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 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f4850afd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from itertools import product\n",
    "import os\n",
    "import sys\n",
    "from PIL import Image\n",
    "from numpy import linalg as la\n",
    "from time import time\n",
    "from scipy.optimize import linprog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b240b11f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def file_extractor(dirname=\"images\"):\n",
    "    files = os.listdir(dirname)\n",
    "    scenes = []\n",
    "    for file in files:\n",
    "        scenes.append(os.path.join(dirname, file))\n",
    "    return scenes\n",
    "\n",
    "def image_extractor(scenes):\n",
    "    image_folder = []\n",
    "    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",
    "                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",
    "\n",
    "def im_distribution(images, num):\n",
    "    \"\"\"\n",
    "    Function that extracts tiff files from specific cameras and returns a list of all\n",
    "    the tiff files corresponding to that camera. i.e. all pictures labeled \"_7.tiff\" or otherwise\n",
    "    specified camera numbers.\n",
    "    \n",
    "    Parameters:\n",
    "        images (list): list of all tiff files, regardless of classification. This is NOT a list of directories but\n",
    "        of specific tiff files that can be opened right away. This is the list that we iterate through and \n",
    "        divide.\n",
    "        \n",
    "        num (str): a string designation for the camera number that we want to extract i.e. \"14\" for double digits\n",
    "        of \"_1\" for single digits.\n",
    "        \n",
    "    Returns:\n",
    "        tiff (list): A list of tiff files that have the specified designation from num. They are the files extracted\n",
    "        from the 'images' list that correspond to the given num.\n",
    "    \"\"\"\n",
    "    tiff = []\n",
    "    for im in images:\n",
    "        if im[-7:-5] == num:\n",
    "            tiff.append(im)\n",
    "    return tiff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d044d19",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_hist(tiff_list, i, tech = \"first\"):\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",
    "    \"\"\"\n",
    "    '''jj = 0\n",
    "    fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(15,12))\n",
    "    for cam, ax in zip(cameras, axs.ravel()):\n",
    "        diff = []\n",
    "        for ii in range(len(cam)):\n",
    "            image = Image.open(cam[ii])    #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",
    "            ar1, ar2 = image.shape\n",
    "            ind1, ind2 = np.random.randint(1,ar1-1), np.random.randint(1,ar2-1) #ind1 randomly selects a row, ind2 randomly selects a column, \n",
    "                                                                            #this is now a random pixel selection within the image\n",
    "            \n",
    "            surrounding = []                                                #initialize a list to be filled the 8 surrounding pixels\n",
    "            for i,j in product(np.arange(-1,2), repeat=2):                  #Iterate through the combinations of surrounding pixel indices\n",
    "                if i == 0 and j == 0:                                       #Avoid the target pixel\n",
    "                    continue\n",
    "                else:\n",
    "                    surrounding.append(image[ind1+i, ind1+j])               #Add the other 8 pixels to the list\n",
    "            diff.append(np.max(surrounding)-np.min(surrounding))\n",
    "        ax.hist(diff)\n",
    "        ax.set_title(f\"tiff {jj}\")\n",
    "        jj += 1\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    return '''\n",
    "\n",
    "    image = tiff_list[i]\n",
    "    image = Image.open(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",
    "    row, col = image.shape\n",
    "    diff = np.empty((row,col))\n",
    "    predict = np.empty([row,col])     # create a empty matrix to update prediction\n",
    "    predict[0,:] = image[0,:]       # keep the first row from the image\n",
    "    predict[:,0] = image[:,0]       # keep the first columen from the image\n",
    "    predict[-1,:] = image[-1,:]       # keep the first row from the image\n",
    "    predict[:,-1] = image[:,-1]       # keep the first columen from the image\n",
    "    diff = np.empty([row,col])\n",
    "    diff[0,:] = np.zeros(col)       # keep the first row from the image\n",
    "    diff[:,0] = np.zeros(row)\n",
    "    diff[-1,:] = np.zeros(col)       # keep the first row from the image\n",
    "    diff[:,-1] = np.zeros(row)\n",
    "    x_s = []\n",
    "    for r in range(1,row-1):                  # loop through the rth row\n",
    "        for cc in range(1,col-1):              # loop through the cth column\n",
    "            surrounding = np.array([image[r-1,cc-1], image[r-1,cc], image[r-1,cc+1], image[r,cc-1]])\n",
    "            #Solve the linear system Ax = v for the coefficients a, b, and c\n",
    "            if tech == \"second\":\n",
    "                v = np.array([image[r-1,cc-1], image[r-1,cc]+image[r-1,cc+1], image[r,cc-1]])\n",
    "                #A = np.array([[-1,-1,1], [0,-1,1], [1,-1,1], [-1,0,1]])\n",
    "                A = np.array([[-1,-1,1], [1,-2,2], [-1,0,1]])\n",
    "            else:\n",
    "                v = np.array([image[r-1,cc-1]+image[r-1,cc], image[r-1,cc+1], image[r,cc-1]])\n",
    "                #A = np.array([[-1,-1,1], [0,-1,1], [1,-1,1], [-1,0,1]])\n",
    "                A = np.array([[-1,-2,2], [1,-1,1], [-1,0,1]])\n",
    "                \n",
    "            x = la.solve(A,v)\n",
    "            x_s.append(x)\n",
    "            c = x[2]\n",
    "            predict[r,cc] = c\n",
    "            diff[r,cc] = (np.max(surrounding)-np.min(surrounding))\n",
    "            \n",
    "            #predict[r,c] = np.mean(surrounding)       # take the mean of the previous 4 pixels\n",
    "\n",
    "\n",
    "    \"\"\"predict = np.ravel(predict)\n",
    "    diff = np.ravel(diff)\n",
    "    n = len(predict)\n",
    "    fig = plt.figure()\n",
    "\n",
    "    ax1 = fig.add_subplot(111, projection='3d')\n",
    "    z3 = np.zeros(n)\n",
    "    \n",
    "    dx = np.ones(n)\n",
    "    dy = np.ones(n)\n",
    "    dz = np.arange(n)\n",
    "    \n",
    "    ax1.bar3d(predict, diff, z3, dx, dy, dz, color=\"red\")\n",
    "    ax1.axis('off')\n",
    "    plt.show()\"\"\"\n",
    "    return image, predict, diff, x_s\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6cdea201",
   "metadata": {},
   "outputs": [],
   "source": [
    "scenes = file_extractor()\n",
    "images = image_extractor(scenes)\n",
    "num_images = im_distribution(images, \"_9\")\n",
    "error_mean = []\n",
    "error_mean1 = []\n",
    "diff_mean = []\n",
    "times = []\n",
    "times1 = []\n",
    "all_error = []\n",
    "for i in range(len(num_images)):\n",
    "    \"\"\"start1 = time()\n",
    "    image_1, predict_1, difference_1, x_s_1 = plot_hist(num_images, i, \"second\")\n",
    "    stop1 = time()\n",
    "    times1.append(stop1-start1)\n",
    "    error1 = np.abs(image_1-predict_1)\n",
    "    error_mean1.append(np.mean(np.ravel(error1)))\"\"\"\n",
    "    start = time()\n",
    "    image, predict, difference, x_s = plot_hist(num_images, i, \"first\")\n",
    "    stop = time()\n",
    "    times.append(stop-start)\n",
    "    error = np.abs(image-predict)\n",
    "    all_error.append(np.ravel(error))\n",
    "    error_mean.append(np.mean(np.ravel(error)))\n",
    "    diff_mean.append(np.mean(np.ravel(difference)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a2b4212b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Error First and Second Added: 20.74347343444824\n",
      "Standard Deviaiton of Mean Errors: 0.13532270001617094\n",
      "Average Difference: 53.3018756866455\n",
      "Average Time per Image for First: 10.643209546804428\n"
     ]
    }
   ],
   "source": [
    "print(f\"Average Error First and Second Added: {np.mean(error_mean)}\")\n",
    "\n",
    "print(f\"Standard Deviaiton of Mean Errors: {np.sqrt(np.var(error_mean))}\")\n",
    "print(f\"Average Difference: {np.mean(diff_mean)}\")\n",
    "print(f\"Average Time per Image for First: {np.mean(times)}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5b6d25f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1., 0., 0., 0., 0., 1., 0., 0., 0., 0., 1., 0., 0., 1., 0., 0., 1.,\n",
       "        2., 0., 1.]),\n",
       " array([19.81767883, 19.84657283, 19.87546682, 19.90436081, 19.9332548 ,\n",
       "        19.96214879, 19.99104279, 20.01993678, 20.04883077, 20.07772476,\n",
       "        20.10661875, 20.13551275, 20.16440674, 20.19330073, 20.22219472,\n",
       "        20.25108871, 20.27998271, 20.3088767 , 20.33777069, 20.36666468,\n",
       "        20.39555868]),\n",
       " <BarContainer object of 20 artists>)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(error_mean, bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "59fd96bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.817678833007815\n",
      "52.82225646972656\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 0\n",
    "print(np.mean(np.ravel(error)))\n",
    "print(np.mean(np.ravel(difference)))\n",
    "z = np.array(list(zip(np.ravel(error), np.ravel(difference))))\n",
    "random = np.random.randint(640,len(z), size=1000)\n",
    "samples = z[random]\n",
    "plt.scatter(z[:,0], z[:,1], alpha=.2)\n",
    "plt.xlabel(\"Error\")\n",
    "plt.ylabel(\"Surrounding Differences\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "0d486682",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist, xedges, yedges = np.histogram2d(samples[:,0], samples[:,1], bins=250, range=[[0, 800], [0, 50]])\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "# Construct arrays for the anchor positions of the 16 bars.\n",
    "xpos, ypos = np.meshgrid(xedges[:-1] + 0.25, yedges[:-1] + 0.25, indexing=\"ij\")\n",
    "xpos = xpos.ravel()\n",
    "ypos = ypos.ravel()\n",
    "zpos = 0\n",
    "\n",
    "# Construct arrays with the dimensions for the 16 bars.\n",
    "dx = dy = 0.5 * np.ones_like(zpos)\n",
    "dz = hist.ravel()\n",
    "\n",
    "ax.bar3d(xpos, ypos, zpos, dx, dy, dz)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "id": "d04d6e06",
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly2(x, y):\n",
    "    a, b, c = np.polyfit(x,y,2)\n",
    "    return a, b, c\n",
    "\n",
    "def poly1(x, y):\n",
    "    m, b = np.polyfit(x,y,1)\n",
    "    return m, b\n",
    "\n",
    "def generate_random(image):\n",
    "    # image is the array of pixel values of a given image\n",
    "    row, col = image.shape\n",
    "    ind1, ind2 = np.random.randint(0,row), np.random.randint(0,col)\n",
    "    points = [image[ind1, ind2-1], image[ind1-1, ind2-1], image[ind1-1, ind2], image[ind1-1, ind2+1]]\n",
    "    points = np.array([np.arange(4), points]).T\n",
    "\n",
    "    x, y = points[:,0], points[:,1]\n",
    "    return x, y, ind1, ind2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "5d97d89b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1D Difference: 5.000000000014552\n",
      "2D Difference: 54.99999999997817\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y, ind1, ind2 = generate_random(image)\n",
    "\n",
    "m, inter = poly1(x,y)\n",
    "a, b, c = poly2(x,y)\n",
    "\n",
    "lin = np.linspace(0,4,50)\n",
    "\n",
    "plt.plot(x,y,'.')\n",
    "plt.plot(lin, m*lin + inter, label=\"1d\")\n",
    "plt.plot(lin, a*lin**2 + b*lin + c, label=\"2d\")\n",
    "\n",
    "plt.scatter(4, image[ind1, ind2], label=\"Actual\")\n",
    "\n",
    "plt.scatter(4, m*4 + inter, label=\"1D approx\")\n",
    "plt.scatter(4, a*4**2 + b*4 + c, label=\"2D approx\")\n",
    "plt.legend()\n",
    "print(f\"1D Difference: {np.abs(image[ind1, ind2] - (m*4 + inter))}\")\n",
    "print(f\"2D Difference: {np.abs(image[ind1, ind2] - (a*4**2 + b*4 +c))}\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "c1c0222e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(512, 640)\n"
     ]
    }
   ],
   "source": [
    "print(image.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "98a4e4e5",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "index 640 is out of bounds for axis 1 with size 640",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_2432/4036596452.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     13\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34mf\"1D Avg: {np.mean(one_d)}\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34mf\"2D Avg: {np.mean(two_d)}\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 15\u001b[1;33m \u001b[0mavg\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mimage\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_2432/4036596452.py\u001b[0m in \u001b[0;36mavg\u001b[1;34m(image)\u001b[0m\n\u001b[0;32m      3\u001b[0m     \u001b[0mtwo_d\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m         \u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mgenerate_random\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mimage\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m         \u001b[0mm\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minter\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpoly1\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m         \u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mc\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpoly2\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_2432/1166824526.py\u001b[0m in \u001b[0;36mgenerate_random\u001b[1;34m(image)\u001b[0m\n\u001b[0;32m     11\u001b[0m     \u001b[0mrow\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcol\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mimage\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m     \u001b[0mind1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mrow\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrandint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mcol\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 13\u001b[1;33m     \u001b[0mpoints\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mimage\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mind1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind2\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mimage\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mind1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind2\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mimage\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mind1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mimage\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mind1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mind2\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     14\u001b[0m     \u001b[0mpoints\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpoints\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     15\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mIndexError\u001b[0m: index 640 is out of bounds for axis 1 with size 640"
     ]
    }
   ],
   "source": [
    "def avg(image):\n",
    "    one_d = []\n",
    "    two_d = []\n",
    "    for i in range(1000):\n",
    "        x, y, ind1, ind2 = generate_random(image)\n",
    "        m, inter = poly1(x, y)\n",
    "        a, b, c = poly2(x, y)\n",
    "        one_diff = np.abs(image[ind1, ind2] - m*4 + inter)\n",
    "        two_diff = np.abs(image[ind1, ind2] - a*4**2 + b*4 + c)\n",
    "        one_d.append(one_diff)\n",
    "        two_d.append(two_diff)\n",
    "\n",
    "    print(f\"1D Avg: {np.mean(one_d)}\")\n",
    "    print(f\"2D Avg: {np.mean(two_d)}\")\n",
    "avg(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "8248910a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n",
      "-53873.666\n",
      "22654\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\calle\\AppData\\Local\\Temp/ipykernel_2432/1182217676.py:7: RuntimeWarning: overflow encountered in ushort_scalars\n",
      "  vec = np.array([-p1+p3-p4, -p1-p2-p3, -p1-p2-p3-p4])\n"
     ]
    }
   ],
   "source": [
    "x_test, y_test, ind1_test, ind2_test = generate_random(image)\n",
    "p1 = image[ind1_test-1, ind2_test-1]\n",
    "p2 = image[ind1_test-1, ind2_test]\n",
    "p3 = image[ind1_test-1, ind2_test+1]\n",
    "p4 = image[ind1_test, ind2_test-1]\n",
    "\n",
    "vec = np.array([-p1+p3-p4, -p1-p2-p3, -p1-p2-p3-p4])\n",
    "mat = np.array([[3, 0, -1], [0, 3, -3], [1,3,-4]])\n",
    "print(np.allclose(np.dot(mat, la.solve(mat,vec)), vec))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "43f46b48",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22605.0\n",
      "22631\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[-1,-1,1], [0,-1,1], [0,-1,2]])\n",
    "b = np.array([p1,p2,p3+p4])\n",
    "print(la.solve(A,b)[2])\n",
    "print(image[ind1_test, ind2_test])\n"
   ]
  }
 ],
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