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image-compression
Commit 1e1a4ced authored by Kelly Chang's avatar Kelly Chang
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.ipynb_checkpoints/Encoding_decoding-checkpoint.ipynb
View file @ 1e1a4ced
......@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 12,
"id": "14f74f21",
"metadata": {},
"outputs": [],
......@@ -24,7 +24,7 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 13,
"id": "c16af61f",
"metadata": {},
"outputs": [],
......@@ -33,7 +33,10 @@
" files = os.listdir(dirname)\n",
" scenes = []\n",
" for file in files:\n",
" scenes.append(os.path.join(dirname, file))\n",
" if file == '.DS_Store':\n",
" continue\n",
" else:\n",
" scenes.append(os.path.join(dirname, file))\n",
" return scenes\n",
"\n",
"def image_extractor(scenes):\n",
......@@ -41,16 +44,12 @@
" for scene in scenes:\n",
" files = os.listdir(scene)\n",
" for file in files:\n",
" image_folder.append(os.path.join(scene, file))\n",
" images = []\n",
" for folder in image_folder:\n",
" ims = os.listdir(folder)\n",
" for im in ims:\n",
" if im[-4:] == \".jp4\" or im[-7:] == \"_6.tiff\":\n",
" #if file[-4:] == \".jp4\" or file[-7:] == \"_6.tiff\":\n",
" if file[-5:] != \".tiff\" or file[-7:] == \"_6.tiff\":\n",
" continue\n",
" else:\n",
" images.append(os.path.join(folder, im))\n",
" return images #returns a list of file paths to .tiff files in the specified directory given in file_extractor\n",
" image_folder.append(os.path.join(scene, file))\n",
" return image_folder #returns a list of file paths to .tiff files in the specified directory given in file_extractor\n",
"\n",
"def im_distribution(images, num):\n",
" \"\"\"\n",
......@@ -79,23 +78,39 @@
},
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 14,
"id": "aceba613",
"metadata": {},
"outputs": [],
"source": [
"def plot_hist(tiff_list):\n",
" \"\"\"\n",
" This function is the leftovers from the first attempt to plot histograms.\n",
" As it stands it needs some work in order to function again. We will\n",
" fix this later. 1/25/22\n",
"def predict_pix(tiff_image):\n",
" \"\"\"\n",
" This function predict the pixel values excluding the boundary.\n",
" Using the 4 neighbor pixel values and MSE to predict the next pixel value\n",
" (-1,1) (0,1) (1,1) => relative position of the 4 other given values\n",
" (-1,0) (0,0) => (0,0) is the one we want to predict\n",
" take the derivative of mean square error to solve for the system of equation \n",
" A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])\n",
" 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)\n",
" and the predicted pixel value is c.\n",
" \n",
" Input:\n",
" tiff_image (string): path to the tiff file\n",
" \n",
" image = tiff_list\n",
" image = Image.open(image) #Open the image and read it as an Image object\n",
" Return:\n",
" image (512 X 640): original image \n",
" predict (325380,): predicted image exclude the boundary\n",
" diff. (325380,): difference between the min and max of four neighbors exclude the boundary\n",
" error (325380,): difference between the original image and predicted image\n",
" A (3 X 3): system of equation\n",
" \"\"\"\n",
" image = Image.open(tiff_image) #Open the image and read it as an Image object\n",
" image = np.array(image)[1:,:] #Convert to an array, leaving out the first row because the first row is just housekeeping data\n",
" image = image.astype(int)\n",
" print(image.shape)\n",
" # use \n",
" A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]]) # the matrix for system of equation\n",
" # where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)\n",
" z0 = image[0:-2,0:-2] # get all the first pixel for the entire image\n",
" z1 = image[0:-2,1:-1] # get all the second pixel for the entire image\n",
" z2 = image[0:-2,2::] # get all the third pixel for the entire image\n",
......@@ -106,7 +121,8 @@
" y2 = np.ravel(-z0-z1-z2-z3)\n",
" y = np.vstack((y0,y1,y2))\n",
" # use numpy solver to solve the system of equations all at once\n",
" predict = np.floor(np.linalg.solve(A,y)[-1])\n",
" #predict = np.floor(np.linalg.solve(A,y)[-1])\n",
" predict = np.round(np.round((np.linalg.solve(A,y)[-1]),1))\n",
" # flatten the neighbor pixlels and stack them together\n",
" z0 = np.ravel(z0)\n",
" z1 = np.ravel(z1)\n",
......@@ -115,21 +131,24 @@
" neighbor = np.vstack((z0,z1,z2,z3)).T\n",
" # calculate the difference\n",
" diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)\n",
" # calculate the error\n",
" error = np.ravel(image[1:-1,1:-1])-predict\n",
" \n",
" # flatten the image to a vector\n",
" image = np.ravel(image[1:-1,1:-1])\n",
" error = image-predict\n",
" \n",
" return image, predict, diff, error, A"
" return image, predict, diff, error, A\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"execution_count": 15,
"id": "6b965751",
"metadata": {},
"outputs": [],
"source": [
"\"\"\"\n",
"this huffman coding code is found online\n",
"https://favtutor.com/blogs/huffman-coding\n",
"\"\"\"\n",
"\n",
"class NodeTree(object):\n",
" def __init__(self, left=None, right=None):\n",
" self.left = left\n",
......@@ -173,65 +192,97 @@
},
{
"cell_type": "code",
"execution_count": 5,
"execution_count": 24,
"id": "b7561883",
"metadata": {},
"outputs": [],
"source": [
"def huffman(image):\n",
" origin, predict, diff, error, A = plot_hist(image)\n",
"def huffman(image, num_bins=4):\n",
" \"\"\"\n",
" This function is used to encode the error based on the difference\n",
" and split the difference into different bins\n",
" \n",
" image = Image.open(image)\n",
" image = np.array(image)[1:,:] #Convert to an array, leaving out the first row because the first row is just housekeeping data\n",
" image = image.astype(int)\n",
" Input:\n",
" image (string): path to the tiff file\n",
" num_bins (int): number of bins\n",
" \n",
" boundary = np.hstack((image[0,:],image[-1,:],image[1:-1,0],image[1:-1,-1]))\n",
" boundary = boundary - image[0,0]\n",
" boundary[0] = image[0,0]\n",
"\n",
" string = [str(i) for i in boundary]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode1 = huffman_code_tree(node)\n",
" Return:\n",
" list_dic (num_bins + 1): a list of dictionary\n",
" image (512, 640): original image\n",
" new_error (512, 640): error that includes the boundary\n",
" diff (510, 638): difference of min and max of the 4 neighbors\n",
" boundary (2300,): the boundary values after subtracting the very first pixel value\n",
" predict (325380,): the list of predicted values\n",
" bins (num_bins)\n",
" A (3 X 3): system of equation\n",
" \n",
" \"\"\"\n",
" # get the prediction error and difference\n",
" image, predict, diff, error, A = predict_pix(image)\n",
" \n",
" mask = diff <= 25\n",
" string = [str(i) for i in error[mask].astype(int)]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode2 = huffman_code_tree(node)\n",
"\n",
" # get the number of points in each bins\n",
" data_points_per_bin = len(diff) // num_bins\n",
" \n",
" mask = diff > 25\n",
" new_error = error[mask]\n",
" mask2 = diff[mask] <= 40\n",
" string = [str(i) for i in new_error[mask2].astype(int)]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode3 = huffman_code_tree(node)\n",
" # sort the difference and create the bins\n",
" sorted_diff = diff.copy()\n",
" sorted_diff.sort()\n",
" bins = [sorted_diff[i*data_points_per_bin] for i in range(1,num_bins)]\n",
" \n",
"\n",
" mask = diff > 40\n",
" new_error = error[mask]\n",
" mask2 = diff[mask] <= 70\n",
" string = [str(i) for i in new_error[mask2].astype(int)]\n",
" # get the boundary \n",
" boundary = np.hstack((image[0,:],image[-1,:],image[1:-1,0],image[1:-1,-1]))\n",
" \n",
" # take the difference of the boundary with the very first pixel\n",
" boundary = boundary - image[0,0]\n",
" boundary[0] = image[0,0]\n",
" \n",
" # huffman encode the boundary\n",
" string = [str(i) for i in boundary]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode4 = huffman_code_tree(node)\n",
" encode = huffman_code_tree(node)\n",
" \n",
" # create a list of huffman table\n",
" list_dic = [encode]\n",
" n = len(bins)\n",
" \n",
" mask = diff > 70\n",
" # loop through different bins\n",
" for i in range (0,n):\n",
" # the fisrt bin\n",
" if i == 0 :\n",
" # get the point within the bin and huffman encode\n",
" mask = diff <= bins[i]\n",
" string = [str(i) for i in error[mask].astype(int)]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode = huffman_code_tree(node)\n",
" list_dic.append(encode)\n",
" \n",
" # the middle bins\n",
" else:\n",
" # get the point within the bin and huffman encode\n",
" mask = diff > bins[i-1]\n",
" new_error = error[mask]\n",
" mask2 = diff[mask] <= bins[i]\n",
" string = [str(i) for i in new_error[mask2].astype(int)]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode = huffman_code_tree(node)\n",
" list_dic.append(encode)\n",
" \n",
" # the last bin \n",
" # get the point within the bin and huffman encode\n",
" mask = diff > bins[-1]\n",
" string = [str(i) for i in error[mask].astype(int)]\n",
" freq = dict(Counter(string))\n",
" freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)\n",
" node = make_tree(freq)\n",
" encode5 = huffman_code_tree(node)\n",
"\n",
" encode = huffman_code_tree(node)\n",
" list_dic.append(encode)\n",
"\n",
" # create a error matrix that includes the boundary (used in encoding matrix)\n",
" new_error = np.copy(image)\n",
" new_error[1:-1,1:-1] = np.reshape(error,(510, 638))\n",
" keep = new_error[0,0]\n",
......@@ -241,31 +292,24 @@
" new_error[1:-1,-1] = new_error[1:-1,-1] - keep\n",
" new_error[0,0] = keep\n",
" \n",
" \n",
" #new_error = np.ravel(new_error)\n",
" \n",
" bins = [25,40,70]\n",
" \n",
" diff = np.reshape(diff,(510,638))\n",
" # return the huffman dictionary\n",
" return encode1, encode2, encode3, encode4, encode5, np.ravel(image), error, new_error, diff, boundary, bins\n",
" \n",
"scenes = file_extractor()\n",
"images = image_extractor(scenes)\n",
"encode1, encode2, encode3, encode4, encode5, image, error, new_error, diff, boundary, bins = huffman(images[0])"
" return list_dic, image, new_error, diff, boundary, predict, bins, A\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"execution_count": 17,
"id": "2eb774d2",
"metadata": {},
"outputs": [],
"source": [
"def encoder(error, list_dic, diff, bound, bins):\n",
" # copy the error matrix (including the boundary)\n",
" encoded = np.copy(error).astype(int).astype(str).astype(object)\n",
" \n",
" diff = np.reshape(diff,(510,638))\n",
" \n",
" #diff = np.reshape(diff,(510,638))\n",
" # loop through all the pixel to encode\n",
" for i in range(encoded.shape[0]):\n",
" for j in range(encoded.shape[1]):\n",
" if i == 0 or i == encoded.shape[0]-1 or j == 0 or j == encoded.shape[1]-1:\n",
......@@ -279,85 +323,171 @@
" else: \n",
" encoded[i][j] = list_dic[4][encoded[i][j]]\n",
"\n",
" \n",
" return encoded"
]
},
{
"cell_type": "code",
"execution_count": 7,
"execution_count": 23,
"id": "8eeb40d0",
"metadata": {},
"outputs": [],
"source": [
"def decoder(A, encoded_matrix, encoding_dict):\n",
"def decoder(A, encoded_matrix, list_dic, bins):\n",
" \"\"\"\n",
" Function that accecpts the prediction matrix A for the linear system,\n",
" the encoded matrix of error values, and the encoding dicitonary.\n",
" \"\"\"\n",
" the_keys = list(encode_dict.keys())\n",
" the_values = list(encode_dict.values())\n",
" error_matrix = encoded_matrix.copy()\n",
" # change the dictionary back to list\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
" the_keys0 = list(list_dic[0].keys())\n",
" the_values0 = list(list_dic[0].values())\n",
" \n",
" the_keys1 = list(list_dic[1].keys())\n",
" the_values1 = list(list_dic[1].values())\n",
" \n",
" the_keys2 = list(list_dic[2].keys())\n",
" the_values2 = list(list_dic[2].values())\n",
" \n",
" the_keys3 = list(list_dic[3].keys())\n",
" the_values3 = list(list_dic[3].values())\n",
" \n",
" the_keys4 = list(list_dic[4].keys())\n",
" the_values4 = list(list_dic[4].values())\n",
" \n",
" error_matrix = np.zeros((512,640))\n",
" # loop through all the element in the matrix\n",
" for i in range(error_matrix.shape[0]):\n",
" for j in range(error_matrix.shape[1]):\n",
" # if it's the very first pixel on the image\n",
" if i == 0 and j == 0:\n",
" error_matrix[i][j] = int(the_keys[the_values.index(error_matrix[i,j])])\n",
" \n",
" error_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])])\n",
" # if it's on the boundary\n",
" elif i == 0 or i == error_matrix.shape[0]-1 or j == 0 or j == error_matrix.shape[1]-1:\n",
" error_matrix[i][j] = int(the_keys[the_values.index(error_matrix[i,j])]) + error_matrix[0][0]\n",
" error_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])]) + error_matrix[0][0]\n",
" # if not the boundary\n",
" else:\n",
" \"\"\"z0, z1, z2, z3 = error_matrix[i-1][j-1], error_matrix[i-1][j], \\\n",
" error_matrix[i-1][j+1], error_matrix[i][j-1]\n",
" y = np.vstack((-z0+z2-z3, z0+z1+z2, -z0-z1-z2-z3))\"\"\"\n",
" # predict the image with the known pixel value\n",
" z0 = error_matrix[i-1][j-1]\n",
" z1 = error_matrix[i-1][j]\n",
" z2 = error_matrix[i-1][j+1]\n",
" z3 = error_matrix[i][j-1]\n",
" y0 = int(-z0+z2-z3)\n",
" y1 = int(z0+z1+z2)\n",
" y2 = int(-z0-z1-z2-z3)\n",
" y = np.vstack((y0,y1,y2))\n",
" difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)\n",
" predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))\n",
" \n",
" # add on the difference by searching the dictionary\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
" if difference <= bins[0]:\n",
" error_matrix[i][j] = int(the_keys1[the_values1.index(encoded_matrix[i,j])]) + int(predict)\n",
" elif difference <= bins[1] and difference > bins[0]:\n",
" error_matrix[i][j] = int(the_keys2[the_values2.index(encoded_matrix[i,j])]) + int(predict)\n",
" elif difference <= bins[2] and difference > bins[1]:\n",
" error_matrix[i][j] = int(the_keys3[the_values3.index(encoded_matrix[i,j])]) + int(predict)\n",
" else:\n",
" error_matrix[i][j] = int(the_keys4[the_values4.index(encoded_matrix[i,j])]) + int(predict)\n",
" \n",
" error_matrix[i][j] = int(the_keys[the_values.index(error_matrix[i,j])])\n",
" \n",
" return error_matrix.astype(int)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "3e0e9742",
"execution_count": 19,
"id": "f959fe93",
"metadata": {},
"outputs": [],
"source": [
"encode1, encode2, encode3, encode4, encode5, image, error, new_error, diff, bound, bins = huffman(images[0])\n",
"encoded_matrix = encoder(np.reshape(new_error,(512,640)), [encode1, encode2, encode3, encode4, encode5], diff, bound, bins)\n",
"\n"
"def compress_rate(image, error, diff, bound, list_dic, bins):\n",
" # the bits for the original image\n",
" o_len = 0\n",
" # the bits for the compressed image\n",
" c_len = 0\n",
" # initializing the varible \n",
" im = np.reshape(image,(512, 640))\n",
" real_b = np.hstack((im[0,:],im[-1,:],im[1:-1,0],im[1:-1,-1]))\n",
" original = im[1:-1,1:-1].reshape(-1)\n",
" diff = diff.reshape(-1)\n",
" \n",
" # calculate the bit for boundary\n",
" for i in range(0,len(bound)):\n",
" o_len += len(bin(real_b[i])[2:])\n",
" c_len += len(list_dic[0][str(bound[i])])\n",
" \n",
" # calculate the bit for the pixels inside the boundary\n",
" for i in range(0,len(original)):\n",
" # for the original image\n",
" o_len += len(bin(original[i])[2:])\n",
" \n",
" # check the difference and find the coresponding huffman table\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
" if diff[i] <= bins[0]:\n",
" c_len += len(list_dic[1][str(int(error[i]))])\n",
" \n",
" elif diff[i] <= bins[1] and diff[i] > bins[0]:\n",
" c_len += len(list_dic[2][str(int(error[i]))])\n",
" \n",
" elif diff[i] <= bins[2] and diff[i] > bins[1]:\n",
" c_len += len(list_dic[3][str(int(error[i]))])\n",
"\n",
" else: \n",
" c_len += len(list_dic[5][str(int(error[i]))])\n",
"\n",
" return c_len/o_len"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "3e0e9742",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(512, 640)\n",
"True\n",
"5\n"
]
}
],
"source": [
"scenes = file_extractor()\n",
"images = image_extractor(scenes)\n",
"list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4)\n",
"encoded_matrix = encoder(new_error, list_dic, diff, bound, bins)\n",
"reconstruct_image = decoder(A, encoded_matrix, list_dic, bins)\n",
"print(np.allclose(image, reconstruct_image))\n",
"print(len(list_dic))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e6ea4f99",
"execution_count": 32,
"id": "004e8ba8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[['01100010001' '11000110' '100101010' ... '101110011' '00010100'\n",
" '1111000100']\n",
" ['10011100' '100001' '111000' ... '10111011' '00111' '1111001101']\n",
" ['10101111' '100100' '100000' ... '111100' '111000' '00010100']\n",
" ...\n",
" ['110001000' '100001' '111011' ... '1010010' '100000' '10011000']\n",
" ['0100011101' '111010' '00110' ... '1000101' '1100100' '10011010']\n",
" ['00100010' '110111101' '110110100' ... '00010010' '10100000'\n",
" '110110101']]\n"
"[26, 40, 62]\n"
]
}
],
"source": [
"print(encoded_matrix)"
"\n",
"print(bins)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0c07a23e",
"id": "a282f9e6",
"metadata": {},
"outputs": [],
"source": []
......@@ -379,7 +509,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.11"
"version": "3.9.1"
}
},
"nbformat": 4,
......
Compression_Rate_Kelly.ipynb
View file @ 1e1a4ced
......@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": null,
"execution_count": 1,
"id": "8868bc30",
"metadata": {},
"outputs": [],
......@@ -20,12 +20,13 @@
"import pandas as pd\n",
"from collections import Counter\n",
"import time\n",
"import numpy.linalg as la"
"import numpy.linalg as la\n",
"from scipy.stats import entropy"
]
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 2,
"id": "0f944705",
"metadata": {},
"outputs": [],
......@@ -88,7 +89,7 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 3,
"id": "b18d5e38",
"metadata": {},
"outputs": [],
......@@ -137,7 +138,7 @@
},
{
"cell_type": "code",
"execution_count": 200,
"execution_count": 4,
"id": "3b0c3eaa",
"metadata": {},
"outputs": [],
......@@ -182,7 +183,7 @@
" \n",
" # calculate the difference\n",
" #diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)\n",
" diff = (np.max(neighbor,axis = 1)*5 - np.min(neighbor, axis=1))\n",
" diff = (np.max(neighbor,axis = 1) - np.min(neighbor, axis=1))\n",
" \n",
" # flatten the image to a vector\n",
" #image = np.ravel(image[1:-1,1:-1])\n",
......@@ -200,7 +201,7 @@
},
{
"cell_type": "code",
"execution_count": 152,
"execution_count": 5,
"id": "35d4f6a0",
"metadata": {},
"outputs": [],
......@@ -246,9 +247,92 @@
" return nodes[0][0]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "9200fa53",
"metadata": {},
"outputs": [],
"source": [
"def encoder(error, list_dic, diff, bound, bins):\n",
" encoded = np.copy(error).astype(int).astype(str).astype(object)\n",
" \n",
" diff = np.reshape(diff,(510,638))\n",
" \n",
" for i in range(encoded.shape[0]):\n",
" for j in range(encoded.shape[1]):\n",
" if i == 0 or i == encoded.shape[0]-1 or j == 0 or j == encoded.shape[1]-1:\n",
" encoded[i][j] = list_dic[0][encoded[i][j]]\n",
" elif diff[i-1][j-1] <= bins[0]:\n",
" encoded[i][j] = list_dic[1][encoded[i][j]]\n",
" elif diff[i-1][j-1] <= bins[1] and diff[i-1][j-1] > bins[0]:\n",
" encoded[i][j] = list_dic[2][encoded[i][j]]\n",
" elif diff[i-1][j-1] <= bins[2] and diff[i-1][j-1] > bins[1]:\n",
" encoded[i][j] = list_dic[3][encoded[i][j]]\n",
" else: \n",
" encoded[i][j] = list_dic[4][encoded[i][j]]\n",
"\n",
" \n",
" return encoded\n",
"\n",
"def decoder(A, encoded_matrix, list_dic, bins):\n",
" \"\"\"\n",
" Function that accecpts the prediction matrix A for the linear system,\n",
" the encoded matrix of error values, and the encoding dicitonary.\n",
" \"\"\"\n",
"\n",
" the_keys0 = list(list_dic[0].keys())\n",
" the_values0 = list(list_dic[0].values())\n",
" \n",
" the_keys1 = list(list_dic[1].keys())\n",
" the_values1 = list(list_dic[1].values())\n",
" \n",
" the_keys2 = list(list_dic[2].keys())\n",
" the_values2 = list(list_dic[2].values())\n",
" \n",
" the_keys3 = list(list_dic[3].keys())\n",
" the_values3 = list(list_dic[3].values())\n",
" \n",
" the_keys4 = list(list_dic[4].keys())\n",
" the_values4 = list(list_dic[4].values())\n",
" \n",
" error_matrix = np.zeros((512,640))\n",
" \n",
" for i in range(error_matrix.shape[0]):\n",
" for j in range(error_matrix.shape[1]):\n",
" if i == 0 and j == 0:\n",
" error_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])])\n",
" \n",
" elif i == 0 or i == error_matrix.shape[0]-1 or j == 0 or j == error_matrix.shape[1]-1:\n",
" error_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])]) + error_matrix[0][0]\n",
" else:\n",
" z0 = error_matrix[i-1][j-1]\n",
" z1 = error_matrix[i-1][j]\n",
" z2 = error_matrix[i-1][j+1]\n",
" z3 = error_matrix[i][j-1]\n",
" y0 = int(-z0+z2-z3)\n",
" y1 = int(z0+z1+z2)\n",
" y2 = int(-z0-z1-z2-z3)\n",
" y = np.vstack((y0,y1,y2))\n",
" difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)\n",
" predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))\n",
"\n",
" if difference <= bins[0]:\n",
" error_matrix[i][j] = int(the_keys1[the_values1.index(encoded_matrix[i,j])]) + int(predict)\n",
" elif difference <= bins[1] and difference > bins[0]:\n",
" error_matrix[i][j] = int(the_keys2[the_values2.index(encoded_matrix[i,j])]) + int(predict)\n",
" elif difference <= bins[2] and difference > bins[1]:\n",
" error_matrix[i][j] = int(the_keys3[the_values3.index(encoded_matrix[i,j])]) + int(predict)\n",
" else:\n",
" error_matrix[i][j] = int(the_keys4[the_values4.index(encoded_matrix[i,j])]) + int(predict)\n",
" \n",
" \n",
" return error_matrix.astype(int)"
]
},
{
"cell_type": "markdown",
"id": "25abd477",
"id": "ca9c0b4a",
"metadata": {},
"source": [
"## use res"
......@@ -256,7 +340,7 @@
},
{
"cell_type": "code",
"execution_count": 154,
"execution_count": 7,
"id": "bd7e39d7",
"metadata": {},
"outputs": [],
......@@ -436,29 +520,206 @@
},
{
"cell_type": "code",
"execution_count": null,
"id": "1b2e63e2",
"execution_count": 10,
"id": "d0a6fac2",
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[8, 32, 88, 181, 383]\n",
"7\n"
]
}
],
"source": [
"scenes = file_extractor()\n",
"images = image_extractor(scenes)\n",
"rate = []\n",
"A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])\n",
"for i in range(len(images)):\n",
" list_dic, image, error, new_error, diff, bound, predict, bins, res = huffman(images[i], 6, True)\n",
" r = compress_rate(image, error, diff, bound, list_dic, bins, res, use_res = True)\n",
" rate.append(r)\n"
"list_dic, image, error, new_error, diff, bound, predict, bins, res = huffman(images[0], 6, True)\n",
"print(bins)\n",
"print(len(list_dic))"
]
},
{
"cell_type": "code",
"execution_count": 232,
"id": "2723b062",
"metadata": {},
"outputs": [],
"source": [
"def rel_freq(x):\n",
" freqs = [x.count(value) / len(x) for value in set(x)] \n",
" return freqs"
]
},
{
"cell_type": "code",
"execution_count": 234,
"id": "e9799985",
"metadata": {},
"outputs": [],
"source": [
"list_diff = list(set(diff))\n",
"en = []\n",
"for i in list_diff:\n",
" mask = diff == i\n",
" list_error = list(error[mask])\n",
" fre = rel_freq(list_error)\n",
" \n",
" en.append(entropy(fre))"
]
},
{
"cell_type": "code",
"execution_count": 249,
"id": "78a370f7",
"metadata": {},
"outputs": [],
"source": [
"list_error = list(error)\n",
"ob = rel_freq(list_error)"
]
},
{
"cell_type": "code",
"execution_count": 271,
"id": "21ba29a6",
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"n = len(bins)\n",
"for i in range (0,n):\n",
" if i == 0 :\n",
" mask = diff <= bins[i]\n",
" list_error = list(error[mask])\n",
" fre = rel_freq(list_error)\n",
" en.append(entropy(fre))\n",
" else:\n",
" mask = diff > bins[i-1]\n",
" error2 = error[mask]\n",
" mask2 = diff[mask] <= bins[i]\n",
" list_error = list(error2[mask2])\n",
" fre = rel_freq(list_error)\n",
" en.append(entropy(fre))\n",
"\n",
"mask = diff > bins[i]\n",
"list_error = list(error[mask])\n",
"fre = rel_freq(list_error)\n",
"en.append(entropy(fre))"
]
},
{
"cell_type": "code",
"execution_count": 272,
"id": "32a94ee7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.2688193009259807\n",
"0.21792128672839872\n"
]
}
],
"source": [
"print(np.mean(en))\n",
"print(np.mean(en)/15)"
]
},
{
"cell_type": "code",
"execution_count": 258,
"id": "51268478",
"metadata": {},
"outputs": [],
"source": [
"uni = np.unique(diff)\n",
"uni_n = len(np.unique(diff))\n",
"en = []\n",
"for i in range(uni_n):\n",
" mask = diff == uni[i]\n",
" mask_error = error[mask]\n",
" en.append(entropy(rel_freq(list(mask_error))))"
]
},
{
"cell_type": "code",
"execution_count": 266,
"id": "2d3238cb",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.2532721868611105\n",
"6.715361332207255\n",
"15\n"
]
}
],
"source": [
"imm = np.ravel(image.reshape(512,640)[1:-1,1:-1])\n",
"print(np.mean(en))\n",
"print(entropy(rel_freq(list(imm))))\n",
"print(len(bin(imm[0])[2:]))"
]
},
{
"cell_type": "code",
"execution_count": 269,
"id": "811f8139",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.44766666666666666"
]
},
"execution_count": 269,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"6.715/15"
]
},
{
"cell_type": "code",
"execution_count": 270,
"id": "6470dfff",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.21666666666666667"
]
},
"execution_count": 270,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"3.25/15"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c2eaf807",
"id": "7a05f000",
"metadata": {},
"outputs": [],
"source": [
"print(f\"Compression rate of huffman with different bins in res: {np.mean(rate)}\")"
"## test compression rate and time"
]
},
{
......@@ -566,7 +827,7 @@
{
"cell_type": "code",
"execution_count": 94,
"id": "7d1985a4",
"id": "9d5f9f50",
"metadata": {},
"outputs": [],
"source": [
......@@ -591,7 +852,7 @@
{
"cell_type": "code",
"execution_count": 97,
"id": "b898324e",
"id": "bceeee73",
"metadata": {},
"outputs": [
{
......@@ -615,7 +876,7 @@
{
"cell_type": "code",
"execution_count": 102,
"id": "45b75db7",
"id": "5b02b4a3",
"metadata": {},
"outputs": [
{
......@@ -637,10 +898,29 @@
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 155,
"id": "2253908b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[46 26 8 ... 13 16 34]\n"
]
}
],
"source": [
"list_dic, image, error, new_error, diff, bound, predict, bins, res = huffman(images[22], 6, False)\n",
"r = compress_rate(image, error, diff, bound, list_dic, bins, res, False)"
]
},
{
"cell_type": "code",
"execution_count": 108,
"id": "55251c97",
"id": "88ed2a4e",
"metadata": {},
"outputs": [
{
......@@ -673,7 +953,7 @@
{
"cell_type": "code",
"execution_count": 109,
"id": "92d3ae31",
"id": "b0a58386",
"metadata": {},
"outputs": [],
"source": [
......@@ -684,7 +964,7 @@
{
"cell_type": "code",
"execution_count": 110,
"id": "4abd8b82",
"id": "1a913350",
"metadata": {},
"outputs": [
{
......@@ -719,7 +999,7 @@
{
"cell_type": "code",
"execution_count": 111,
"id": "07bb76a7",
"id": "6e9bc2e7",
"metadata": {},
"outputs": [
{
......@@ -734,10 +1014,31 @@
"print(slope,intercept)"
]
},
{
"cell_type": "code",
"execution_count": 100,
"id": "8ccd4336",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([315196, 495220, 360208, ..., 748984, 340447, 885631])"
]
},
"execution_count": 100,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new"
]
},
{
"cell_type": "code",
"execution_count": 113,
"id": "fca0420b",
"id": "689f98c0",
"metadata": {},
"outputs": [
{
......@@ -770,7 +1071,7 @@
{
"cell_type": "code",
"execution_count": 197,
"id": "70285459",
"id": "b08d924b",
"metadata": {},
"outputs": [
{
......@@ -794,7 +1095,7 @@
{
"cell_type": "code",
"execution_count": 195,
"id": "21b94965",
"id": "98c47af2",
"metadata": {},
"outputs": [
{
......@@ -815,7 +1116,7 @@
{
"cell_type": "code",
"execution_count": 196,
"id": "68eb383d",
"id": "3c37a08f",
"metadata": {},
"outputs": [
{
......@@ -833,7 +1134,7 @@
{
"cell_type": "code",
"execution_count": null,
"id": "3fdebf92",
"id": "3ca79c1f",
"metadata": {},
"outputs": [],
"source": []
......
Encoding_decoding.ipynb
View file @ 1e1a4ced
......@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 63,
"execution_count": 12,
"id": "14f74f21",
"metadata": {},
"outputs": [],
......@@ -24,7 +24,7 @@
},
{
"cell_type": "code",
"execution_count": 64,
"execution_count": 13,
"id": "c16af61f",
"metadata": {},
"outputs": [],
......@@ -78,23 +78,39 @@
},
{
"cell_type": "code",
"execution_count": 65,
"execution_count": 14,
"id": "aceba613",
"metadata": {},
"outputs": [],
"source": [
"def plot_hist(tiff_list):\n",
" \"\"\"\n",
" This function is the leftovers from the first attempt to plot histograms.\n",
" As it stands it needs some work in order to function again. We will\n",
" fix this later. 1/25/22\n",
"def predict_pix(tiff_image):\n",
" \"\"\"\n",
" This function predict the pixel values excluding the boundary.\n",
" Using the 4 neighbor pixel values and MSE to predict the next pixel value\n",
" (-1,1) (0,1) (1,1) => relative position of the 4 other given values\n",
" (-1,0) (0,0) => (0,0) is the one we want to predict\n",
" take the derivative of mean square error to solve for the system of equation \n",
" A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])\n",
" 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)\n",
" and the predicted pixel value is c.\n",
" \n",
" Input:\n",
" tiff_image (string): path to the tiff file\n",
" \n",
" image = tiff_list\n",
" image = Image.open(image) #Open the image and read it as an Image object\n",
" Return:\n",
" image (512 X 640): original image \n",
" predict (325380,): predicted image exclude the boundary\n",
" diff. (325380,): difference between the min and max of four neighbors exclude the boundary\n",
" error (325380,): difference between the original image and predicted image\n",
" A (3 X 3): system of equation\n",
" \"\"\"\n",
" image = Image.open(tiff_image) #Open the image and read it as an Image object\n",
" image = np.array(image)[1:,:] #Convert to an array, leaving out the first row because the first row is just housekeeping data\n",
" image = image.astype(int)\n",
" print(image.shape)\n",
" # use \n",
" A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]]) # the matrix for system of equation\n",
" # where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)\n",
" z0 = image[0:-2,0:-2] # get all the first pixel for the entire image\n",
" z1 = image[0:-2,1:-1] # get all the second pixel for the entire image\n",
" z2 = image[0:-2,2::] # get all the third pixel for the entire image\n",
......@@ -118,16 +134,21 @@
" # calculate the error\n",
" error = np.ravel(image[1:-1,1:-1])-predict\n",
" \n",
" return image, predict, diff, error, A"
" return image, predict, diff, error, A\n"
]
},
{
"cell_type": "code",
"execution_count": 66,
"execution_count": 15,
"id": "6b965751",
"metadata": {},
"outputs": [],
"source": [
"\"\"\"\n",
"this huffman coding code is found online\n",
"https://favtutor.com/blogs/huffman-coding\n",
"\"\"\"\n",
"\n",
"class NodeTree(object):\n",
" def __init__(self, left=None, right=None):\n",
" self.left = left\n",
......@@ -171,14 +192,33 @@
},
{
"cell_type": "code",
"execution_count": 67,
"execution_count": 24,
"id": "b7561883",
"metadata": {},
"outputs": [],
"source": [
"def huffman(image, num_bins):\n",
"def huffman(image, num_bins=4):\n",
" \"\"\"\n",
" This function is used to encode the error based on the difference\n",
" and split the difference into different bins\n",
" \n",
" Input:\n",
" image (string): path to the tiff file\n",
" num_bins (int): number of bins\n",
" \n",
" Return:\n",
" list_dic (num_bins + 1): a list of dictionary\n",
" image (512, 640): original image\n",
" new_error (512, 640): error that includes the boundary\n",
" diff (510, 638): difference of min and max of the 4 neighbors\n",
" boundary (2300,): the boundary values after subtracting the very first pixel value\n",
" predict (325380,): the list of predicted values\n",
" bins (num_bins)\n",
" A (3 X 3): system of equation\n",
" \n",
" \"\"\"\n",
" # get the prediction error and difference\n",
" image, predict, diff, error, A = plot_hist(image)\n",
" image, predict, diff, error, A = predict_pix(image)\n",
" \n",
" # get the number of points in each bins\n",
" data_points_per_bin = len(diff) // num_bins\n",
......@@ -252,14 +292,15 @@
" new_error[1:-1,-1] = new_error[1:-1,-1] - keep\n",
" new_error[0,0] = keep\n",
" \n",
" diff = np.reshape(diff,(510,638))\n",
" # return the huffman dictionary\n",
" return list_dic, np.ravel(image), error, new_error, diff, boundary, predict, bins\n",
" return list_dic, image, new_error, diff, boundary, predict, bins, A\n",
" \n"
]
},
{
"cell_type": "code",
"execution_count": 68,
"execution_count": 17,
"id": "2eb774d2",
"metadata": {},
"outputs": [],
......@@ -267,7 +308,7 @@
"def encoder(error, list_dic, diff, bound, bins):\n",
" # copy the error matrix (including the boundary)\n",
" encoded = np.copy(error).astype(int).astype(str).astype(object)\n",
" diff = np.reshape(diff,(510,638))\n",
" #diff = np.reshape(diff,(510,638))\n",
" # loop through all the pixel to encode\n",
" for i in range(encoded.shape[0]):\n",
" for j in range(encoded.shape[1]):\n",
......@@ -287,7 +328,7 @@
},
{
"cell_type": "code",
"execution_count": 69,
"execution_count": 23,
"id": "8eeb40d0",
"metadata": {},
"outputs": [],
......@@ -298,6 +339,7 @@
" the encoded matrix of error values, and the encoding dicitonary.\n",
" \"\"\"\n",
" # change the dictionary back to list\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
" the_keys0 = list(list_dic[0].keys())\n",
" the_values0 = list(list_dic[0].values())\n",
" \n",
......@@ -338,6 +380,7 @@
" predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))\n",
" \n",
" # add on the difference by searching the dictionary\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
" if difference <= bins[0]:\n",
" error_matrix[i][j] = int(the_keys1[the_values1.index(encoded_matrix[i,j])]) + int(predict)\n",
" elif difference <= bins[1] and difference > bins[0]:\n",
......@@ -353,7 +396,7 @@
},
{
"cell_type": "code",
"execution_count": 70,
"execution_count": 19,
"id": "f959fe93",
"metadata": {},
"outputs": [],
......@@ -380,6 +423,7 @@
" o_len += len(bin(original[i])[2:])\n",
" \n",
" # check the difference and find the coresponding huffman table\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
" if diff[i] <= bins[0]:\n",
" c_len += len(list_dic[1][str(int(error[i]))])\n",
" \n",
......@@ -397,65 +441,53 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 25,
"id": "3e0e9742",
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(512, 640)\n",
"True\n",
"5\n"
]
}
],
"source": [
"scenes = file_extractor()\n",
"images = image_extractor(scenes)\n",
"#bins = [25,40,70]\n",
"A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])\n",
"list_dic, image, error, new_error, diff, bound, predict, bins = huffman(images[0], 4)\n",
"encoded_matrix = encoder(np.reshape(new_error,(512,640)), list_dic, diff, bound, bins)\n",
"list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4)\n",
"encoded_matrix = encoder(new_error, list_dic, diff, bound, bins)\n",
"reconstruct_image = decoder(A, encoded_matrix, list_dic, bins)\n",
"print(np.allclose(image.reshape(512,640), reconstruct_image))\n",
"print(np.allclose(image, reconstruct_image))\n",
"print(len(list_dic))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f0948ab2",
"metadata": {},
"outputs": [],
"source": [
"rate1 = []\n",
"rate2 = []\n",
"rate3 = []\n",
"bins1 = [25,40,70]\n",
"bins2 = [50,100,150]\n",
"bins3 = [30,50,100]\n",
"B = [bins1, bins2, bins3]\n",
"for i in range(len(images)):\n",
" for j, bins in enumerate(B):\n",
" list_dic, image, error, new_error, diff, bound, predict = huffman(images[i], bins)\n",
" r = compress_rate(image, error, diff, bound, list_dic, bins)\n",
" if j == 0:\n",
" rate1.append(r)\n",
" elif j == 1:\n",
" rate2.append(r)\n",
" else:\n",
" rate3.append(r)\n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7d615dcd",
"execution_count": 32,
"id": "004e8ba8",
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[26, 40, 62]\n"
]
}
],
"source": [
"print(f\"Compression rate of huffman with bins {bins1}: {np.mean(rate1)}\")\n",
"print(f\"Compression rate of huffman with bins {bins2}: {np.mean(rate2)}\")\n",
"print(f\"Compression rate of huffman with bins {bins3}: {np.mean(rate3)}\")\n"
"\n",
"print(bins)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "67cb360d",
"id": "a282f9e6",
"metadata": {},
"outputs": [],
"source": []
......
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