in as parameters a eigenvector matrix and performs the gram Schmidt process on it, returning the orthogonal eigenvectors
W: 2D numpy array
'''
def gram_schmidt(self, W):
# Set the first vector to v
v = [W[0]]
for y in range(1, len(W)):
vtemp = W[y]
temp = 0
# projection calculations for vector y
for x in range(1, y+1):
temp += self.calc_projection(vtemp, W[x-1])
vtemp -= temp
# Append the new orthonormal array to the
v.append(vtemp)
return np.array(v)
'''
This function takes in as a parameters an eigenvalue array and the corresponding eigenvector arrays and sorts them in decreasing order based on the eigenvalues
A: numpy array
B: 2D numpy array
'''
def same_sort(self, A, B):
# Sort the eigenvectors and eigenvalues
for x in range(len(A)):
for y in range(len(A)):
if(A[x] > A[y]):
A[x], A[y] = A[y], A[x]
for i in range(len(B)):
B[x][i], B[y][i] = B[y][i], B[x][i]
return A, B
'''
This function is the main process of the entire compressor class for an RGB image
'''
def process3D(self):
# The columns and rows for the original shape
or_cols = self.single_val_array[0].shape[1]
or_rows = self.single_val_array[0].shape[0]
# columns and rows for the new shape
cols = self.single_val_array[0].shape[1]
rows = self.single_val_array[0].shape[0]
if(self.eigenvalues_to_keep > min(cols, rows)):
self.eigenvalues_to_keep = min(cols, rows)
else:
self.eigenvalues_to_keep = int(
self.eigenvalues_to_keep / 100 * min(cols, rows))
# Checking if it is vertical
if rows > cols:
for i in range(3):
self.single_val_array[i] = self.single_val_array[i].T
cols = self.single_val_array[0].shape[1]
rows = self.single_val_array[0].shape[0]
self.rotate = True
self.rgb = []
for j in range(3):
# Calculating A^T * A
A_TA = np.matmul(
self.single_val_array[j].T, self.single_val_array[j])
# Find the eigenvalues and eigenvectors
eigval_ATA, eigvec_ATA = LA.eig(A_TA)
# Conduct Gram schmidt process
eigvec_ATA = self.gram_schmidt(eigvec_ATA.T)
# Sort the values
eigval_ATA, eigvec_ATA = self.same_sort(eigval_ATA, eigvec_ATA)
# initiate the U matrix
U = []
for i in range(rows):
temp = np.matmul(self.single_val_array[j], eigvec_ATA[i])
temp = temp/np.sqrt(eigval_ATA[i])
U.append(temp)
U = np.array(U)
# Find the single values of the Sigma matrix
for x in range(min(cols, rows)):
try:
eigval_ATA[x] = np.sqrt(
eigval_ATA[x]) if eigval_ATA[x] >= 0 else eigval_ATA[x]
except:
pass
# Discard extra eigenvalues if necessary
if(self.eigenvalues_to_keep < min(cols, rows)):
for x in range(min(cols, rows)):
if x > self.eigenvalues_to_keep:
eigval_ATA[x] = 0
# Instantiiate Sigma array
Sigma = np.zeros((rows, cols))
# Create Diagnal Sigma array with single values
for x in range(min(cols, rows)):
Sigma[x][x] = eigval_ATA[x]
# Calculate the final vector matrix
final_image = np.matmul(np.matmul(U.T, Sigma), eigvec_ATA)
final_image = final_image.astype(np.int64)
# Rotate if necessary
if self.rotate:
final_image = final_image.T
self.rgb.append(final_image)
# Create image matrix
self.final = []
for y in range(or_rows):
mid = []
for x in range(or_cols):
mid.append([self.rgb[c][y][x] for c in range(3)])
self.final.append(mid)
# Convert matrix to array
self.final = np.array(self.final)
'''
This function is the main process of the entire compressor class
'''
def process(self):
# The columns and rows for the original shape
or_cols = self.single_val_array.shape[1]
or_rows = self.single_val_array.shape[0]
# columns and rows for the new shape
cols = self.single_val_array.shape[1]
rows = self.single_val_array.shape[0]
if(self.eigenvalues_to_keep > min(cols, rows)):
self.eigenvalues_to_keep = min(cols, rows)
else:
self.eigenvalues_to_keep = int(
self.eigenvalues_to_keep / 100 * min(cols, rows))
# Checking if it is vertical
if rows > cols:
self.single_val_array = self.single_val_array.T
cols = self.single_val_array.shape[1]
rows = self.single_val_array.shape[0]
self.rotate = True
# Calculating A^T * A
A_TA = np.matmul(self.single_val_array.T, self.single_val_array)
# Find the eigenvalues and eigenvectors
eigval_ATA, eigvec_ATA = LA.eig(A_TA)
# Conduct Gram schmidt process
eigvec_ATA = self.gram_schmidt(eigvec_ATA.T)
# Sort the values
eigval_ATA, eigvec_ATA = self.same_sort(eigval_ATA, eigvec_ATA)
# initiate the U matrix
U = []
for i in range(rows):
temp = np.matmul(self.single_val_array, eigvec_ATA[i])
temp = temp/np.sqrt(eigval_ATA[i])
U.append(temp)
U = np.array(U)
# Find the single values of the Sigma matrix
for x in range(min(cols, rows)):
try:
eigval_ATA[x] = np.sqrt(
eigval_ATA[x]) if eigval_ATA[x] >= 0 else eigval_ATA[x]
except:
pass
# Discard extra eigenvalues if necessary
if(self.eigenvalues_to_keep < min(cols, rows)):
for x in range(min(cols, rows)):
if x > self.eigenvalues_to_keep:
eigval_ATA[x] = 0
# Instantiiate Sigma array
Sigma = np.zeros((rows, cols))
# Create Diagnal Sigma array with single values
for x in range(min(cols, rows)):
Sigma[x][x] = eigval_ATA[x]
# Calculate the final vector matrix
final_image = np.matmul(np.matmul(U.T, Sigma), eigvec_ATA)
final_image = final_image.astype(np.int64)
# Rotate if necessary
if self.rotate:
final_image = final_image.T
# Create image matrix
self.final = []
for y in range(or_rows):
mid = []
for x in range(or_cols):
mid.append([final_image[y][x] for c in range(3)])
self.final.append(mid)
# Convert matrix to array
self.final = np.array(self.final)
'''
This function shows the original and the compressed image
'''
def show(self):
# Create 2 subplots, for the original and for the compressed
f, axarr = plt.subplots(2, 1)
f.set_figheight(8)
f.set_figwidth(8)
axarr[0].set_title("Un-Compressed")
axarr[0].imshow(self.image, interpolation='nearest')
axarr[1].set_title("Compressed")
axarr[1].imshow(self.final, interpolation='nearest')
plt.show()
'''
This function begins the process of compression
'''
def start(self):
# Read file
self.image = np.asarray(Image.open(self.image_dir))
# Save the width and the height of the image
width = self.image.shape[0]
height = self.image.shape[1]
if len(self.image.shape) == 2:
self.single_val_array = np.array([[[0 for y in range(height)]
for x in range(width)]for i in range(3)])
for x in range(width):
for y in range(height):
self.single_val_array[x][y] = self.image[x][y]
self.single_val_array = np.array(
self.single_val_array).astype(np.float64)
# Start the process
self.process()
else:
# Instantiate the single value array
self.single_val_array = np.array([[[0 for y in range(height)]
for x in range(width)]for i in range(3)])
# Set each value in the single value array to the average of the 3 RGB values in the image array
for i in range(3):
for x in range(width):
for y in range(height):
self.single_val_array[i][x][y] = self.image[x][y][i]
# convert it into an array
self.single_val_array = np.array(
self.single_val_array).astype(np.float64)
# Start the process
self.process3D()
if __name__ == '__main__':
to_keep = 50
compressor = LinearPress("images/rgb.png", to_keep)
compressor.start()
compressor.show()
print(compressor.final)
im = Image.fromarray(np.uint8(compressor.final))
im.save('../testimages/test.png')