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image-compression
Commit e4fa4e0f authored by Bryce Hepner's avatar Bryce Hepner
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just had to walk back one thing

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BryceCheckpoint.py 0 → 100644
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# %%
import numpy as np
from matplotlib import pyplot as plt
from itertools import product
import os
import sys
from PIL import Image
from scipy.optimize import minimize,linprog
import time
import seaborn as sns
from sklearn.neighbors import KernelDensity
import pandas as pd
from collections import Counter
import time
import numpy.linalg as la
# %%
def file_extractor(dirname="images"):
files = os.listdir(dirname)
scenes = []
for file in files:
if file == '.DS_Store':
continue
else:
scenes.append(os.path.join(dirname, file))
return scenes
def image_extractor(scenes):
image_folder = []
for scene in scenes:
files = os.listdir(scene)
for file in files:
if file[-5:] != ".tiff" or file[-7:] == "_6.tiff":
continue
else:
image_folder.append(os.path.join(scene, file))
return image_folder #returns a list of file paths to .tiff files in the specified directory given in file_extractor
def im_distribution(images, num):
"""
Function that extracts tiff files from specific cameras and returns a list of all
the tiff files corresponding to that camera. i.e. all pictures labeled "_7.tiff" or otherwise
specified camera numbers.
Parameters:
images (list): list of all tiff files, regardless of classification. This is NOT a list of directories but
of specific tiff files that can be opened right away. This is the list that we iterate through and
divide.
num (str): a string designation for the camera number that we want to extract i.e. "14" for double digits
of "_1" for single digits.
Returns:
tiff (list): A list of tiff files that have the specified designation from num. They are the files extracted
from the 'images' list that correspond to the given num.
"""
tiff = []
for im in images:
if im[-7:-5] == num:
tiff.append(im)
return tiff
# %%
def predict_pix(tiff_image_path, difference = True):
"""
This function predict the pixel values excluding the boundary.
Using the 4 neighbor pixel values and MSE to predict the next pixel value
(-1,1) (0,1) (1,1) => relative position of the 4 other given values
(-1,0) (0,0) => (0,0) is the one we want to predict
take the derivative of mean square error to solve for the system of equation
A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])
A @ [a, b, c] = [-z0+z2-z3, z0+z1+z2, -z0-z1-z2-z3] where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)
and the predicted pixel value is c.
Input:
tiff_image_path (string): path to the tiff file
Return:
image ndarray(512 X 640): original image
predict ndarray(325380,): predicted image excluding the boundary
diff. ndarray(325380,): IF difference = TRUE, difference between the min and max of four neighbors exclude the boundary
ELSE: the residuals of the four nearest pixels to a fitted hyperplane
error ndarray(325380,): difference between the original image and predicted image
A ndarray(3 X 3): system of equation
"""
image_obj = Image.open(tiff_image_path) #Open the image and read it as an Image object
image_array = np.array(image_obj)[1:,:].astype(int) #Convert to an array, leaving out the first row because the first row is just housekeeping data
# image_array = image_array.astype(int)
A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]]) # the matrix for system of equation
# where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)
z0 = image_array[0:-2,0:-2] # get all the first pixel for the entire image
z1 = image_array[0:-2,1:-1] # get all the second pixel for the entire image
z2 = image_array[0:-2,2::] # get all the third pixel for the entire image
z3 = image_array[1:-1,0:-2] # get all the forth pixel for the entire image
# calculate the out put of the system of equation
y0 = np.ravel(-z0+z2-z3)
y1 = np.ravel(z0+z1+z2)
y2 = np.ravel(-z0-z1-z2-z3)
y = np.vstack((y0,y1,y2))
# use numpy solver to solve the system of equations all at once
#predict = np.floor(np.linalg.solve(A,y)[-1])
predict = np.round(np.round((np.linalg.solve(A,y)[-1]),1))
#Matrix system of points that will be used to solve the least squares fitting hyperplane
points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])
# flatten the neighbor pixlels and stack them together
z0 = np.ravel(z0)
z1 = np.ravel(z1)
z2 = np.ravel(z2)
z3 = np.ravel(z3)
neighbor = np.vstack((z0,z1,z2,z3)).T
if difference:
# calculate the difference
diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)
else:
#Compute the best fitting hyperplane using least squares
#The res is the residuals of the four points used to fit the hyperplane (summed distance of each of the
#points to the hyperplane), it is a measure of gradient
f, diff, rank, s = la.lstsq(points, neighbor.T, rcond=None)
diff = diff.astype(int)
# calculate the error
error = np.ravel(image_array[1:-1,1:-1])-predict
return image_array, predict, diff, error, A
# %%
"""
this huffman encoding code is found online
https://favtutor.com/blogs/huffman-coding
"""
class NodeTree(object):
def __init__(self, left=None, right=None):
self.left = left
self.right = right
def children(self):
return self.left, self.right
def __str__(self):
return self.left, self.right
def huffman_code_tree(node, binString=''):
'''
Function to find Huffman Code
'''
if type(node) is str:
return {node: binString}
(l, r) = node.children()
d = dict()
d.update(huffman_code_tree(l, binString + '0'))
d.update(huffman_code_tree(r, binString + '1'))
return d
def make_tree(nodes):
'''
Function to make tree
:param nodes: Nodes
:return: Root of the tree
'''
while len(nodes) > 1:
(key1, c1) = nodes[-1]
(key2, c2) = nodes[-2]
nodes = nodes[:-2]
node = NodeTree(key1, key2)
nodes.append((node, c1 + c2))
#reverse True, decending order
sorted_nodes = sorted(nodes, key=lambda x: x[1], reverse=True)
return sorted_nodes[0][0]
# %%
def huffman(tiff_image_path, num_bins=4, difference = True):
"""
This function is used to encode the error based on the difference
and split the difference into different bins
Input:
tiff_image_path (string): path to the tiff file
num_bins (int): number of bins
Return:
list_dic list (num_bins + 1): a list of dictionary
image_array array (512, 640): original image
new_error array (512, 640): error that includes the boundary
diff array (510, 638): difference of min and max of the 4 neighbors
boundary (2300,): the boundary values after subtracting the very first pixel value
predict (325380,): the list of predicted values
bins (num_bins - 1,): a list of threshold to cut the bins
A (3 X 3): system of equation
"""
# get the image_array, etc
image_array, predict, diff, error, A = predict_pix(tiff_image_path, difference)
# calculate the number of points that will go in each bin
data_points_per_bin = diff.size // num_bins
# sort the difference and create the bins
sorted_diff = np.sort(diff.copy())
bins = [sorted_diff[i*data_points_per_bin] for i in range(1,num_bins)]
# get the boundary
boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))
# take the difference of the boundary with the very first pixel
boundary = boundary - image_array[0,0]
#boundary is 1dim, so boundary[0] is just the first element
boundary[0] = image_array[0,0]
# huffman encode the boundary
bound_vals_as_string = [str(i) for i in boundary]
freq = dict(Counter(bound_vals_as_string))
freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
node = make_tree(freq)
huffman_encoding_dict = huffman_code_tree(node)
# create a list of huffman table
huffman_encoding_list = [huffman_encoding_dict]
n = len(bins)
# loop through different bins
for i in range (0,n):
# the first bin
if i == 0 :
# get the point within the bin and huffman huffman_encoding_dict
mask = diff <= bins[i]
line_as_string = [str(i) for i in error[mask].astype(int)]
freq = dict(Counter(line_as_string))
freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
node = make_tree(freq)
huffman_encoding_dict = huffman_code_tree(node)
huffman_encoding_list.append(huffman_encoding_dict)
# the middle bins
else:
# get the point within the bin and huffman huffman_encoding_dict
mask = diff > bins[i-1]
new_error = error[mask]
mask2 = diff[mask] <= bins[i]
line_as_string = [str(i) for i in new_error[mask2].astype(int)]
freq = dict(Counter(line_as_string))
freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
node = make_tree(freq)
huffman_encoding_dict = huffman_code_tree(node)
huffman_encoding_list.append(huffman_encoding_dict)
# the last bin
# get the point within the bin and huffman huffman_encoding_dict
mask = diff > bins[-1]
line_as_string = [str(i) for i in error[mask].astype(int)]
freq = dict(Counter(line_as_string))
freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)
node = make_tree(freq)
huffman_encoding_dict = huffman_code_tree(node)
huffman_encoding_list.append(huffman_encoding_dict)
# create a error matrix that includes the boundary (used in encoding matrix)
new_error = np.copy(image_array)
new_error[1:-1,1:-1] = np.reshape(error,(510, 638))
keep = new_error[0,0]
new_error[0,:] = new_error[0,:] - keep
new_error[-1,:] = new_error[-1,:] - keep
new_error[1:-1,0] = new_error[1:-1,0] - keep
new_error[1:-1,-1] = new_error[1:-1,-1] - keep
new_error[0,0] = keep
diff = np.reshape(diff,(510,638))
# return the huffman dictionary
return huffman_encoding_list, image_array, new_error, diff, boundary, predict, bins, A
# %%
def encoder(error, list_dic, diff, bound, bins):
"""
This function encode the matrix with huffman coding tables
Input:
error (512, 640): a matrix with all the errors
list_dic (num_dic + 1,): a list of huffman coding table
bound (2300,): the boundary values after subtracting the very first pixel value
bins (num_bins - 1,): a list of threshold to cut the bins
Return:
encoded (512, 640): encoded matrix
"""
# copy the error matrix (including the boundary)
encoded = np.copy(error).astype(int).astype(str).astype(object)
#diff = np.reshape(diff,(510,638))
# loop through all the pixel to encode
for i in range(encoded.shape[0]):
for j in range(encoded.shape[1]):
if i == 0 or i == encoded.shape[0]-1 or j == 0 or j == encoded.shape[1]-1:
encoded[i][j] = list_dic[0][encoded[i][j]]
elif diff[i-1][j-1] <= bins[0]:
encoded[i][j] = list_dic[1][encoded[i][j]]
elif diff[i-1][j-1] <= bins[1] and diff[i-1][j-1] > bins[0]:
encoded[i][j] = list_dic[2][encoded[i][j]]
elif diff[i-1][j-1] <= bins[2] and diff[i-1][j-1] > bins[1]:
encoded[i][j] = list_dic[3][encoded[i][j]]
else:
encoded[i][j] = list_dic[4][encoded[i][j]]
return encoded
# %%
def decoder(A, encoded_matrix, list_dic, bins, use_diff):
"""
This function decodes the encoded_matrix.
Input:
A (3 X 3): system of equation
list_dic (num_dic + 1,): a list of huffman coding table
encoded_matrix (512, 640): encoded matrix
bins (num_bins - 1,): a list of threshold to cut the bins
Return:
decode_matrix (512, 640): decoded matrix
"""
# change the dictionary back to list
# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins
the_keys0 = list(list_dic[0].keys())
the_values0 = list(list_dic[0].values())
the_keys1 = list(list_dic[1].keys())
the_values1 = list(list_dic[1].values())
the_keys2 = list(list_dic[2].keys())
the_values2 = list(list_dic[2].values())
the_keys3 = list(list_dic[3].keys())
the_values3 = list(list_dic[3].values())
the_keys4 = list(list_dic[4].keys())
the_values4 = list(list_dic[4].values())
#Matrix system of points that will be used to solve the least squares fitting hyperplane
points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])
decode_matrix = np.zeros((512,640))
# loop through all the element in the matrix
for i in range(decode_matrix.shape[0]):
for j in range(decode_matrix.shape[1]):
# if it's the very first pixel on the image
if i == 0 and j == 0:
decode_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])])
# if it's on the boundary
elif i == 0 or i == decode_matrix.shape[0]-1 or j == 0 or j == decode_matrix.shape[1]-1:
decode_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])]) + decode_matrix[0][0]
# if not the boundary
else:
# predict the image with the known pixel value
z0 = decode_matrix[i-1][j-1]
z1 = decode_matrix[i-1][j]
z2 = decode_matrix[i-1][j+1]
z3 = decode_matrix[i][j-1]
y0 = int(-z0+z2-z3)
y1 = int(z0+z1+z2)
y2 = int(-z0-z1-z2-z3)
y = np.vstack((y0,y1,y2))
if use_diff:
difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)
else:
f, difference, rank, s = la.lstsq(points, [z0,z1,z2,z3], rcond=None)
difference = difference.astype(int)
predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))
# add on the difference by searching the dictionary
# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins
if difference <= bins[0]:
decode_matrix[i][j] = int(the_keys1[the_values1.index(encoded_matrix[i,j])]) + int(predict)
elif difference <= bins[1] and difference > bins[0]:
decode_matrix[i][j] = int(the_keys2[the_values2.index(encoded_matrix[i,j])]) + int(predict)
elif difference <= bins[2] and difference > bins[1]:
decode_matrix[i][j] = int(the_keys3[the_values3.index(encoded_matrix[i,j])]) + int(predict)
else:
decode_matrix[i][j] = int(the_keys4[the_values4.index(encoded_matrix[i,j])]) + int(predict)
return decode_matrix.astype(int)
# %%
def compress_rate(image, new_error, diff, bound, list_dic, bins):
'''
This function is used to calculate the compression rate.
Input:
image (512, 640): original image
new_error (512, 640): error that includes the boundary
diff (510, 638): difference of min and max of the 4 neighbors
bound (2300,): the boundary values after subtracting the very first pixel value
list_dic (num_dic + 1,): a list of huffman coding table
bins (num_bins - 1,): a list of threshold to cut the bins
Return:
compression rate
'''
# the bits for the original image
o_len = 0
# the bits for the compressed image
c_len = 0
# initializing the varible
im = np.reshape(image,(512, 640))
real_b = np.hstack((image[0,:],image[-1,:],image[1:-1,0],image[1:-1,-1]))
original = image[1:-1,1:-1].reshape(-1)
diff = diff.reshape(-1)
error = new_error[1:-1,1:-1].reshape(-1)
# calculate the bit for boundary
for i in range(0,len(bound)):
o_len += len(bin(real_b[i])[2:])
c_len += len(list_dic[0][str(bound[i])])
# calculate the bit for the pixels inside the boundary
for i in range(0,len(original)):
# for the original image
o_len += len(bin(original[i])[2:])
# check the difference and find the coresponding huffman table
# !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins
if diff[i] <= bins[0]:
c_len += len(list_dic[1][str(int(error[i]))])
elif diff[i] <= bins[1] and diff[i] > bins[0]:
c_len += len(list_dic[2][str(int(error[i]))])
elif diff[i] <= bins[2] and diff[i] > bins[1]:
c_len += len(list_dic[3][str(int(error[i]))])
else:
c_len += len(list_dic[4][str(int(error[i]))])
return c_len/o_len
# %%
scenes = file_extractor()
images = image_extractor(scenes)
list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4, False)
encoded_matrix = encoder(new_error, list_dic, diff, bound, bins)
reconstruct_image = decoder(A, encoded_matrix, list_dic, bins, False)
print(np.allclose(image, reconstruct_image))
print(len(list_dic))
# %%
compress_rate(image, new_error, diff, bound, list_dic, bins)
# %%
print(sys.getsizeof(encoded_matrix))
print(sys.getsizeof(reconstruct_image))
# %%
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