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image-compression
Commit 2659c0f6 authored by Kelly Chang's avatar Kelly Chang
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.DS_Store
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.ipynb_checkpoints/Encoding_decoding-checkpoint.ipynb
View file @ 2659c0f6
......@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 12,
"execution_count": 59,
"id": "14f74f21",
"metadata": {},
"outputs": [],
......@@ -19,12 +19,13 @@
"from sklearn.neighbors import KernelDensity\n",
"import pandas as pd\n",
"from collections import Counter\n",
"import time"
"import time\n",
"import numpy.linalg as la"
]
},
{
"cell_type": "code",
"execution_count": 13,
"execution_count": 49,
"id": "c16af61f",
"metadata": {},
"outputs": [],
......@@ -78,12 +79,12 @@
},
{
"cell_type": "code",
"execution_count": 14,
"id": "aceba613",
"execution_count": 61,
"id": "8172fa41",
"metadata": {},
"outputs": [],
"source": [
"def predict_pix(tiff_image):\n",
"def predict_pix(tiff_image, difference = True):\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",
......@@ -99,16 +100,15 @@
" \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",
" predict (325380,): predicted image excluding the boundary\n",
" diff. (325380,): IF difference = TRUE, difference between the min and max of four neighbors exclude the boundary\n",
" ELSE: the residuals of the four nearest pixels to a fitted hyperplane\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",
" image = image.astype(int) \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",
......@@ -123,23 +123,37 @@
" # 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.round(np.round((np.linalg.solve(A,y)[-1]),1))\n",
" \n",
" #Matrix system of points that will be used to solve the least squares fitting hyperplane\n",
" points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])\n",
" \n",
" # flatten the neighbor pixlels and stack them together\n",
" z0 = np.ravel(z0)\n",
" z1 = np.ravel(z1)\n",
" z2 = np.ravel(z2)\n",
" z3 = np.ravel(z3)\n",
" neighbor = np.vstack((z0,z1,z2,z3)).T\n",
" \n",
" if difference:\n",
" # calculate the difference\n",
" diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)\n",
" \n",
" else:\n",
" #Compute the best fitting hyperplane using least squares\n",
" #The res is the residuals of the four points used to fit the hyperplane (summed distance of each of the \n",
" #points to the hyperplane), it is a measure of gradient\n",
" f, diff, rank, s = la.lstsq(points, neighbor.T, rcond=None) \n",
" diff = diff.astype(int)\n",
" \n",
" # calculate the error\n",
" error = np.ravel(image[1:-1,1:-1])-predict\n",
" \n",
" return image, predict, diff, error, A\n"
" return image, predict, diff, error, A"
]
},
{
"cell_type": "code",
"execution_count": 15,
"execution_count": 62,
"id": "6b965751",
"metadata": {},
"outputs": [],
......@@ -192,12 +206,12 @@
},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": 63,
"id": "b7561883",
"metadata": {},
"outputs": [],
"source": [
"def huffman(image, num_bins=4):\n",
"def huffman(image, num_bins=4, difference = True):\n",
" \"\"\"\n",
" This function is used to encode the error based on the difference\n",
" and split the difference into different bins\n",
......@@ -218,7 +232,7 @@
" \n",
" \"\"\"\n",
" # get the prediction error and difference\n",
" image, predict, diff, error, A = predict_pix(image)\n",
" image, predict, diff, error, A = predict_pix(image, difference)\n",
" \n",
" # get the number of points in each bins\n",
" data_points_per_bin = len(diff) // num_bins\n",
......@@ -300,18 +314,23 @@
},
{
"cell_type": "code",
"execution_count": 17,
"execution_count": 64,
"id": "2eb774d2",
"metadata": {},
"outputs": [],
"source": [
"def encoder(error, list_dic, diff, bound, bins):\n",
" \"\"\"\n",
<<<<<<< HEAD
" This function en\n",
=======
" This function \n",
>>>>>>> a352868acf14cebeaa7ea2a58e879b1d36b066ad
" This function encode the matrix with huffman coding tables\n",
" \n",
" Input:\n",
" error (512, 640): a matrix with all the errors\n",
" list_dic (num_dic + 1,): a list of huffman coding table \n",
" bound (2300,): the boundary values after subtracting the very first pixel value\n",
" bins (num_bins - 1,): a list of threshold to cut the bins\n",
" \n",
" Return:\n",
" encoded (512, 640): encoded matrix\n",
" \"\"\"\n",
" # copy the error matrix (including the boundary)\n",
" encoded = np.copy(error).astype(int).astype(str).astype(object)\n",
......@@ -335,15 +354,22 @@
},
{
"cell_type": "code",
"execution_count": 23,
"execution_count": 79,
"id": "8eeb40d0",
"metadata": {},
"outputs": [],
"source": [
"def decoder(A, encoded_matrix, list_dic, bins):\n",
"def decoder(A, encoded_matrix, list_dic, bins, use_diff):\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",
" This function decodes the encoded_matrix.\n",
" Input:\n",
" A (3 X 3): system of equation\n",
" list_dic (num_dic + 1,): a list of huffman coding table \n",
" encoded_matrix (512, 640): encoded matrix\n",
" bins (num_bins - 1,): a list of threshold to cut the bins\n",
" \n",
" Return:\n",
" decode_matrix (512, 640): decoded matrix\n",
" \"\"\"\n",
" # change the dictionary back to list\n",
" # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins\n",
......@@ -362,62 +388,85 @@
" the_keys4 = list(list_dic[4].keys())\n",
" the_values4 = list(list_dic[4].values())\n",
" \n",
" error_matrix = np.zeros((512,640))\n",
" #Matrix system of points that will be used to solve the least squares fitting hyperplane\n",
" points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])\n",
" \n",
" decode_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",
" for i in range(decode_matrix.shape[0]):\n",
" for j in range(decode_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_keys0[the_values0.index(encoded_matrix[i,j])])\n",
" decode_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_keys0[the_values0.index(encoded_matrix[i,j])]) + error_matrix[0][0]\n",
" elif i == 0 or i == decode_matrix.shape[0]-1 or j == 0 or j == decode_matrix.shape[1]-1:\n",
" decode_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])]) + decode_matrix[0][0]\n",
" # if not the boundary\n",
" else:\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",
" z0 = decode_matrix[i-1][j-1]\n",
" z1 = decode_matrix[i-1][j]\n",
" z2 = decode_matrix[i-1][j+1]\n",
" z3 = decode_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",
" if use_diff:\n",
" difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)\n",
" else:\n",
" \n",
" f, difference, rank, s = la.lstsq(points, [z0,z1,z2,z3], rcond=None) \n",
" difference = difference.astype(int)\n",
" \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",
" decode_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",
" decode_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",
" decode_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",
" decode_matrix[i][j] = int(the_keys4[the_values4.index(encoded_matrix[i,j])]) + int(predict)\n",
" \n",
" \n",
" return error_matrix.astype(int)"
" return decode_matrix.astype(int)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"execution_count": 74,
"id": "f959fe93",
"metadata": {},
"outputs": [],
"source": [
"def compress_rate(image, error, diff, bound, list_dic, bins):\n",
"def compress_rate(image, new_error, diff, bound, list_dic, bins):\n",
" '''\n",
" This function is used to calculate the compression rate.\n",
" Input:\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",
" bound (2300,): the boundary values after subtracting the very first pixel value\n",
" list_dic (num_dic + 1,): a list of huffman coding table \n",
" bins (num_bins - 1,): a list of threshold to cut the bins\n",
" \n",
" Return:\n",
" compression rate\n",
" '''\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",
" real_b = np.hstack((image[0,:],image[-1,:],image[1:-1,0],image[1:-1,-1]))\n",
" original = image[1:-1,1:-1].reshape(-1)\n",
" diff = diff.reshape(-1)\n",
" error = new_error[1:-1,1:-1].reshape(-1)\n",
" \n",
" # calculate the bit for boundary\n",
" for i in range(0,len(bound)):\n",
......@@ -426,6 +475,7 @@
" \n",
" # calculate the bit for the pixels inside the boundary\n",
" for i in range(0,len(original)):\n",
"\n",
" # for the original image\n",
" o_len += len(bin(original[i])[2:])\n",
" \n",
......@@ -441,14 +491,14 @@
" 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",
" c_len += len(list_dic[4][str(int(error[i]))])\n",
"\n",
" return c_len/o_len"
]
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 80,
"id": "3e0e9742",
"metadata": {},
"outputs": [
......@@ -456,7 +506,6 @@
"name": "stdout",
"output_type": "stream",
"text": [
"(512, 640)\n",
"True\n",
"5\n"
]
......@@ -465,30 +514,32 @@
"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",
"list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4, False)\n",
"encoded_matrix = encoder(new_error, list_dic, diff, bound, bins)\n",
"reconstruct_image = decoder(A, encoded_matrix, list_dic, bins)\n",
"reconstruct_image = decoder(A, encoded_matrix, list_dic, bins, False)\n",
"print(np.allclose(image, reconstruct_image))\n",
"print(len(list_dic))"
]
},
{
"cell_type": "code",
"execution_count": 32,
"execution_count": 81,
"id": "004e8ba8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[26, 40, 62]\n"
"data": {
"text/plain": [
"0.4437662760416667"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"print(bins)"
"compress_rate(image, new_error, diff, bound, list_dic, bins)"
]
},
{
......
Encoding_decoding.ipynb
View file @ 2659c0f6
......@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 34,
"execution_count": 59,
"id": "14f74f21",
"metadata": {},
"outputs": [],
......@@ -19,12 +19,13 @@
"from sklearn.neighbors import KernelDensity\n",
"import pandas as pd\n",
"from collections import Counter\n",
"import time"
"import time\n",
"import numpy.linalg as la"
]
},
{
"cell_type": "code",
"execution_count": 35,
"execution_count": 49,
"id": "c16af61f",
"metadata": {},
"outputs": [],
......@@ -78,12 +79,12 @@
},
{
"cell_type": "code",
"execution_count": 36,
"id": "aceba613",
"execution_count": 61,
"id": "8172fa41",
"metadata": {},
"outputs": [],
"source": [
"def predict_pix(tiff_image):\n",
"def predict_pix(tiff_image, difference = True):\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",
......@@ -99,16 +100,15 @@
" \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",
" predict (325380,): predicted image excluding the boundary\n",
" diff. (325380,): IF difference = TRUE, difference between the min and max of four neighbors exclude the boundary\n",
" ELSE: the residuals of the four nearest pixels to a fitted hyperplane\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",
" image = image.astype(int) \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",
......@@ -123,23 +123,37 @@
" # 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.round(np.round((np.linalg.solve(A,y)[-1]),1))\n",
" \n",
" #Matrix system of points that will be used to solve the least squares fitting hyperplane\n",
" points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])\n",
" \n",
" # flatten the neighbor pixlels and stack them together\n",
" z0 = np.ravel(z0)\n",
" z1 = np.ravel(z1)\n",
" z2 = np.ravel(z2)\n",
" z3 = np.ravel(z3)\n",
" neighbor = np.vstack((z0,z1,z2,z3)).T\n",
" \n",
" if difference:\n",
" # calculate the difference\n",
" diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)\n",
" \n",
" else:\n",
" #Compute the best fitting hyperplane using least squares\n",
" #The res is the residuals of the four points used to fit the hyperplane (summed distance of each of the \n",
" #points to the hyperplane), it is a measure of gradient\n",
" f, diff, rank, s = la.lstsq(points, neighbor.T, rcond=None) \n",
" diff = diff.astype(int)\n",
" \n",
" # calculate the error\n",
" error = np.ravel(image[1:-1,1:-1])-predict\n",
" \n",
" return image, predict, diff, error, A\n"
" return image, predict, diff, error, A"
]
},
{
"cell_type": "code",
"execution_count": 37,
"execution_count": 62,
"id": "6b965751",
"metadata": {},
"outputs": [],
......@@ -192,12 +206,12 @@
},
{
"cell_type": "code",
"execution_count": 38,
"execution_count": 63,
"id": "b7561883",
"metadata": {},
"outputs": [],
"source": [
"def huffman(image, num_bins=4):\n",
"def huffman(image, num_bins=4, difference = True):\n",
" \"\"\"\n",
" This function is used to encode the error based on the difference\n",
" and split the difference into different bins\n",
......@@ -218,7 +232,7 @@
" \n",
" \"\"\"\n",
" # get the prediction error and difference\n",
" image, predict, diff, error, A = predict_pix(image)\n",
" image, predict, diff, error, A = predict_pix(image, difference)\n",
" \n",
" # get the number of points in each bins\n",
" data_points_per_bin = len(diff) // num_bins\n",
......@@ -300,7 +314,7 @@
},
{
"cell_type": "code",
"execution_count": 39,
"execution_count": 64,
"id": "2eb774d2",
"metadata": {},
"outputs": [],
......@@ -340,12 +354,12 @@
},
{
"cell_type": "code",
"execution_count": 40,
"execution_count": 79,
"id": "8eeb40d0",
"metadata": {},
"outputs": [],
"source": [
"def decoder(A, encoded_matrix, list_dic, bins):\n",
"def decoder(A, encoded_matrix, list_dic, bins, use_diff):\n",
" \"\"\"\n",
" This function decodes the encoded_matrix.\n",
" Input:\n",
......@@ -353,6 +367,7 @@
" list_dic (num_dic + 1,): a list of huffman coding table \n",
" encoded_matrix (512, 640): encoded matrix\n",
" bins (num_bins - 1,): a list of threshold to cut the bins\n",
" \n",
" Return:\n",
" decode_matrix (512, 640): decoded matrix\n",
" \"\"\"\n",
......@@ -373,6 +388,9 @@
" the_keys4 = list(list_dic[4].keys())\n",
" the_values4 = list(list_dic[4].values())\n",
" \n",
" #Matrix system of points that will be used to solve the least squares fitting hyperplane\n",
" points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])\n",
" \n",
" decode_matrix = np.zeros((512,640))\n",
" # loop through all the element in the matrix\n",
" for i in range(decode_matrix.shape[0]):\n",
......@@ -394,7 +412,13 @@
" y1 = int(z0+z1+z2)\n",
" y2 = int(-z0-z1-z2-z3)\n",
" y = np.vstack((y0,y1,y2))\n",
" if use_diff:\n",
" difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)\n",
" else:\n",
" \n",
" f, difference, rank, s = la.lstsq(points, [z0,z1,z2,z3], rcond=None) \n",
" difference = difference.astype(int)\n",
" \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",
......@@ -414,15 +438,24 @@
},
{
"cell_type": "code",
"execution_count": 41,
"execution_count": 74,
"id": "f959fe93",
"metadata": {},
"outputs": [],
"source": [
"def compress_rate(image, error, diff, bound, list_dic, bins):\n",
"def compress_rate(image, new_error, diff, bound, list_dic, bins):\n",
" '''\n",
" This function is used to calculate the compression rate.\n",
" Input:\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",
" bound (2300,): the boundary values after subtracting the very first pixel value\n",
" list_dic (num_dic + 1,): a list of huffman coding table \n",
" bins (num_bins - 1,): a list of threshold to cut the bins\n",
" \n",
" Return:\n",
" compression rate\n",
" '''\n",
" # the bits for the original image\n",
" o_len = 0\n",
......@@ -433,6 +466,7 @@
" real_b = np.hstack((image[0,:],image[-1,:],image[1:-1,0],image[1:-1,-1]))\n",
" original = image[1:-1,1:-1].reshape(-1)\n",
" diff = diff.reshape(-1)\n",
" error = new_error[1:-1,1:-1].reshape(-1)\n",
" \n",
" # calculate the bit for boundary\n",
" for i in range(0,len(bound)):\n",
......@@ -441,6 +475,7 @@
" \n",
" # calculate the bit for the pixels inside the boundary\n",
" for i in range(0,len(original)):\n",
"\n",
" # for the original image\n",
" o_len += len(bin(original[i])[2:])\n",
" \n",
......@@ -456,14 +491,14 @@
" 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",
" c_len += len(list_dic[4][str(int(error[i]))])\n",
"\n",
" return c_len/o_len"
]
},
{
"cell_type": "code",
"execution_count": 42,
"execution_count": 80,
"id": "3e0e9742",
"metadata": {},
"outputs": [
......@@ -471,7 +506,6 @@
"name": "stdout",
"output_type": "stream",
"text": [
"(512, 640)\n",
"True\n",
"5\n"
]
......@@ -480,30 +514,32 @@
"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",
"list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4, False)\n",
"encoded_matrix = encoder(new_error, list_dic, diff, bound, bins)\n",
"reconstruct_image = decoder(A, encoded_matrix, list_dic, bins)\n",
"reconstruct_image = decoder(A, encoded_matrix, list_dic, bins, False)\n",
"print(np.allclose(image, reconstruct_image))\n",
"print(len(list_dic))"
]
},
{
"cell_type": "code",
"execution_count": 33,
"execution_count": 81,
"id": "004e8ba8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(512, 640)\n"
"data": {
"text/plain": [
"0.4437662760416667"
]
},
"execution_count": 81,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"\n",
"print(encoded_matrix.shape)"
"compress_rate(image, new_error, diff, bound, list_dic, bins)"
]
},
{
......
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