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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CT Reconstruction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this exercise we will play with some of the mechanics of how CT scanner generates images. You will see snippets of code in this notebook and some snippets will have comments that start with the word _TASK_. These are yours to fill - read task description and write code that completes the snippet\n",
    "\n",
    "We have talked about the \"Tomography\" part and now will talk about computation. In this notebook we have some sample code that will load a real CT image and will go through the steps similar to the ones a scanner is going through to do the computation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sinograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each time a detector is taking an image, it is computing the amount of photons passing through the body. Let's simulate this by passing a bunch of rays through a phantom image.\n",
    "\n",
    "> _Phantoms_ are commonly used in medical imaging. The word may refer to physically-accurate phantoms which are used by medical physicists to calibrate scanners and other devices, and images of phantoms, which could be synthetic 2D or 3D images used to calibrate and test medical software. Take a look at this adorable fetus phantom:  \n",
    "> <img src=\"Exercise. CT backprojection.img/baby_phantom.jpg\" width=\"300\" align=\"left\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading image and computing a single projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<PIL.Image.Image image mode=L size=200x200 at 0x20F8AA87850>\n"
     ]
    }
   ],
   "source": [
    "# Our human body will be represented by a jpeg image, so we will use PIL library to load and manipulate it\n",
    "\n",
    "from PIL import Image\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.ndimage as nd\n",
    "\n",
    "im = Image.open(\"phantom.bmp\").convert(\"L\")\n",
    "print(im)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us visualize the image here. As you can see it's a few grayscale geometric figures, quite typical for phantoms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f89749e20>"
      ]
     },
     "execution_count": 51,
     "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.imshow(im, cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us compute a projection now. For the sake of simlicity we are assuming that our xrays are following from left to right, all rays are parallel, passing through the entire image. Note that we are just summing all values of pixels that rays meet along the path. In real world the ray would be attenuated by the tissues, and the intensity (or the amount of photons) is decreased as the ray passess through matter, this the detector is effectively subtracting the measured value from a known maximum value. Again, for the sake of simplicity we will do the inverse here - just add everything up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "projection = []\n",
    "m = np.array(im)\n",
    "for x in range(0, im.width):\n",
    "    projection.append(np.sum(m[x]))\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's visualize it by plotting the accumulated intensities encountered along each ray. Effectively, this is a 1-dimensional \"x-ray\" of our thin slice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20f894ddca0>]"
      ]
     },
     "execution_count": 29,
     "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.plot(projection)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rotate and project again\n",
    "\n",
    "Now let's simulate rotation of our xray tube/detector gantry and compute another projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f89542670>"
      ]
     },
     "execution_count": 31,
     "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": [
    "im_r = im.rotate(60)\n",
    "plt.imshow(im_r, cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20f89596a00>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lU6M1AzVGmgyUYzW09+H1BbVmMEKVhRkc1BFFaow0GSjHqrWaPDQZjMzcogyMef+6KTUamgyUY2kyGJ2zrKU6wrO1lRoNTQbKsWqbu8lP95CdqrOOR2JWfholWcm8vEfnbarR02SgHKu2pfvEZvfqzESEi+YV8nptGwP+4JlPUCqCJgPlSMYYHVY6BpfMK6C730/VwWNnPlipCJoMlCO1dg/Q0efTYaWjtGpOPolu4eU9uqqvGh1NBsqRtPN4bNKSEvjAzDztN1CjpslAOVJtiyaDsVpdmc/epm6aO712h6ImEE0GypH2NXeT5nFTnJVsdygTzqo5+QC8vq/V5kjURKLJQDnSvpZuZhemE1rxXI3GguJMclITea2mze5Q1ASiyUA5Um2zrkk0Vi6X8MHZ+byxrxVr3ymlzkiTgXKc7n4/jR1eZmt/wZitmpNPY4eX/a09doeiJghNBspxdlrLKcyzNmxRo3f+7DwAthzQ+QZqZDQZKMd5ZW8LCS7hA7Ny7Q5lwpqRm4onwcWBNq0ZqJHRZKAc5+U9LZw7I4eMZN3zeKxcLmF6bip12kykRkiTgXKUpk4vuxs7uXheod2hTHgVeakcbOu1Oww1QWgyUI7yyt7QMgoXzS2wOZKJryIvjbq2Hh1RpEZEk4FylI17WyjISGJ+sXYej9eM/DS8viDNXf12h6ImgBElAxG5R0SaRWRnRFmuiDwvIjXW1xyrXETkpyJSKyLVInJOxDnrrONrRGRdRPm5IrLDOuenojONpqx3DrWzYmauTjaLgoq8VAAOaL+BGoGR1gzuBdYMKrsDeNEYUwm8aH0PcDVQad3WA3dCKHkA3wI+AKwAvhVOINYx6yPOG/xaagpo7vLS0N7HsvJsu0OZFCry0gA4qCOK1AiMKBkYYzYCgwcsrwXus+7fB1wfUX6/CdkEZItIMXAV8Lwx5pgx5jjwPLDGeizTGPOmCTVu3h/xXGoKqT4cml+wRJNBVJRkp5DoFuq0E1mNwHj6DIqMMY0A1tfw8I9S4HDEcfVW2enK64coP4WIrBeRKhGpamnR9donm+317bhdwsKSTLtDmRTcLqE8N1VrBmpEYtGBPFRjrxlD+amFxtxtjFlujFleUKCjTSabbYfbmVuUQaonwe5QJo2KvDQOtGrNQJ3ZeJJBk9XEg/U1vJtGPVAecVwZcOQM5WVDlKspxBjD9sPtLC3PsjuUSWVWfhr7W7rxB3RPZHV640kGG4DwiKB1wBMR5Z+0RhWtBDqsZqTngCtFJMfqOL4SeM56rEtEVlqjiD4Z8Vxqiqhr66XT62dJmfYXRNOisiz6/UFqrJ3jlBrOiOrjIvIQcDGQLyL1hEYFfR94VERuBQ4BN1qHPw1cA9QCvcCnAIwxx0Tk34Et1nH/ZowJd0p/ntCIpRTgGeumppA9R7sAmF+s/QXRtNhKrtX17Xpt1WmNKBkYY24Z5qHLhjjWAF8Y5nnuAe4ZorwKOHsksajJKdzJWZGfZnMkk0tFXiqZyQlsr+/gr86zOxrlZDoDWTlCXVsPuWkeslJ0cbpoEhEWl2VTXd9udyjK4TQZKEeoa+1lhjVjVkXXorIs3mvswusL2B2KcjBNBsoR6tp6mJmnTUSxsKQsC3/QsLux0+5QlINpMlC28/oCNHZ4maHJICbCncg7rB3klBqKJgNlu/Ca+xX52kwUC8VZyWSlJPKeNWJLqaFoMlC2q7NGEs3UkUQxISLMK8qgpkmTgRqeJgNlu/DWjNpMFDtzp6Wz52iXbnSjhqXJQNmurq1Xh5XG2LyiDDq9fpo6daMbNTRNBsp2B9t6dFhpjM0tCu0ct0ebitQwNBko2zW091GWo8kglsLJYK92IqthaDJQtgoGDY3tXkqyk+0OZVLLSfNQmJGkNQM1LE0GylZtPQMMBIKUZKXYHcqkN29aBns1GahhaDJQtjrS3geEtmhUsVVZmEFNU7eOKFJD0mSgbNXYEUoGxVnaTBRrpTkp9PkCdPT57A5FOZAmA2WrhnYvAKVaM4i5aZmhhHu002tzJMqJNBkoWzW295GS6CY7VecYxNq0rCQAjnZoMlCn0mSgbHWko4/i7GRCO56qWCrMCNUMmrRmoIagyUDZ6ki7V5uI4qQo3EzUobOQ1ak0GShbHWnv087jOPEkuMhL82ifgRqSJgNlmwF/kJbufh1WGkdFmcnaTKSGpMlA2aap04sx6ISzOJqWlawdyGpIY04GIjJPRLZF3DpF5Esi8m0RaYgovybinK+JSK2I7BGRqyLK11hltSJyx3h/KDUx6ISz+CvKTKK5S5OBOlXCWE80xuwBlgKIiBtoAB4DPgX8pzHmPyKPF5EFwM3AQqAEeEFE5loP/xy4AqgHtojIBmPMu2ONTU0M4XVyZhXoPgbxUpSZTGv3AAP+IJ4EbRhQ74vWu+EyYJ8x5uBpjlkLPGyM6TfGHABqgRXWrdYYs98YMwA8bB2rJrnthzvIT0/SDuQ4Ck8809qBGixayeBm4KGI728TkWoRuUdEcqyyUuBwxDH1Vtlw5acQkfUiUiUiVS0tLVEKXdmlur6dJWVZOscgjoqydK6BGtq4k4GIeIAPA7+1iu4EZhNqQmoEfhw+dIjTzWnKTy005m5jzHJjzPKCgoJxxa3s1d3vp7alm0VlWXaHMqUUZehcAzW0MfcZRLgaeNsY0wQQ/gogIr8AnrS+rQfKI84rA45Y94crV5PUroYOjIElZdl2hzKlTMvS9YnU0KLRTHQLEU1EIlIc8dgNwE7r/gbgZhFJEpGZQCXwFrAFqBSRmVYt42brWDWJVdd3ALBYawZxlZOaiMft0j4DdYpx1QxEJJXQKKDPRhT/UESWEmrqqQs/ZozZJSKPAu8CfuALxpiA9Ty3Ac8BbuAeY8yu8cSlnG97fTul2SnkpSfZHcqUIiLkpXto6x6wOxTlMONKBsaYXiBvUNknTnP8d4HvDlH+NPD0eGJRE8ueo10sKMm0O4wpKS/dQ2u39hmok+lAY2WL1u7+E8McVXzlpydpzUCdQpOBijt/IMjxXh956R67Q5mS8tKStGagTqHJQMXdsZ7Qp9J87S+wRX5GqM9A90JWkTQZqLhr7Q4nA60Z2CE/LYmBQJBOr9/uUJSDaDJQcRduotCRRPbIzwgl4TZtKoq5lq5+vv/Me7T3Or+PRpOBiru2ntA/IW0mskdeWui6t2onckwN+IN84YG3ueuVfTyy5fCZT7CZJgMVd+GRLNqBbI9wEtaaQWz9v6d381bdMXLTPDxZ3Wh3OGekyUDFXUt3Px63i4ykaKyGokYr3FfT2qM1g1h5ZW8L975Rx19/sILPXzSbHQ0d1LX22B3WaWkyUHHX1j1AfrpHVyu1SW6alQy6tGYQCx19Pv7pd9upLEznjqvP4prFoRV6ntrh7NqBJgMVd63d/dp5bKMEt4uc1MQTfTcquu5/o46mzn5+fNMSkhPdlGancO6MHB7cfMjRHcmaDFTctXUPaH+BzfLTk2jtcu4/pomq3x/g/k0HuXheAYsjVuT95w/Np6Wrny8+9A6BoDPnd2gyUHHX1t2vI4lslpfu0ZpBDPxxeyMtXf3cesHMk8qXTc/hX9cu5NWaVp6sduYK/ZoMVFwZY2jVmoHt8tOTdGhpDPx600HmFWVwwZz8Ux67aXk52amJvFrTakNkZ6bJQMVVV7+fgUCQAq0Z2CqUDLRmEE3Hegaorm/n2sXFQw6OcLuEVbPzeb221ZFLgWgyUHEVHsGiNQN75ad76PL68foCdocyabyxrxVjYFXlqbWCsFVz8mns8LLfgcNMNRmouGqzxraHZ8Eqe0zLSgHgaIfueBYtr9e2kpGUwOLS4XfvCzcfvV7rvKYiTQYqrtq6tWbgBCXWXshHOvpsjmTyeK22lZWz80hwD/9vdXpeKuW5KbzmwH4DTQYqrtp7fQBkp2oysFNxdqhm0NiuNYNoONTWy+Fjfaw+TRNR2OrKAl6vbaXf76wmOk0GKq66+0PLJmck61IUdioO1wzatWYQDc/tOgow5CiiwS6fX0jPQIA397XFOqxR0WSg4iq8hn66R5OBnZIT3eSleTiifQbjZozhoS2HOGd6NrMK0s94/Adn55PqcfP8u01xiG7kNBmouOr2+klPSsDl0nWJ7FacnUyj9hmM21sHjrG/pYdbVkwf0fHJiW4urCzghd1NjhpiOu5kICJ1IrJDRLaJSJVVlisiz4tIjfU1xyoXEfmpiNSKSLWInBPxPOus42tEZN1441LO1OX1aRORQxRnpWifQRQ8+NYhMpITuHZxyYjPuXxBEU2d/VTXd8QwstGJVs3gEmPMUmPMcuv7O4AXjTGVwIvW9wBXA5XWbT1wJ4SSB/At4APACuBb4QSiJpfu/lDNQNmvNDtF+wzGacAf5Pl3m7h2cQkpHveIz7vsrEKSE13c/er+GEY3OrFqJloL3Gfdvw+4PqL8fhOyCcgWkWLgKuB5Y8wxY8xx4HlgTYxiUzbq8vq1ZuAQxVnJdPX76fL67A5lwnrn0HF6BwJcPK9gVOflpHn43EWzeaq6kS11x2IU3ehEIxkY4E8islVE1ltlRcaYRgDra6FVXgpE7v9Wb5UNV34SEVkvIlUiUtXS0hKF0FW8dfX7SU9OtDsMRcTwUu1EHrPXa1txCayclTfqcz974WyKs5L57lO7YxDZ6EUjGawyxpxDqAnoCyJy4WmOHarX0Jym/OQCY+42xiw3xiwvKBhdJlbOoH0GzhGeeNagTUVj9lptK0vKs8lKGf0HnBSPm7/+YAXbDrc7Yib4uJOBMeaI9bUZeIxQm3+T1fyD9bXZOrweKI84vQw4cppyNcl0ef263aVDlOjEs3Hp9PrYXt8xorkFw1ldGfpQ+5oDlqcYVzIQkTQRyQjfB64EdgIbgPCIoHXAE9b9DcAnrVFFK4EOqxnpOeBKEcmxOo6vtMrUJNOtfQaOUZiRhEvQ4aVj9OreVgJBw6pxJIOzpmWQn+5xxFpF4/2rLAIes5ZrTQAeNMY8KyJbgEdF5FbgEHCjdfzTwDVALdALfArAGHNMRP4d2GId92/GGGf0qqio8QWC9PkCpCdpn4ETJLhdZKd6OO7grRidqqffz/ee2U1FXirnTB/7wEeXS/jg7Hxes5a1tnNf8HElA2PMfmDJEOVtwGVDlBvgC8M81z3APeOJRzlbjy5F4TgpiW56B5y1Rs5E8INn36OhvY9HP3s+noTxtbZfMCefDduPUNPczdyijChFOHo6A1nFTVd4KQpNBo6R6nHTp8lgVLr7/Ty4+RC3rJjOeRW5436+8P4Hf36v+QxHxpYmAxU34WSQqcnAMVI9WjMYrTf3teEPGq5dXByV5yvNTuHcGTk8uuWwrctTaDJQcROe3KR9Bs6RojWDUXu1poVUj5tzZ0RvkYRbVkxnf2sPmw/Y11WqyUDFjS5f7TypngR6fX67w5hQNu5tYeWsPJISRr78xJlcu7iYzOQEHtx8KGrPOVqaDFTchJuJNBk4R4o2E43KobZe6tp6uXAEm9iMRnKim+uXlfLsrqP0DtiTnDUZqLjp6tcOZKdJTdRmotHYWBNaBmf13OivgHDZ/CIG/EG21B2P+nOPhCYDFTfhPoNMXZvIMbQDeXRerWmhNDuFWflpUX/uFRW5eNwu2yagaTJQcdPl9ZPgEpLGOS5bRU+KJ0FrBiPkCwR5o7aNC+cWxGRyWIrVKf1qjSYDNcmFl6Kwc5alOlmqx81AIIg/ELQ7FMfbfridrn5/1PsLIl1Qmc/uxk5au/tj9hrD0WSg4qbL69P+AodJtTZk6fVp7eBMNu5twSXwwXGsRXQm4XWO7Ggq0mSg4qa730+GzjFwlPDuXNpUdGYba1pZOsblqkdqUWkWpdkp/PDZPRzrie+aUZoMVNx0ev1aM3CYEzUDTQan9ezORrYdbuey+UUxfR23S/ifj51DS3c/f/fQO3GdkazJQMVNt9evS1E4TEpi6Pdh19j2iaC2uYuvPLqdpeXZfHr1zJi/3pLybP7xynm8VttKbXN3zF8vTJOBipuufh/purGNo6RqM9EZ/WLjAUSEuz5+blRnHZ/OmrOnAfHd9EaTgYqbvoEAqZoMHCVFm4lOyxjDa7WtrJqTxzRrm9B4KM9NpeW5PUwAABE5SURBVCIvNa4dyZoMVNz0DQRISYzPJys1MuHfhyaDoR1s66WhvW9cW1uO1ao5+WzafwxfnIb9ajJQcWGModcXONEsoZzhRDORLlY3pHAzzQWV0V9+4kwumJNPd7+f6vr2uLyeJgMVF/3+IMaEFuRSzpHqCXcga81gKK/XtlKanUJFXmrcX/v82XmIwMa98Wkq0mSg4sJrTWrSZiJn0XkGw/MHgryxr41Vc/JsmTWfnephWXl23HZA02Sg4iL8yVObiZxF5xkM7+U9LXT0+WI+t+B0Ll9QxI6GDho7+mL+WpoMVFz0hWsGmgwcJdHtItEtmgyG8OBbhyjMSOLSswpti+HKBaFE9MLu2NcOxpwMRKRcRF4Skd0isktEbrfKvy0iDSKyzbpdE3HO10SkVkT2iMhVEeVrrLJaEbljfD+ScqJwM4T2GThPSqKbPp10dpKG9j5e3tPMX51XTqLbvs/MswvSqchL5fl3m2L+WuMZ9O0HvmKMeVtEMoCtIvK89dh/GmP+I/JgEVkA3AwsBEqAF0RkrvXwz4ErgHpgi4hsMMa8O47YlMNon4FzpXoStGYwyO+q6jHATcvLbY1DRLhiQRH3vlFHl9dHRgz3AhlzyjPGNBpj3rbudwG7gdLTnLIWeNgY02+MOQDUAiusW60xZr8xZgB42DpWTSLaZ+BcqR63rlo6yEt7mllWnk15bvxHEQ121cJp+AKGF2PcVBSV+o+IVADLgM1W0W0iUi0i94hIjlVWChyOOK3eKhuufKjXWS8iVSJS1dLSEo3QVZyE+wy0mch5Ujy69WWkjj4f1fXttswtGMo503OYlpnMUzsaY/o6404GIpIO/B74kjGmE7gTmA0sBRqBH4cPHeJ0c5ryUwuNudsYs9wYs7ygwBm/KDUyXu1AdqzQ1pfaZxD25r42ggZbZh0PxeUSrl40jVf2tpzYOjYmrzOek0UkkVAieMAY8wcAY0yTMSZgjAkCvyDUDAShT/yRDXBlwJHTlKtJpE+biRxLt7482eu1raR63Cwtz7Y7lBM+tKiYAX8wpk1F4xlNJMCvgN3GmJ9ElBdHHHYDsNO6vwG4WUSSRGQmUAm8BWwBKkVkpoh4CHUybxhrXMqZwn0G2oHsPKmJbu1AjvB6bSsfmJmLx0F7dZ8zPYfirGQe39YQs9cYz2iiVcAngB0iss0q+zpwi4gsJdTUUwd8FsAYs0tEHgXeJTQS6QvGmACAiNwGPAe4gXuMMbvGEZdyIO0zcK5QM5EmA4C3Dx1nf2sPH1s5w+5QTuJyCTeeW8Z/v1RL/fFeynKi37E95mRgjHmNodv7nz7NOd8FvjtE+dOnO09NfF5fAJdAkoM+bamQFI/7RLKeyry+AP/42+2UZqdw0/Iyu8M5xU3nlfPfL9Xy6JbD/P2V86L+/PqXqeKi11q+2o41XtTpaQdyyJ0v72NfSw/f/8iimI7nH6uynFQumlvAI1WH8cdgWWtNBiou+nwBHUnkUCmeBLy+IMFg/PbbdaInq4+wujKf1Q4ZUjqUj66YzvFeH7sbu6L+3JoMVFx4BwLaX+BQ7+9pMHWbihra+9jX0sNFc52bCAAuPauQt75+GYvKsqL+3JoMVFz06cY2jpVm/V56pnBT0at7Q5NYnZ4MEtwuslM9MXluTQYqLnp1y0vHykwJtY939sVuQpPTbaxpYVpmMnMK0+0OxTa6O7nD9PT76R0IkJzoOqkTy+sL0OV9/5NbZkoCSQkT559rn0+biZwqx/qkeaxnaiaDQNDwWk0ra86eNqUHOGgysEEwaNi0v432Ph+NHV7e3NdGa3c/LV39NLS/v4nFwpJMpuem0t7rY+uh4wz43x9B4HG7OKs4A4D89NCa67lpoT9ql0BlUQaz8tMc8+b2+gLkpcWmeqvGJ/y+Od47YHMk9the306n1+/ojuN40GQQBwP+IAOBIOlJCbyxr5V/++O7vHf0/dEAM/PTKM9NZXpuKresKCcr1cOx7gHe3N/KvpZukhPdfHLlDGbkpYIIGMPh4328e6STBLdQ09w15NZ4pdkpfP7i2Zw7IzR7MVZtjSPRNxAgJUdrBk6UnRqqgbZP0WSwcW8LIs5Zi8gumgxixBhDvz9ITVM3tz/yDkc7vFwyr5BndjZSnpvKT25awsKSLDKSEyjJThnyOW6ncsSvdehYL15fqObgCwTZ2dDBI1WH+efHQ6uBJCe6+Oa1C5k3LYNOr48LKwtwu+JXa+jV0USOFW4mOt47NZuJXq1pZXFZNjlTvOaqySAG6lp7+NIj29h2uB2AwowkLp5XwNM7G7lucQnf+4tFpCVF79KLCDPy0k4qO7s0i786r5x3DrdztMPLA5sP8vXHdpx4fFZBGn93aSXXLSmJS1Lw+rQD2alSPW48bhfHe6ZezaCjz8e2w+387cWz7Q7FdpoMoqTT68M7EOB3b9fz8z/XkuB2cftllWQkJ3DDslLy0pNivlPRYCLCOdND20msWTiNJ3c04nEL/qDhZ3+u5UuPbOOnf66JS1LQoaXOJSLkpCVOyT6DN/e1EggaLnT4kNJ40GQwTl5fgO8/8x73vlF3ouzy+YX869qzKR3U/GPnFHeXS/jwkpIT319zdjHP7TrKf71YcyIp3H5ZJR9eUhL1TmdjTGgGstYMHCsn1TMlm4le2dtCelKCo5artosmg3Hw+gJ87Jeb2XrwOLesmM784gwWlmRy7oxcu0M7o9CGGcVctXDaiaRw+8Pb+OP2Rn70l4uj2n7a7w9iDCRrzcCxslMTp1wzkdcX4KnqRi45q9DWTe+dQpPBGBlj+PofdrD14HH+6+alrF16uu2fnSsyKfzfG3V8/5ndfOTON3h4/UoKM5Oj8honNrbRmoFj5aZ52HM0+uvdONlT1Y10ev3cssLeTe+dQtPhGNQ0dfGpe7fwh3ca+PLlcydsIojkcgm3XjCTBz+zkqOdXm7+xSYOtfVG5bn7dMtLx8tO9dA+xZqJHnrrEDPz0zh/Vp7doTiCJoNRqmnq4ob/eYOtB4/zjWvm88VL59gdUlSdV5HLfX+zgtaufq7971f54/Yj417NMrxxig4tda6c1FAH8lRZuXRvUxdVB49zy4pyx0zMtJsmg1Ho6PXxmfurSE508+yXLuQzF87CFcex+vFyXkUuT/3daqbnpfLFh97h2v9+jeYu75ifz+sL73+srZJOlZPqIWg4acmTyezBzYfwuF385bnaRBSmyWAU/uWJnTS093HXx885ZaTQZFOem8rjf7uKH9+4hPeOdnLv63Vjfq4TzURaM3Cs9yeeTf5OZK8vwB/erueqs6edWIpDaTIYsWd3HmXD9iN88dJKllc4f7RQNCS4XXzk3DIum1/EI1sO0+8f23r34Q7kFI++3ZwqJy007PnYFEgGT+/QjuOh6F/nCPQNBPiXJ3aysCSTz0/BmYqfWDmDtp4Bnt15dEzna5+B84VrBlNhfaLfbDqoHcdD0GQwAg9sPkhLVz/f/vDCKTke+YI5+VTkpfJ/r9dhzOg7GLXPwPlONBNN8mWs3zl0nLcPtbPu/BnacTyIY/6zicgaEdkjIrUicofd8YT1DQS465V9XDAnn/OmSPPQYC6XcOvqWWw73M6m/cdGfX5rdz+gfQZONlX6DH712gEykhO4cbk2EQ3miGQgIm7g58DVwALgFhFZYG9UoU+0X/tDNa3dA9x++chWEJ2sbjy3jPz0JP7n5dpRnXf4WC8/fbGGxWVZFGYkxSg6NV4ZyQm4XTKpk8Hrta08s/MoH10xPaoLRU4WTrkiK4BaY8x+ABF5GFgLvBvtF/rGYzt468DIPt229/lo6erny5fPnbK1grDkRDefWT2T7z3zHpf/5BVGWsFu6xnAAD//6DmTchjuZOFyCdkpifxm0yH+tKvJ7nCizh80HGjtoTQ7hb+5YKbd4TiSU5JBKXA44vt64AODDxKR9cB6gOnTp4/phUqyU6gsGtk+pyLCjeeWcfG8wjG91mTz8ZUz2N/SQ1f/yNuV54rwiZUzKM9NjWFkKhpuu3QOW+pG3ww4UXx0xXQ+cf4MHcgwDBlLh2DUgxC5EbjKGPNp6/tPACuMMV8c7pzly5ebqqqqeIWolFKTgohsNcYsH1zuiD4DQjWByB6dMuCITbEopdSU45RksAWoFJGZIuIBbgY22ByTUkpNGY7oMzDG+EXkNuA5wA3cY4zZZXNYSik1ZTgiGQAYY54GnrY7DqWUmoqc0kyklFLKRpoMlFJKaTJQSimlyUAppRQOmXQ2FiLSAhwc4+n5QGsUw4kWp8YFzo1N4xodjWv0nBrbWOOaYYwpGFw4YZPBeIhI1VAz8Ozm1LjAubFpXKOjcY2eU2OLdlzaTKSUUkqTgVJKqambDO62O4BhODUucG5sGtfoaFyj59TYohrXlOwzUEopdbKpWjNQSikVQZOBUkqpqZcMRGSNiOwRkVoRucPGOMpF5CUR2S0iu0Tkdqv82yLSICLbrNs1NsRWJyI7rNevsspyReR5EamxvubEOaZ5Eddkm4h0isiX7LpeInKPiDSLyM6IsiGvkYT81HrPVYvIOXGO60ci8p712o+JSLZVXiEifRHX7q44xzXs705EvmZdrz0iclWc43okIqY6Edlmlcfzeg33/yF27zFjzJS5EVoeex8wC/AA24EFNsVSDJxj3c8A9gILgG8D/2DzdaoD8geV/RC4w7p/B/ADm3+PR4EZdl0v4ELgHGDnma4RcA3wDCDASmBznOO6Ekiw7v8gIq6KyONsuF5D/u6sv4PtQBIw0/qbdccrrkGP/xj4pg3Xa7j/DzF7j021msEKoNYYs98YMwA8DKy1IxBjTKMx5m3rfhewm9Be0E61FrjPun8fcL2NsVwG7DPGjHUG+rgZYzYCgzcMHu4arQXuNyGbgGwRKY5XXMaYPxlj/Na3mwjtJBhXw1yv4awFHjbG9BtjDgC1hP524xqXiAhwE/BQLF77dE7z/yFm77GplgxKgcMR39fjgH/AIlIBLAM2W0W3WVW9e+LdHGMxwJ9EZKuIrLfKiowxjRB6owKFNsQVdjMn/4Hafb3ChrtGTnrf/Q2hT5BhM0XkHRF5RURW2xDPUL87p1yv1UCTMaYmoizu12vQ/4eYvcemWjKQIcpsHVsrIunA74EvGWM6gTuB2cBSoJFQNTXeVhljzgGuBr4gIhfaEMOQJLQt6oeB31pFTrheZ+KI952IfAPwAw9YRY3AdGPMMuDvgQdFJDOOIQ33u3PE9QJu4eQPHXG/XkP8fxj20CHKRnXNployqAfKI74vA47YFAsikkjoF/2AMeYPAMaYJmNMwBgTBH5BjKrHp2OMOWJ9bQYes2JoClc7ra/N8Y7LcjXwtjGmyYrR9usVYbhrZPv7TkTWAdcCHzNWI7PVDNNm3d9KqG1+brxiOs3vzgnXKwH4C+CRcFm8r9dQ/x+I4XtsqiWDLUCliMy0PmHeDGywIxCrPfJXwG5jzE8iyiPb+W4Adg4+N8ZxpYlIRvg+oc7HnYSu0zrrsHXAE/GMK8JJn9bsvl6DDHeNNgCftEZ8rAQ6wlX9eBCRNcBXgQ8bY3ojygtExG3dnwVUAvvjGNdwv7sNwM0ikiQiM6243opXXJbLgfeMMfXhgnher+H+PxDL91g8esaddCPU676XUFb/ho1xXECoGlcNbLNu1wC/BnZY5RuA4jjHNYvQSI7twK7wNQLygBeBGutrrg3XLBVoA7Iiymy5XoQSUiPgI/Sp7NbhrhGhKvzPrffcDmB5nOOqJdSeHH6f3WUd+xHrd7wdeBu4Ls5xDfu7A75hXa89wNXxjMsqvxf43KBj43m9hvv/ELP3mC5HoZRSaso1EymllBqCJgOllFKaDJRSSmkyUEophSYDpZRSaDJQSimFJgOllFLA/wdEMmEz4yFORQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "projection = []\n",
    "m = np.array(im_r)\n",
    "for x in range(0, im_r.width):\n",
    "    projection.append(np.sum(m[x]))\n",
    "plt.plot(projection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TASK: Can you see the \"tooth\" pattern on the rectangle projection on the right? Where is it coming from, what do you think? \n",
    "# NOTE: You don't need to write code, just type your answer here\n",
    "\n",
    "# SOLUTION(TODO): this is happening because our rotation algorithm is not applying any anti-aliasing strategies and thus \n",
    "# straight, axis-aligned lines turn into \"ladders\" that are not smooth when rotated. \n",
    "# Therefore, we are seeing sudden \"jumps\" when summing pixels along neighboring rays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing the Sinogram\n",
    "\n",
    "Now, let's assume that our scanner is doing a full 180° rotation, sampling a projection every 3 degrees. What you will end up is a collection of projections (1D \"X-ray\" images) from every angle. Let's store projections in a list of tuples so that we keep track of what angle was used to compute a projection."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "projections = []\n",
    "for angle in range(0, 180, 3):\n",
    "    p = []\n",
    "    im_r = im.rotate(angle)\n",
    "    for x in range(0, im.width):\n",
    "        p.append(np.sum(np.array(im_r)[x]))\n",
    "    projections.append((angle, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/UUT2A7Pw9wQCh5IKgErnfo2I5KtqlTOcVDvSmozp19nTy3ObjvDGnjpe3lFNUW4y//m5C7miOMft0lzxwVk5PLvpCNuPNHFBYbrb5RgPGtEwkYgsBb4OfFRV2wPac0TE59yfjn+iuNwZ/mkRkUXOXkS3Ac87q60GVjj3VwS0GzNiL2yt4p5nt7HxUAN3fHAGf/r7D7DknFycndgizuKiHESwoSIzqDP2DETkSeAKIFtEKoBv4d97KA5Y43y43nH2HLoc+K6I9AC9wB2q2j/5/CX8eyYl4J9j6J9n+BHwtIjcDhwCbg7KT2Yi2r7aVmJ8wrp7rgzrS1gGS2ZSLHMnpfHm3jq+clWR2+UYDzpjGKjqLQM0PzrIss8AzwzyWClw3gDt9cBVZ6rDmLNxoK6NyZmJFgQBFhfl8Ms3ymjr7CFpHFzRzQSXfVLMuFR+tJVp2clul+EpJVMz6FPYUtHodinGgywMzLjT26ccrG9nRk6S26V4yvxC/8H9dp4iMxALAzPuVDYep6unj2nZFgaB0hJjKMpNZtMh6xmY01kYmHFnf10rANNzbJjoVAsmZ7DpUINdG9mcxsLAjDvldW0ATLdhotMsnJJBY3s35Ufb3C7FeIyFgRl3DhxtIyU+mqxxdpH7YFgwxT9vsNHmDcwpLAzMuFHf2snL26vYUtHI9JzkiD3AbCjTs5PISIyh9OCxMy9sIortbGzGhV+s3ccDb5TR0e2/vOMnS4Y8kW7EiooSLpyaybsHLAzMySwMTNg7VN/OfWv2cuU5uXz5ihl09fYxJz/N7bI86+LpWby6s4bqpo5xfQ1oc3YsDEzYe+69IwB878bzmJSe4HI13nfxtEwA3j1Qz7J5k86wtIkUNmdgwpqq8sfNR1g0PdOCYJjOzU8lJT6ad8rr3S7FeIiFgQlrmw83cuBoGx+fb3MEw+Vz5g1e21XLnU9ssjOZGsDCwIS5l3dUE+MTlp4fWZeyHK0rz8mlrqWTV3dU88MXd9lBaMbCwIS3dfvrmV+YQWp8jNulhJXPXDyZ7d+5lu8tO4/d1S2U2nEHEc/CwIStpuPdbD/SxKIZWW6XEnZEhOS4aD46byIp8dH89zvvu12ScZmFgQlb6w8co0/hkukWBiOVGBvNJxYU8NK2ajYdst5BJLMwMGGlo7v3xP11++uJjY5i/mS7pu9ofHnJDPLT47nt0fVsOWxnNI1UFgYmLKgqj687yNzvvMoDr5cBsK68npIpGcTH+NwtLszlpsTz1MpFpMZH86/Pb7fJ5AhlYWDCwkNvlvOvz+8gKdbHf7y2jx+9tJtdVc0sKc51u7RxIT8tgS9dMYMtFU12ErsINawwEJFVIlIrItsD2jJFZI2I7HO+ZjjtIiL3i0iZiGwVkQUB66xwlt8nIisC2heKyDZnnfvFzjBmTvHCtkoWTsnglX+4nIRYHw+9uZ8rz8nl85dNdbu0ceMTCwtIS4hh1V8OuF2KccFwewa/AZae0nYPsFZVi4C1zvcA1wFFzm0l8CD4wwP4FnAxcBHwrf4AcZZZGbDeqa9lIlhTezc7KptZXJRNbko8/3bzBdw4byL/79Pz7YL3QZQYG80tF03m5e3V1DR3uF2OCbFhfZJU9S3g1NMcLgMec+4/BtwY0P64+r0DpItIPnAtsEZVj6lqA7AGWOo8lqqq69Q/WPl4wHMZw7sH6lGFS2dkA3D17Dx+vnw+ibF2aq1gu+H8fPrUv6eWiSyj+bcqT1WrAJyv/YO3k4DDActVOG1DtVcM0H4aEVkpIqUiUlpXZ4fQR4q/7q8nPiaKCwrtTKRj7Zz8FBJifDZvEIHGoo890Hi/jqD99EbVh1W1RFVLcnJyRlGiCSfvlNdTMiWTuGjba2isxfiimFeYbmEQgUYTBjXOEA/O11qnvQIoDFiuAKg8Q3vBAO3G0Njexe7qFi6xo4xDZuGUDHZWNdPW2eN2KSaERhMGq4H+PYJWAM8HtN/m7FW0CGhyhpFeAa4RkQxn4vga4BXnsRYRWeTsRXRbwHOZCHfAuXB7cV6Ky5VEjoVTM+jtU7ZU2AFokWS4u5Y+CawDikWkQkRuB34EXC0i+4Crne8BXgTKgTLgEeDLAKp6DPgesMG5fddpA/gS8Gtnnf3AS6P/0cx4UNFwHICCTLtWQagsKPTv5LfxoA0VRZJh7Y6hqrcM8tBVAyyrwJ2DPM8qYNUA7aXAecOpxUSWI43+MLAL14ROWmIMRbnJbLZTU0QU20nbeFpFQztpCTGk2CmqQ+qc/FT21LS4XYYJIQsD42kVDccpyLBeQagV5yVT0XDcJpEjiIWB8bQjFgauKHIm7PfVtrpciQkVCwPjWapKRcNxJqUnul1KxOnfe2tvtQ0VRQoLA+NZDe3dHO/utZ6BCwozE4mPibJ5gwhiYWA8q6KhHYBJFgYh54sSZuYms9fCIGJYGBjPOnGMgYWBK2blpVgYRBALA+NZR06Egc0ZuKE4L4Wa5k6a2rvdLsWEgIWB8ayKhnZS4qJJS7BjDNwwMzcZgP1HbY+iSGBhYDzrSGMHE+3IY9fkpMQBUN/a5XIlJhQsDIxn1bZ0kJcW73YZESsr2R8Gx9o6Xa7EhIKFgfGs6qYOJqTGuV1GxMpKigXgqPUMIoKFgfGknt4+jrZ2MiHVegZuiY/xkRTr41ibhUEksDAwnlTX2kmfQq6Fgasyk2Opb7VhokhgYWA8qabZ/wfIegbuykqKo956BhHBwsB4UnVTBwATbALZVVlJsbY3UYSwMDCeVNPsD4Ncm0B2VVZyrM0ZRAgLA+NJNc0dREcJ2UkWBm7KTIqjvq0T/wUMzXg24jAQkWIR2RxwaxaRu0Xk2yJyJKD9+oB17hWRMhHZIyLXBrQvddrKROSe0f5QJvxVN3eQmxJHVJS4XUpEy06OpbtXabGL3Ix7w7oG8kBUdQ8wD0BEfMAR4Dng88DPVPXfApcXkdnAcmAOMBF4TURmOQ8/AFwNVAAbRGS1qu4caW0m/NU02wFnXpDpHGtQ39pFql16dFwL1jDRVcB+VX1/iGWWAU+paqeqHgDKgIucW5mqlqtqF/CUs6yJYNVNHeSlWBi4rT8M7Cjk8S9YYbAceDLg+7tEZKuIrBKRDKdtEnA4YJkKp22wdhPBaps7bU8iD8h2TklhRyGPf6MOAxGJBT4K/N5pehCYgX8IqQq4r3/RAVbXIdoHeq2VIlIqIqV1dXWjqtt4V1tnDy2dPeTZMQau+1vPwMJgvAtGz+A6YJOq1gCoao2q9qpqH/AI/mEg8P/HXxiwXgFQOUT7aVT1YVUtUdWSnJycIJRuvKja2a00z3Yrdd3f5gxsmGi8C0YY3ELAEJGI5Ac89jFgu3N/NbBcROJEZBpQBKwHNgBFIjLN6WUsd5Y1Eaqm/4Az6xm4Lj7GR3JctB2FHAFGvDcRgIgk4t8L6O8Cmn8iIvPwD/Uc7H9MVXeIyNPATqAHuFNVe53nuQt4BfABq1R1x2jqMuGtpsXpGdicgSdkJdtRyJFgVGGgqu1A1ilttw6x/A+AHwzQ/iLw4mhqMeNHdZN/SMLmDLwhM8mOQo4EdgSy8Zya5g6S46JJjhvV/yomSDISY2k8bmEw3lkYGM+pbuqwyWMPSUuIobG92+0yzBizMDCeU9PSYccYeEhaQgxNxy0MxjsLA+M5NXb0saekJcTQ0tFDb5+drG48szAwntLXp9S2dNqeRB6Snug/J1Gz9Q7GNQsD4ylH2zrp6VM7xsBD0hL8YdBoYTCuWRgYT6lttt1Kvaa/Z2DzBuObhYHxlP7LXdreRN5xomfQbruXjmcWBsZT+s9LZHsTeUdagv/8RNYzGN8sDIyn1DR3ECWQk2w9A6+wYaLIYGFgPKWmuYPs5DiiffbW9Ir+YaImO/BsXLNPnPGUupZOclKsV+AlMb4okmJ9Z7U3UVXTcZb+/C0eeL3spPbmjm5uevCv/Msft6Nqxy14iZ38xXhKW2cvKfH2tvSaU49CPnysnYb2Lv66v54/vneEhVMy+PiCScT6fPSqcu+z29hd3cLu6j0kxvoomZIJwE9e2U3p+w2Uvt9ATkocX7mqyK0fyZzCPnXGU9q6euwYAw9KS4w9cX6il7ZV8eUnNtH/j/3cgjR+X1rBb989dGJ5X5Sw6nMlrHr7IN/5086TnusnN83lnfJ6/n3NXmbnp/Kh2Xkh+znM4CwMjKe0dfaQaGcr9Zy0hGiaj3fzfn0b//yHrcwtSOfvl8ykIDOBcyakUtvcwdaKphPLT85KZFZeCpfOyGZdeT29vf7kyE2NY25BOsvmTWR3VQtf+8MWXr77cjuuxAPsU2c8pa2rl6RYn9tlmFOkJ8RSfrSVH7ywCxF44NPzKchIPPF4bmo8H5p9+h/0+BgfS4pzT2uPi/bxi0/P58P3v833X9jFL26ZP6b1mzOzCWTjKe2dPSRZz8Bz0hJiONbWzbryem6Ym39SEIzUjJxkbi4p4NUd1bR19gShSjMaFgbGM/r6lPZu6xl4UXpiDEdbO2np6OGiaZlBe94bzs+ns6ePtbtrg/acZmQsDIxnHO/uRRWbM/CgNOfAM4ALpwYvDEqmZpKbEscLWyuD9pxmZEYdBiJyUES2ichmESl12jJFZI2I7HO+ZjjtIiL3i0iZiGwVkQUBz7PCWX6fiKwYbV0m/LR1+YcKbJjIe/oPPJuYFh+UIaJ+vijh+vPzeX1PHS0ddlCbm4LVM1iiqvNUtcT5/h5graoWAWud7wGuA4qc20rgQfCHB/At4GLgIuBb/QFiIkd7Zy+ADRN5ULpzfqJgDhH1u2ZOHl09fbxbfizoz22Gb6yGiZYBjzn3HwNuDGh/XP3eAdJFJB+4FlijqsdUtQFYAywdo9qMR/X3DBJjrWfgNf09gwvHIAzmF2YQHSVsOtQQ9Oc2wxeMMFDgVRHZKCIrnbY8Va0CcL7271s2CTgcsG6F0zZY+0lEZKWIlIpIaV1dXRBKN17S1t8ziLOegdfMn5zOLRdN5vrz8oP+3AmxPuZMTGXj+xYGbgpGGFymqgvwDwHdKSKXD7GsDNCmQ7Sf3KD6sKqWqGpJTk7OyKo1nmVzBt6VFBfNDz9+PhlJsWPy/AunZLKlopHu3r4xeX5zZqMOA1WtdL7WAs/hH/OvcYZ/cL727zdWARQGrF4AVA7RbiLI3+YMLAwizcIpGXR097GzstntUiLWqMJARJJEJKX/PnANsB1YDfTvEbQCeN65vxq4zdmraBHQ5AwjvQJcIyIZzsTxNU6biSB/mzOwYaJIs3CKf38RGypyz2j/BcsDnhOR/ud6QlVfFpENwNMicjtwCLjZWf5F4HqgDGgHPg+gqsdE5HvABme576qq7VoQYdo7bZgoUk1Ii2dSegIbDzXwBaa5XU5EGtWnTlXLgQsGaK8HrhqgXYE7B3muVcCq0dRjwltbl00gR7K5BWnssmEi19gRyMYz2jp7iI4SYu0qZxFpVl4KB+vb6OjudbuUiGSfOuMZ7V29JMb6cIYdTYQpnpBCn0JZbavbpUQkCwPjGW12xtKINisvBYC9NS0uVxKZLAyMZ7R1WRhEsqlZicT6othjYeAKCwPjGW2ddvrqSBbti2JGbjJ7qy0M3GBhYDyjvavHzksU4YrzktlbY3MGbrAwMJ7R1tlrw0QRbtaEFI40HqfZTmcdchYGxjPau3rsGIMIV9w/iWxDRSFnYWA8o7Wz14aJItx5k9IA2FrR5HIlkcfCwHhGe1ePTSBHuLzUePLT4tl8uNHtUiKOhYHxhL4+pb3L5gwMzCtMtzBwgYWB8YTj3XZeIuM3rzCdQ8faqW/tdLuUiGJhYDyhrdMueWn85hWmA1jvIMQsDIwn2BlLTb/zC9LwRYmFQYhZGBhP6O8Z2FXOTGJsNLPyUnjvkIVBKFkYGE9otQvbmAAXT8tkw8FjdjrrELIwMJ7QdNx/xGlaQozLlRgvuKI4h86ePt4pr3e7lIhhYWA8oandHwbpiRYGBhZNzyIuOoo39tS5XUrEsDAwntB4vAuAjMRYlysxXhAf4+OSGVm8udfCIFRGHAYiUigir4vILhHZISJfddq/LSJHRGSzc7s+YJ17RaRMRPaIyLUB7UudtjIRuWd0P5IJR43t3cT4hEQ7Atk4lhTncuBoGyBhs80AAArpSURBVAePtrldSkQYzWxdD/B/VHWTiKQAG0VkjfPYz1T13wIXFpHZwHJgDjAReE1EZjkPPwBcDVQAG0RktaruHEVtJsw0Hu8mLSHWLnlpTrhsZjYA6w8cY2p2ksvVjH8jDgNVrQKqnPstIrILmDTEKsuAp1S1EzggImXARc5jZapaDiAiTznLWhhEkMb2LpsvMCeZlp1EfEyUXQYzRIIyZyAiU4H5wLtO010islVEVolIhtM2CTgcsFqF0zZY+0Cvs1JESkWktK7OxhLHk8b2btJtTyITwBclFOWm2GUwQ2TUYSAiycAzwN2q2gw8CMwA5uHvOdzXv+gAq+sQ7ac3qj6sqiWqWpKTkzPa0o2HNLZ3W8/AnGZWXgp77NoGITGqMBCRGPxB8FtVfRZAVWtUtVdV+4BH+NtQUAVQGLB6AVA5RLuJIE3OnIExgYonJFPb0klDW5fbpYx7o9mbSIBHgV2q+u8B7fkBi30M2O7cXw0sF5E4EZkGFAHrgQ1AkYhME5FY/JPMq0dalwlPNmdgBjKr/8pnNlQ05kazN9FlwK3ANhHZ7LR9A7hFRObhH+o5CPwdgKruEJGn8U8M9wB3qmovgIjcBbwC+IBVqrpjFHWZMNPV00dbV6/NGZjTFE/4WxhcPD3L5WrGt9HsTfQ2A4/3vzjEOj8AfjBA+4tDrWfGt/5TUaQn2TCROdmE1HhS4qNtEjkE7Ahk47om5+hj6xmYU4kIxXkp7K1udbuUcc/CwLiu0c5LZIZwbn4qO6ua6e0bcCdDEyQWBsZ1J8LA9iYyA7igMJ3Wzh7211nvYCxZGBjXNR63noEZ3InLYNrFbsaUhYFxXWO7f84gzcLADGB6dhIp8dG8Z5fBHFMWBsZ1je3d+KKEFLvKmRlAVJQwrzDdrok8xiwMjOsaj3eRlhBjZyw1g5pXmM6e6mbau3rcLmXcsjAwrrOT1JkzmVeYTp/Ctoomt0sZtywMjKu6e/s4dKzdJo/NkE5MIttQ0ZixMDCuOXi0jZse/CtbK5q4Zs4Et8sxHpaVHEdhZoKFwRiyGTsTUj29feyubuHtsqP8Yu0+on1RPPiZBVx3fv6ZVzYRbV5hBqUHj7ldxrhlYWBCora5g++9sIs/76qhrasXgEumZ3HfJy9gYnqCy9WZcDCvMJ0/bamkprmDvNR4t8sZdywMzJhq7ezhqfWH+MWfy+jo7uUTCwu4eFomJVMzmWQhYM5C/7zBe4caWXqeDSsGm4WBCTpVpay2lec3V/L4uoM0d/Rw2cwsvrvsPGbkJLtdnglTcyamEuMTNh+2MBgLFgYmqFo6urnpwXXsqWlBBJbOmcDffXDGif/qjBmp+Bgf5+ansvlwg9uljEsWBiao7nt1L3trW/j2R2bzodl5FGQkul2SGUcWTM7gqQ2H6OjuJT7G53Y544rtWmqCZmtFI4+vO8iti6bwucumWRCYoFtyTi4d3X38peyo26WMOxYGJihUle/9z04yk+L4p2uL3S7HjFOLpmeSHBfNmp01bpcy7lgYmKD48+5aNhxs4O4PFZEab0cTm7ERF+3jg8U5vLarlj672E1QeSYMRGSpiOwRkTIRucfteszwdfb08uOXdzMtO4lPXVjodjlmnLv63DyOtnbaKa2DzBNhICI+4AHgOmA2cIuIzHa3KjMcqso3nt3O3ppWvnH9ucT4PPGWMuPYkuJcEmN9fPO5bTS0dbldzrjhlb2JLgLKVLUcQESeApYBO4P9Qt98bhvrD9gh7cHS06ccONrG3R8q4urZeW6XYyJAWmIMv7p1Ibc/VsrVP3uTjMTIu1zqoysuZHJWcHfQ8EoYTAIOB3xfAVx86kIishJYCTB58uQRvdDE9ASK8uzAp2D6xIJJ3LlkpttlmAiyuCiH33z+Qn777iFUI2/uIDY6+D1wr4TBQFc1Oe03rKoPAw8DlJSUjOgdYH+0jBkfLp2RzaUzst0uY9zwygBvBRA481gAVLpUizHGRByvhMEGoEhEpolILLAcWO1yTcYYEzE8MUykqj0ichfwCuADVqnqDpfLMsaYiOGJMABQ1ReBF92uwxhjIpFXhomMMca4yMLAGGOMhYExxhgLA2OMMYCE69F7IlIHvD/C1bMBL54Q3at1gXdrs7rOjtV19rxa20jrmqKqOac2hm0YjIaIlKpqidt1nMqrdYF3a7O6zo7Vdfa8Wluw67JhImOMMRYGxhhjIjcMHna7gEF4tS7wbm1W19mxus6eV2sLal0ROWdgjDHmZJHaMzDGGBPAwsAYY0zkhYGILBWRPSJSJiL3uFhHoYi8LiK7RGSHiHzVaf+2iBwRkc3O7XoXajsoItuc1y912jJFZI2I7HO+ZoS4puKAbbJZRJpF5G63tpeIrBKRWhHZHtA24DYSv/ud99xWEVkQ4rp+KiK7ndd+TkTSnfapInI8YNs9FOK6Bv3dici9zvbaIyLXhriu3wXUdFBENjvtodxeg/19GLv3mKpGzA3/6bH3A9OBWGALMNulWvKBBc79FGAvMBv4NvBPLm+ng0D2KW0/Ae5x7t8D/Njl32M1MMWt7QVcDiwAtp9pGwHXAy/hv6LfIuDdENd1DRDt3P9xQF1TA5dzYXsN+LtzPgdbgDhgmvOZ9YWqrlMevw/4Vxe212B/H8bsPRZpPYOLgDJVLVfVLuApYJkbhahqlapucu63ALvwXwvaq5YBjzn3HwNudLGWq4D9qjrSI9BHTVXfAo6d0jzYNloGPK5+7wDpIpIfqrpU9VVV7XG+fQf/lQRDapDtNZhlwFOq2qmqB4Ay/J/dkNYlIgJ8EnhyLF57KEP8fRiz91ikhcEk4HDA9xV44A+wiEwF5gPvOk13OV29VaEejnEo8KqIbBSRlU5bnqpWgf+NCuS6UFe/5Zz8AXV7e/UbbBt56X33Bfz/QfabJiLvicibIrLYhXoG+t15ZXstBmpUdV9AW8i31yl/H8bsPRZpYSADtLm6b62IJAPPAHerajPwIDADmAdU4e+mhtplqroAuA64U0Qud6GGAYn/sqgfBX7vNHlhe52JJ953IvJNoAf4rdNUBUxW1fnAPwJPiEhqCEsa7Hfnie0F3MLJ/3SEfHsN8Pdh0EUHaDurbRZpYVABFAZ8XwBUulQLIhKD/xf9W1V9FkBVa1S1V1X7gEcYo+7xUFS10vlaCzzn1FDT3+10vtaGui7HdcAmVa1xanR9ewUYbBu5/r4TkRXAh4HPqDPI7AzD1Dv3N+Ifm58VqpqG+N15YXtFAx8HftffFurtNdDfB8bwPRZpYbABKBKRac5/mMuB1W4U4oxHPgrsUtV/D2gPHOf7GLD91HXHuK4kEUnpv49/8nE7/u20wllsBfB8KOsKcNJ/a25vr1MMto1WA7c5e3wsApr6u/qhICJLga8DH1XV9oD2HBHxOfenA0VAeQjrGux3txpYLiJxIjLNqWt9qOpyfAjYraoV/Q2h3F6D/X1gLN9joZgZ99IN/6z7Xvyp/k0X6/gA/m7cVmCzc7se+C9gm9O+GsgPcV3T8e/JsQXY0b+NgCxgLbDP+ZrpwjZLBOqBtIA2V7YX/kCqArrx/1d2+2DbCH8X/gHnPbcNKAlxXWX4x5P732cPOct+wvkdbwE2AR8JcV2D/u6Abzrbaw9wXSjrctp/A9xxyrKh3F6D/X0Ys/eYnY7CGGNMxA0TGWOMGYCFgTHGGAsDY4wxFgbGGGOwMDDGGIOFgTHGGCwMjDHGAP8fezKEzY4903EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RShG5C/ghkAxs7DeE9CqgRER2Ar8G7lZVX4/U54CfAKV4awy+fobvANeLyCHgeue5MUFhR0Ujbxys495rZgftNY3Hy+K8NAC2V1hTUSQacq1dVV0zQPFPB9n3BeCFQbYVA4sGKK8Hrh0qDmPcsP6twyTHRfOJFTPcDmXCZSbFMSMzgR3WbxCRbAayMYOobmrn5V3VfOyS/JC5RsFYLclPY3vFKbfDMC6wZGDMAPr6lG/9bh99qnzqsgK3wwmYpflp1DR32qJ1EciSgTED+Pf/3svvSqr5yo3zyc9IcDucgFnirMBqQ0wjjyUDY/rZXdXEE389wqcuK+Du9810O5yAWpibQmx0FDusEzniWDIwpp9fbjlGfEwUX7p+Ls56ihEjNjqKC6amWCdyBLJkYIxj/4lmTjR18NKOKm5ZPDUsZxoPx9L8dEqqGunutUthRhJLBsbgnU+w6v++yeUP/om2rl4+GQFDSQezZHoaHd19HDjR4nYoJoAiY7ycMUN45M+lpMRHn7ly2UV5qW6H5Jql+e9NPls0LXLPQ6SxZGAiXmltC6/sqeF/XDObL98wz+1wXJeXPomspFh2HGvkjpWRW0OKNNZMZCLeo6+XEx8TxdoImk9wPiLCkvx0m3wWYSwZmIh2vLGd326vYvUl08N+7aGRWDo9jfK6Vpraut0OxQSIJQMT0R5/sxyAz1xZ6HIkwcXXb7Cj0oaYRgpLBiZiNbZ18ezWCm5ZMpW89MiZZTwcF+alIoLNN4gglgxMxPrt9irau3v5zBWRNct4OJLjY5iTk2T9BhHEkoGJWL/aVskFU1NYODXF7VCC0tL8dHZWNOJcyNCEOUsGJiLtPd7MnuPNfHRZ3tA7R6gl09M41dbNkfq2oXc2Ic/mGZiI8a+/3U1JVROfvryAF96tIsYj3LJkmtthBa1LCrzXe95cXk9hVqLL0ZiJZjUDEzE27q1hZ0UjX3h2B5vL6vn8NXPISIx1O6ygNSs7kSkp8bxVetLtUEwAWM3ARISWjm5ONHfwhWvncElBBhdOSyU1ITIXohsuEeGy2Zm8tr+Wvj4lKiqyVnCNNMOqGYjIehGpFZHdfmUZIrJRRA459+lOuYjIQyJSKiIlInKx3zFrnf0Pichav/JlIrLLOeYhibR1g82EK6trBWDh1BSumJNliWCYrpidxam2bvadaHY7FDPBhttM9ASwql/ZfcAmVZ0DbHKeA9wEzHFu64BHwJs8gAeAFcBy4AFfAnH2Wed3XP/3MmbE/EfBlNaeBmBOTpJb4YSky2dnAfAXayoKe8NKBqr6BtDQr/hW4Enn8ZPAbX7lT6nXZiBNRHKBG4GNqtqgqqeAjcAqZ1uKqr6t3r/ep/xey5gR213VxNr1W1n0wCscrffWCA7VthDriWJ6BF3CcjxMTolndk4Sb5fVux2KmWBj6UCerKrVAM59jlM+Dajw26/SKTtfeeUA5caMWF+f8ndPvMOuqiY6e/r4xeajAJTVnqYgK4Foj42ZGKkFuSmU1p12OwwzwSbiL2Og9n4dRfm5LyyyTkSKRaS4rq5uDCGacHWo9jR1LZ3cd9N8blw0heeLK2nv6qW09jSzrYloVAozE6g61U5nT6/boZgJNJZkUOM08eDc1zrllUC+3355wPEhyvMGKD+Hqj6mqkWqWpSdnT2G0E242nLY25xx6cxM7lg5g6b2bp4vruBYQxuzsy0ZjEZBViJ9ChUNNvksnI0lGWwAfCOC1gIv+ZXf6YwqWgk0Oc1IrwA3iEi603F8A/CKs61FRFY6o4ju9HstY0ZkS3kDU1PjyUufxIrCDC6YmsIDG/bQpzDLagaj4ptwdvikJYNwNtyhpc8AbwPzRKRSRO4CvgNcLyKHgOud5wAvA+VAKfA48A8AqtoAfBN4x7n9u1MG8DngJ84xZcDvx/6jmUijqmw5XM+KmZmICCLCL+5awepL8kmKi+bi6elDv4g5hy8ZHDnZ6nIkZiINa9KZqq4ZZNO1A+yrwD2DvM56YP0A5cXAouHEYsxgyupOc/J0FysKM86UpSfG8p0PX8R3PnyRi5GFtrSEWNISYjhcb8kgnNnQChM2th72Lre8Ymamy5GEn4LMRA7XWTIIZ5YMTNgoqWwkLSGGgkybSzDeCrMSOWI1g7BmycCEjZLKJi6cloqtZjL+CrMSqW7qoL3LhpeGK0sGJix0dPdysKaFi/JS3Q4lLBU4nchHG6x2EK4sGZiwsK+6mZ4+5cJpaW6HEpZ8TW9HbHhp2LJkYMLCrqomAKsZTJD8dG8yqDxlySBcWTIwYaGksomspFhyU+PdDiUspSXEkBQXTeWpdrdDMRPEkoEJC7us83hCiQh56ZNsSYowZsnAhLyO7l5K606zaJo1EU2k/IwEKqyZKGxZMjAh72BNC719yoLcFLdDCWv56QlUNLSfddEgEz4sGZiQt7+6BcCSwQTLS59Ee3cv9a1dbodiJoAlAxPy9lY3kxDrYYZdxWxC5Tvn1/oNwpMlAxPy9lU3M29KMlFR1nk8kfIzJgHYiKIwZcnAhDRVZV91szURBYBvroF1IocnSwYmpB1v6qC5o8eSQQAkxkWTkRhLRYPVDMKRJQMT0vYdbwZgwZRklyOJDPnpk2wWcpiyZGBC2sFa70iieZYMAmJmdhIHa1rcDsNMAEsGJqTVNHWQEh9NcnyM26FEhMV5qdQ0d1LdZE1F4caSgQlpNc2d5KTYekSBsjjfuyrszopGlyMx482SgQlpNS0dTE6JczuMiLEgN4UYj7CjosntUMw4G3UyEJF5IrLD79YsIl8UkW+ISJVf+c1+x9wvIqUickBEbvQrX+WUlYrIfWP9oUzkqG3uZHKy1QwCJT7Gw8LcFHZUnHI7FDPORp0MVPWAqi5R1SXAMqANeNHZ/APfNlV9GUBEFgKrgQuAVcCPRMQjIh7gYeAmYCGwxtnXmPNSVWpbOqyZKMAW56exq7KJ3j5boyicjFcz0bVAmaoePc8+twLPqmqnqh4GSoHlzq1UVctVtQt41tnXmPM61dZNd69aM1GALc5Lo7Wrl7K6026HYsbReCWD1cAzfs/vFZESEVkvIulO2TSgwm+fSqdssPJziMg6ESkWkeK6urpxCt2EqprmDgAmW80goHxLhe+rbnY5EjOexpwMRCQWuAX4lVP0CDALWAJUA9/37TrA4Xqe8nMLVR9T1SJVLcrOzh5T3Cb0vZcMrGYQSFOcq8nVNne6HIkZT9Hj8Bo3Ae+qag2A7x5ARB4H/tt5Wgnk+x2XBxx3Hg9WbsygfF9GOdaBHFAp8dHERUdR29LhdihmHI1HM9Ea/JqIRCTXb9vtwG7n8QZgtYjEiUghMAfYCrwDzBGRQqeWsdrZ15jz8tUMspOtZhBIIkJOShw1VjMIK2OqGYhIAnA98Pd+xd8VkSV4m3qO+Lap6h4ReR7YC/QA96hqr/M69wKvAB5gvaruGUtcJjLUtHSQlhBDfIzH7VAiTk5yvNUMwsyYkoGqtgGZ/cruOM/+3wa+PUD5y8DLY4nFRJ4am2Pgmskpcew/YWsUhRObgWxCVm1zBznWeeyKnOR46qyZKKxYMjAhq7al04aVuiQ7OY6Wzh7au3rdDsWME0sGJiT19amTDKxm4IYcp9Pe+g3ChyUDE5LqW7vo7VOrGbjEtwRIbYs1FYULSwYmJPmGldocA3f4amQ28Sx8WDIwIcnXPGEdyO7wJWFrJgoflgxMSPJNeLJmInekJ8QQ4xGbeBZGLBmYkHRm9nGS1QzcICJkJ8VZzSCMWDIwIam2pZPMxFhio+0j7JbslHjqrAM5bNhfkglJ3gln1kTkpsnJcdaBHEYsGZiQVNNscwzclpUcR32rJYNwYcnAhKSa5g5bl8hlmYmxNLR20WeXvwwLlgxMyOnp7ePkaasZuC0jMZY+hcb2brdDMePAkoEJOfWtXfSptwPTuCcjMRaABmsqCguWDEzIOXO5S7uojasyE73nv/50l8uRmPFgycCEnFqbcBYU3qsZWDIIB5YMTMipcSY6WTJwV2aSNxnUWzIIC5YMTMipae5EBLKcLyPjjvQEqxmEE0sGJuQ0tXWRHBdNtMc+vm6KjY4iOT7akkGYGPNfk4gcEZFdIrJDRIqdsgwR2Sgih5z7dKdcROQhESkVkRIRudjvddY6+x8SkbVjjcuEr5aOHlImxbgdhsE718CaicLDeP1rdbWqLlHVIuf5fcAmVZ0DbHKeA9wEzHFu64BHwJs8gAeAFcBy4AFfAjGmv+aOHpLjLRkEg8ykOBtaGiYmqp59K/Ck8/hJ4Da/8qfUazOQJiK5wI3ARlVtUNVTwEZg1QTFZkJcc0c3yfHRbodh8I4osqGl4WE8koECr4rINhFZ55RNVtVqAOc+xymfBlT4HVvplA1WfhYRWScixSJSXFdXNw6hm1DU0tFDiiWDoGDNROFjPP6iLlfV4yKSA2wUkf3n2VcGKNPzlJ9doPoY8BhAUVGRLYgSoVo6ukmOT3Y7DIO3ZnCqtQtVRWSgP2MTKsZcM1DV4859LfAi3jb/Gqf5B+e+1tm9Esj3OzwPOH6ecmPOYTWD4JGRGEtPn9Lc3uN2KGaMxpQMRCRRRJJ9j4EbgN3ABsA3Imgt8JLzeANwpzOqaCXQ5DQjvQLcICLpTsfxDU6ZMWdRVadmYB3IweC9iWfWiRzqxvrv1WTgRad6GA08rap/EJF3gOdF5C7gGPBRZ/+XgZuBUqAN+DsAVW0QkW8C7zj7/buqNowxNhOGWrt66VOsAzlIZDjrEzW0djEz2+VgzJiM6S9KVcuBxQOU1wPXDlCuwD2DvNZ6YP1Y4jHhr6XDu1yy1QyCQ2aiLUkRLmwKpwkpLR3etumUSVYzCAbpTjI4Zckg5FkyMCHFagbBJSnOm5RPd1oHcqizZGBCSrNTM7A+g+CQGOsBoK2r1+VIzFhZMjAhpdm5xKINLQ0O0Z4o4qKjaLWaQcizZGBCypk+A2smChqJcdG0dlkyCHWWDExIaTnTTGTJIFgkxnlo7bRmolBnycCElJaObqKjhPgY++gGi8TYaGsmCgPW8BoBGtu6eKv0JH1+qzlFCVwxO4u0hFgOnGjhQE3LmW0rCjOYnBJPRUMb2ysaz5RfMDWFWdlJnGjqYOuRBmI9wvvm5jAp1sOW8npqWryzUD0iXDU3i+T4GHZXNVF+svXMa1w2K5OspDjK606z+3jzmfKiGelMTZs05M/iW7HU1sEJHtZMFB4sGYS56qZ2PvH4Fg77fSH7zJ+SzP03L+CzTxbT1dt3pnxKSjw/+PgS7v7FNpqcDluA+JgovnLjfH70WumZSUYXT0/jkoIMfvxG+VmvvSQ/jXuuns3dv9hGr18WmpGZwH/cfiGffar4rBEoOclx/OGLV525yPpgWuxaBkEnIdZzpvnOhC5LBmGss6eXNY9t5uTpLtZ/qojpGYlnth2saeHzz2xn7fqtFGQm8PAnLyYu2kNNcweffaqYNY9vJiMxlhc+dxmpk2Lo7Onlvhd28c3/3su0tEn8+u5LqTjVxld/vYt3jzWy+pJ8PnPlTAB2VDTyT7/ayWefKmb+lGT+3+qleKKEYw2t3P2Ld/nkT7aQmxrPs+tWkhAbTXVTO3c9Ucw//7qEx+9cdt7/+r1XObOPbTBJiovmRFOH22GYMbK/qjD2dlk9R+rbeOSTF3PN/MlnbZudk0RLRzePvVHOY3cWMSs76Uz5f65Zyrd+t4/vfeQils1474JzT392BT/ffJTbl04jN3USRQUZ5KcncLDmNGuW55/5Ep+dk0RTezfPv1PBT9YWkZeecKb8+x9dzA82HuShNUtZNC31TPk/r5rHt363jzcPneSquYMvctPS0U1ynNUMgklCbLTNMwgDlgzC2KZ9tcTHRHH1/JwBt3/8kul8/JLp55Rfu2Ay1y6YfE55cnwM//D+2WeVFRVkUFSQcc6+d11RyF1XFJ5T/qHFU/nQ4qnnlP/tyhl8/9WD/HFfzRDJoIfpGQmDbjeBlxTnsRnIYcCGZIQpVWXTvhqunJNNfIzH7XCGFB/j4Yo5WWzaV4t3PcOBNbfb8tXBJiEumjbrQA55lgzC1P4TLRxv6uC6BQPXCoLRdQtyqGpsP2tkU3/WZxB8kuKi6e5VOnusqShOtJQAABCOSURBVCiUWTIIU3/a77243GBNRMHo6nneWDftqx1we1+fcrrLRhMFmwTf+kQ28SykWTIIU8VHGpg3OZmc5Hi3Qxm2nJR4LpyWyp8PDJwMTnf1oGrrEgWbRFu5NCxYMghTe443c8HUFLfDGLEVhRmUVDbR7TfvwaepzVmkbpLVDIJJYqw3GdiIotBmySAM1bV0UtvSycIQTAaL89Po7OnjwIlz+w2azqxYaskgmCTGeZuJrGYQ2iwZhKE9x5sAuGBqqsuRjNyS/DQAdlY2nrPNt3x1qtUMgoqvmWiiRxSdb5SZGbtRJwMRyReR10Rkn4jsEZEvOOXfEJEqEdnh3G72O+Z+ESkVkQMicqNf+SqnrFRE7hvbj2T2OGv+hGLNIC99EhmJseysGCAZdFgyCEa+ZqKJXKxuZ0Ujy/9jE1d+90986mdb+exTxWwur5+w94tEY+mJ6wH+UVXfFZFkYJuIbHS2/UBV/7f/ziKyEFgNXABMBf4oInOdzQ8D1wOVwDsiskFV944htoi293gz+RmTQvJLU0RYnJfKzoqmc7b5molSE0Lv5wpnvmai8VzGuqG160xTYUdPL1/5VQlx0VEsmppK5al2apo7uHP9Vr543Rxqmzt5/7xs3j8vdEbOBaNRJwNVrQaqncctIrIPmHaeQ24FnlXVTuCwiJQCy51tpapaDiAizzr7WjIYpT3Hm7ggN/SaiHwW56fx54OHON3Zc+Yau+DfZ2CjiYKJr5lovFYuVVU+9bOtlFS+9w9Bcnw0z3x2BXMmJwNwqrWLtT/bynf/cABPlPDEX4/wtyunc8viaSybkY4nyla1Halx+asSkQJgKbAFuBy4V0TuBIrx1h5O4U0Um/0Oq+S95FHRr3zFeMQViVo6ujlS38aHL85zO5RRW5yfhirsrmpi5czMM+VN7d14ouSsBGHc914z0fjUDH6/+wQllU380w1zWTbDu9TJrOxEclLeGyadnhjLr+6+lIqGdqamxfPg7/fz881H+cXmY3y8KJ8HP3LRuMQSScbcgSwiScALwBdVtRl4BJgFLMFbc/i+b9cBDtfzlA/0XutEpFhEiuvq6sYaelja4bS1X+R0xIaixXlOJ3K/foPm9h5S7FoGQSc+JoooGXufwfHGdl7aUcX/fvUAc3KS+Nz7Z3PprEwunZV5ViLwiYv2MDsniYTYaP7t1kVs/9cbWHvpDJ4rruCvZSfHFEskGlMyEJEYvIngl6r6GwBVrVHVXlXtAx7nvaagSiDf7/A84Ph5ys+hqo+papGqFmVnD76YWSR758gposR7nYFQlZEYy/SMhHNGFDW1d4dkP0i4ExESY6PHNLS0uaOb2x7+C194dgflda3886r5I27qSU2I4f6bFzAjM4H7f7OL3VXn9juZwY1lNJEAPwX2qer/8SvP9dvtdmC383gDsFpE4kSkEJgDbAXeAeaISKGIxOLtZN4w2rgiXfGRBhbkpoT8kg2L89PO6URuau+2CWdBKnGMi9V9/5UD1J3u5GefuoS3vno11y88d9Xc4YiP8fC9jyymsa2bD/7nWzz8WumoY4o0Y6kZXA7cAVzTbxjpd0Vkl4iUAFcDXwJQ1T3A83g7hv8A3OPUIHqAe4FXgH3A886+ZoS6e/vYfqyRSwZYUjrULM5LpaqxndqW9y6aYjWD4JUQ5xl1n0FJZSNPbT7KnStncPX8nDPXvxit5YUZvPnVq1l1wRR+sPEgpbWnx/R6kWIso4neYuD2/pfPc8y3gW8PUP7y+Y4zw7P3eDPt3b0UFaQPvXOQ800+K6lo4rqF3vbi5o5upqUPfZ1kE3hJo7wOcm+f8i8v7iI7KY5/vHHeuMWTEh/Dt25fxF/KTvKNDXv4+V3Lra9pCDYDOYy8c6QBgKIZoV8zuGBqKp4oOavfoLm925aiCFIJsZ5RdSD//O0j7K5q5usfWjjuv9uspDi+fP1c3io9yZuHrEN5KJYMwsi7x06Rlz6JKamhs1LpYCbFepg3OfnM6ChVtWaiIJYYGz3iZqLu3j5++FopV8zO4gMX5g59wCh8YsV0pqTEW9/BMFgyCCM7K5pYOj30m4h8vJ3Ijagq7d29dPeqJYMglTiKZqLX9tdy8nQXf3d5wYQ14cRFe/jsVTPZcriBYqfmbAZmySBM1LZ0UNXYzuK80J153N+S/FSaO3o4Ut9Gc7v3i8aSQXBKjBt5M9HzxZVkJ8fxvvNc83o8rFmeT0ZirNUOhmDJIEyUOMMwl4TwZLP+Fue/N/nszFIUdsnLoJSWEEtjW/ewVxatbengtQO1/M3F04j2TOzXUEJsNJ++vIDXDtSdWdHXnMuSQZjYWdmIJ0pCctnqwczOTmJSjIcdfsnAagbBKSMhlp4+pbljeLWDZ7dW0NunfHRZ/tA7j4M7Li0gOS6aH71WFpD3C0WWDMLEjopG5k1OZpJzPdpwEO2J4sJpqeystGQQ7DISYwHvaqND6eju5Ym/HuGa+TnMzkma6NAA7+fmjktn8PLuaioa2gLynqHGkkEYUFV2VjSeaVYJJ4vzU9lzvJn6052AJYNglZHkSwadQ+77q+IKGlq7uPt9syY6rLN8tCgfVWyY6SAsGYSBI/VtNHf0sCQ/fJqIfBbnp9HV08dWZySIzTMITplOzaD+9NA1gyffPsrS6WlcEuDJkQWZCWQnx7HlsF0UZyCWDMKAb3XPcKwZLJuRTpTA70qqAWxtoiA13GaiprZuSmtPc8PCKQGfESwirCjMYEt5g11CcwCWDMLAjopGEmI9zMlJdjuUcZebOonvfWQxPX1Kcly0XbQkSGUmxgFQP0QyKKlyllh3aQj0isIMTjR3UNHQ7sr7BzMbpxcGdlY2smhaath+UX54WR6ZSbEcrbeOv2A1KdbDpBgPp4ZKBs7VyxZNcykZOBdL2nK4numZY1sQL9xYzSDEdfX0sed4c1jNLxjI++flsPayArfDMOeRkRg7ZDNRSWUjhVmJrg0EmJ2dRHpCDFsO22zk/iwZhLgDJ1ro6uk7c3UwY9ySkRg7dDNRZZNrTUQAUVHC0unplPS7cJKxZBDydlS62wZrjM9QNYPalg6qmzq40KUmIp/5U5Ipr2ulq6fP1TiCjSWDELezopHMxFjybJ1/47LMIZLBLqe/wO1Rb/NzU+jpU8rq7KI3/iwZhDBV5e2yeooK0u3CHcZ13maiwSed7ajwLZmSEsCozjV/infU3f4Tza7GEWwsGYSwsrrTVDW2c9UEr/pozHBkJMXS0d036LWQtx09xYLcZBJi3R3EWJiVSIxH2H+ixdU4go0lgxD2+kHvtPqr5lgyMO7LPM/Es57ePnZWNHJxEFxvI8YTxeycZA5YMjiLJYMQ9vrBOmZmJ5KfYeOljfsynIlnAyWDAzUttHb1smyG+8kAvE1F+6stGfgLmmQgIqtE5ICIlIrIfW7HE+w6unvZUl4/4RcGMWa4fEtSDDS89N2jpwCComYA3mRwormDprZut0MJGkGRDETEAzwM3AQsBNaIyEJ3owpevX3KAy/tobOnj2vm57gdjjHAe8mgruXcTuR3jzWSnRwXNKPe5ud6O7F/+pfDtk6RI1iWo1gOlKpqOYCIPAvcCuwd7zf62ou72Brisw/bu3upPNXO56+ZzRWzs9wOxxgAspPj8EQJ971QwqN/LjtreZRjDW1cPS8naEa9XT4rkw9elMtDmw7x4vZK4qND6zogP117ybgvpxEsyWAaUOH3vBJY0X8nEVkHrAOYPn36qN5oatok5kwOzAU1JtI9V89mzfLRnQNjJkJSXDQv/sNlbNpXy6Has9vj505ODqrlRKI9UfznmqVcOiuTv5SG3vUNYqPHv1FHgqGKJCIfBW5U1c84z+8Alqvq5wc7pqioSIuLiwMVojHGhAUR2aaqRf3Lg6LPAG9NwP9iqHnAcZdiMcaYiBMsyeAdYI6IFIpILLAa2OByTMYYEzGCos9AVXtE5F7gFcADrFfVPS6HZYwxESMokgGAqr4MvOx2HMYYE4mCpZnIGGOMiywZGGOMsWRgjDHGkoExxhiCZNLZaIhIHXB0lIdnAcE47TBY44Lgjc3iGhmLa+SCNbbRxjVDVc9Z4TJkk8FYiEjxQDPw3BascUHwxmZxjYzFNXLBGtt4x2XNRMYYYywZGGOMidxk8JjbAQwiWOOC4I3N4hoZi2vkgjW2cY0rIvsMjDHGnC1SawbGGGP8WDIwxhgTeclARFaJyAERKRWR+1yMI19EXhORfSKyR0S+4JR/Q0SqRGSHc7vZhdiOiMgu5/2LnbIMEdkoIoec+4Be2VxE5vmdkx0i0iwiX3TrfInIehGpFZHdfmUDniPxesj5zJWIyMUBjut7IrLfee8XRSTNKS8QkXa/c/dogOMa9HcnIvc75+uAiNwY4Lie84vpiIjscMoDeb4G+36YuM+YqkbMDe/y2GXATCAW2AksdCmWXOBi53EycBBYCHwD+CeXz9MRIKtf2XeB+5zH9wEPuvx7PAHMcOt8AVcBFwO7hzpHwM3A7wEBVgJbAhzXDUC08/hBv7gK/Pdz4XwN+Ltz/g52AnFAofM36wlUXP22fx/4ugvna7Dvhwn7jEVazWA5UKqq5araBTwL3OpGIKpararvOo9bgH14rwUdrG4FnnQePwnc5mIs1wJlqjraGehjpqpvAA39igc7R7cCT6nXZiBNRHIDFZeqvqqqPc7TzXivJBhQg5yvwdwKPKuqnap6GCjF+7cb0LhERICPAc9MxHufz3m+HybsMxZpyWAaUOH3vJIg+AIWkQJgKbDFKbrXqeqtD3RzjEOBV0Vkm4isc8omq2o1eD+oQI4Lcfms5uw/ULfPl89g5yiYPnefxvsfpE+hiGwXkddF5EoX4hnodxcs5+tKoEZVD/mVBfx89ft+mLDPWKQlAxmgzNWxtSKSBLwAfFFVm4FHgFnAEqAabzU10C5X1YuBm4B7ROQqF2IYkHgvi3oL8CunKBjO11CC4nMnIl8DeoBfOkXVwHRVXQp8GXhaRFICGNJgv7ugOF/AGs7+pyPg52uA74dBdx2gbETnLNKSQSWQ7/c8DzjuUiyISAzeX/QvVfU3AKpao6q9qtoHPM4EVY/PR1WPO/e1wItODDW+aqdzXxvouBw3Ae+qao0To+vny89g58j1z52IrAU+CHxSnUZmpxmm3nm8DW/b/NxAxXSe310wnK9o4G+A53xlgT5fA30/MIGfsUhLBu8Ac0Sk0PkPczWwwY1AnPbInwL7VPX/+JX7t/PdDuzuf+wEx5UoIsm+x3g7H3fjPU9rnd3WAi8FMi4/Z/235vb56mewc7QBuNMZ8bESaPJV9QNBRFYBXwVuUdU2v/JsEfE4j2cCc4DyAMY12O9uA7BaROJEpNCJa2ug4nJcB+xX1UpfQSDP12DfD0zkZywQPePBdMPb634Qb1b/motxXIG3GlcC7HBuNwM/B3Y55RuA3ADHNRPvSI6dwB7fOQIygU3AIec+w4VzlgDUA6l+Za6cL7wJqRroxvtf2V2DnSO8VfiHnc/cLqAowHGV4m1P9n3OHnX2/bDzO94JvAt8KMBxDfq7A77mnK8DwE2BjMspfwK4u9++gTxfg30/TNhnzJajMMYYE3HNRMYYYwZgycAYY4wlA2OMMZYMjDHGYMnAGGMMlgyMMcZgycAYYwzw/wGQzd09m8Nt0AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# TASK: can you visualize projections from several interesting angles (like all angles divisible by 15)?\n",
    "\n",
    "## SOLUTION(TODO: where do we put it?)\n",
    "for p in projections:\n",
    "    if (p[0] % 15) == 0:\n",
    "        plt.figure()\n",
    "        plt.plot(p[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point our `projections` variable contains a collection of all projections. Effectively, this is what we get once our measurements are done. Let's plot all projections stacked together as a single image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f89a3b490>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w8z4B1eyF+fccvi4O3xd51OXGxkaj5YvvgSjCMtK2/TsXIsh18W63W2ZE9P12u12sra2V24jlyMd2mcx/THRvRdo6E93fvCyKOD6pgg5CCCHOGD3AhRCipZy5hOJEFiiuacjRbRH5VCOK1ovWa0p+dZDEWdE+8j6zvMBRdvnUmxPrnCR+PJdSLly4AGB6LXJL4Wg0qhSt4PNpqk3J0ZneduvWrYp0EiUDMrPKtuPxOIyky+2LbH3M95sfo672Yb/fL9fLoy95H4sKOkSRnU3T9263W7GpsdTissna2lpZVOLGjRuV/t2t5OOeL2v6W4+uC18DJ2/rdDphrc18fZZN+e8n+ntYZA3VG7gQQrQUPcCFEKKlrIyEAlRlFE7y05R4KHKXRL/4NkVpciRUlLiK9xXtrykKj5flkhDLRDxdy2WFk4jY9H27G4Sndbk0UpdvO78+XPOR3SB+bh71WRRFxaXDcBtLJ/zvuvPJtwPmE4px3VJflss+nHjI5Yoo9zj3tympFF/bKJlVPtXnNu9LFLE5GAxw7ty5uTblBY/zcfPfWS6N8Hjz+nX54VnO4usU5an36+GuLM6jHyXO4r95SShCCHGHoge4EEK0FD3AhRCipayUBu647sP6sMOWr2UjMp26upvAvD2oKRJqWQvSotqcURvr/Lm+xpa9KDryKHhhB9en9/b2Sl2VrwUXd/B+5EnqORthpJu7ZdHMKhGodRY71w79WJPJpPweRWxGGjlrk5G1LPodApjaCF0D53Xza9Dtdiv95DGLMm26Fr+3t1fRTsfjcWWbtbW1MtrSt+VITG9TRObtMeP7k3/fyO+VXq9XKfTBmrbf86x35/VJ2XLKBVG4Hqp/+n3Bn3kRFV6vjoVv4Gb2ejP7pJk9a2ZfNLMfm7XfZ2YfN7PnZp+vWrQvIYQQx8cyEsoYwD9OKX0TgHcA+BEz+2YAjwP4RErpTQA+Mfu3EEKIU2KhhJJSugTg0uz7DTN7FsDrADwC4K/NVnsSwKcAvP84O8fRSSwp5FPuOvkjSlBUV/ghsidGHMWixXY1JpeE+HyihFm8PCrCcFByCYX3x8UWWDrxvrHE4styWYWlhNw+tQi2/XEtzty+yPCyXNKqS1wVjW2+D54eNyVDimyjURGKKIrUx5uj+iLZha1um5ubAKbFHQDgypUrlTG5W8htoGZW3rdsAcyTgvX7/UqkcdTGcolvy/dOfp9PJpM5+yAwX/uVl+WySlEUx2sjNLM3AngLgE8DeHD2cPeH/GsOsi8hhBBHY+kfMc3sPIBfA/DjKaXry6ZeNLPHADx2uO4JIYSoY6kHuJn1MX14/1JK6ddnzS+b2cWU0iUzuwjgcrRtSukJAE/M9nNg/SGP6mMHQhQxybJKU7KpOpcKr3MQ8v2yXNIU2RntY1F/uc2ngixN5LLGsty8eRPANDLTEzexsyGaduZRZhsbG5WIyfF4XDojooRVTWPW7XZDuSWXm6L9RvdK5HRhV0LuOuCpMkseec7xoigqEaN1ic04KtSPwfKQH8u3YemKx96XcZ7yfBzvJjgBGEseuezE15TllWi9fH/sVsqT2kVOkqIoQscJS5O+nm/LfyvH4UIxAB8E8GxK6Wdp0VMAHp19fxTAxxbtSwghxPGxzBv4OwH8fQCfN7PPzdr+GYAPAPhVM3sfgK8C+IGT6aIQQoiIZVwovwugbt7/ruPtjhBCiGVZyUjMReQaI9vW2JIX6Z51OndTZsFo/ZymQhGL9MhltGBeHmVmZO0/t8Jx9rMm7d+zEhZFUWp0vF2eIZHtgd6n0WhURgb6sl6vV+p6rAXn5xhl2+NjuA4Z6c2RlbTb7YaFPvJxZBtfbk1dW1sLoylzXb4uQ2IelcpRnFz/krVvXy8vDsDZ8dgu5zqu2wl7vV55/e4GWM/OfyNgHZv17jyycm1tLdTPI7uxb5dHcbMG7uNfFEV57y/SwP07r7/oOioXihBCtBQ9wIUQoqW0UkJxcgsbECevabKQLbL4NdkOD2M3XHYfTQm7HLbY8fpRZGdeb4+lCccTTY1GIwyHw/I7MJ1+5smauPAD2+Dysbp58+bcNNPXy6143E+2zuXnk5+bH9+3cSaTSSnncJJ8nyJ73zkJke/PbZQsSbH9L29jmYrlHLYe+rL8WvJYMFF0aJ5waTAYzFkKAeDcuXPY3t6u7O9Owswq0ghbKiObJVtD8zGLrKRNciNHibM04n83LI34343/LXEbyyb5estYQfUGLoQQLUUPcCGEaCmtllAiWBbIp7TR9JWnTctEYh7ErXLQfOWLJJkmiYf/HUWARuvniZZ8LK5fv44LFy4AuD2di+pkcqQjSxl53vL9/f1yPxzV6Mtd5mBnh08n6845j4LjbXx6zMmFfKrMNQpZcsnHjGWWKHFV5G7J98XweefuqeFwWIkMTClVxqDf74fuF9/Wc7ifP38eN27cKPt/J8GukTwPOjtJWFbJ1+Nc3k5UQ5fz8ufrsQvFZRN2nPBnLo2MRqPKeouSVtWhN3AhhGgpeoALIURL0QNcCCFayh2ngTNR8YA8CTtrn8vaDXNYJ4sKRiyyAzVFXeb9yJflGvGijIccMVhX3IITzvu5jUajiv1uf3+/kph+fX29Yk9kmyfb6vJMghw5yXZD7x/3N6prmR+DsyWyZTGPeuz1eqVOmkdO8rGaMsPxNeHfVdi+6MtyayGfN0ds5gU02NLo/eXIV1+2ublZbstFOtqKmZXn6J/r6+tz2rd/ekZGtgnmf+scVRz97Tqsc+cURVFq3z7Go9FoLpoZmOrjvp5/HlbvjtAbuBBCtBQ9wIUQoqXc0RJKBBeGYNiO5USySiSvRPU062SOZeyDh0nG33SMyOLGEZs5nFzep4Lnzp2rJLVnSxxvy9N7J0/glH/3/eW1LiPLYCSJRcmkWE7i/fkxOArP95kXgFhUGIQtgXkCsP39/Uq/2JrG0kieYIvvT+9TSqkcUy484VN4T2bFBTnaKKH4ufl9tLGxUZ6Pt21ubpZt/lknreVSap1ski+Plvl47u3tzX0HppHMLqG4XHLSNk69gQshREvRA1wIIVrKXSeh1MHTd6fb7YYJhaLox0hiaWJZl8qy6y2KIm3Ki52vw7+m33vvveVylwhcetjY2KjkVWYpgd0nef5uzovtcGImh6+J94+dKewyyRNSjcfjcsrN45PLLrxe7ujgyE3Oyx05CSK5JL8e3W630sYyB99vucQ0Go0qx1hbWyulE09Gtr6+XrZ5ROZxOh9OAh+TjY0NnD9/HsDtyNLNzc3yfPL7DYilDofXi6QRXhZFXfrfwc7ODoDbY3zz5s3y+1nKVHoDF0KIlqIHuBBCtBQ9wIUQoqVIA28g0sVZK4v0tabMg8tmKmQOYymMWKZYBev4XhDAsxK+6lWvCrMRRto6F0pwmqJiuVBCrvtyNCX3N48i5d8heNv8XHn/XGuzLoNjXZEJhy2O+VgMBoPK/cMWTbateb/YWpjXxOSiGn5uo9Go7LNrxqPRCFtbWwCAV155BcBqauDdbrf8jcX7u7W1VZ7HcVBn46vLMgjc/t1ge3sbV65cATDVvJv2d1boDVwIIVqKHuBCCNFSJKEcEC5s4ER1E5eN4uRowaYkVcvaE48axem4NcptVHt7e6XFzhmPx2VkIBdl4LqbwHyUa13EpJPXySyKoiK18HeWRPI6mWzj4yITUbQlF4FguPZhk+zFCan4mE3SEY9PJAlxQQzvG0cd5ritjWt8uv1uOBwemxx3WFwaecMb3gAAePWrX33ofS2SRhZJHXnRkZdeegkvvfTSXFsb0Bu4EEK0lIUPcDNbN7PfN7NnzOyLZvYvZu0Pm9mnzew5M/uImQ0W7UsIIcTxsYyEMgTw7Smlm2bWB/C7ZvZbAH4CwM+llD5sZr8A4H0Afv4E+7qyRLIKgIpbhWtyRvUVm2SSujzfy0orB8XPx39939vbqyQUGgwGleRLvV6vMlWfTCaNEhNLClFir1zC4DZ3ZXDULCemymUVvgZNUbaLrkl+3tx3/sxzUXMyK16Wyyr7+/tzSaz4WIyZlefLScQ8mvGee+4BAFy9evVUJRQ/7pvf/OZTOyawnEvkmWeeKZ0mbWfhG3iacnP2z/7svwTg2wH8t1n7kwDecyI9FEIIEbKUBm5mXTP7HIDLAD4O4M8AXEspudr/IoDX1Wz7mJk9bWZPH0eHhRBCTFnqAZ5SmqSUvgXAQwDeDuCbotVqtn0ipfS2lNLbDt9NIYQQOQeyEaaUrpnZpwC8A8CWmfVmb+EPAXjpBPrXaiILmcM6aJM+7CyrlefbHBVPTL+9vV3WG/S2wWBQWwgBmNeH/RzZEthUf3JRtGtuVaw730iXztt4HwfViaP6l011VjmykzXwaD0fH86CmN8rrJ/7NVhbWyt/r3AtfG1trbSEHieDwaC0Bb72ta899v030WQZ/NrXvgYA+OpXvzpXWOROYxkXygNmtjX7vgHgOwA8C+CTAL5/ttqjAD52Up0UQghRZZk38IsAnjSzLqYP/F9NKf2Gmf0xgA+b2b8E8IcAPniC/RRCCJGx8AGeUvojAG8J2r+MqR4uDkGTvBJNleuKRhw2YnPZdX3aXRRFWPPRZQNPeN/v9ytRhevr6xXrXt3x87qEHGnpUgEnzMplmHxfeXIsll9Y1onsi74ssjHmUZJRgi3uH7dF60XXMbdZsqzCckleT9PMysRbLqVsbW2V0bXLykR8/QDgvvvuK5NPeZIzHt+6IgsHga9tE6PRqEy4du3aNQBTq+SdLJdEKBJTCCFaih7gQgjRUvQAF0KIlqJshCtIVEgCmNdCgXnbHdOklUdFJSJyi9aNGzfKpPuui/f7/TD5vvfdddiiKCoaeKTzA6gUIY507MlkUrbx+edtrKfy+USFcaPfHLwfUWqAaJxy21+n05kr7OzkGRlTSmFB7dwqyQWjI52ddW+3evp4bm5ulst9GfffsxZyAWEPh3cNnG2jTHQPNtGklXNaCtfsb968Wf7G4qkddnZ2WpU18KTQG7gQQrQUPcCFEKKlSEJpET7NXiSvLBN9yETL8qntzs5OOY31qfVkMimnuSyN5MnyzaxS35EjS/1zbW1triZkXT+5yIKTF5vwffhxvWDDZDIp98NtuTwVRZE6vV6v7CfLG1wr1Jc1STJ8Dt4Xb+Nal0xuI1xfXw/74vtziWtra6tcj+UVX+5RtnWWz5ymZZxxsW45MJVI/P7hTy9M4W3D4XAla3quAnoDF0KIlqIHuBBCtBRJKHcITfIKJ45it0VdFGfkXhkOh2XEm7tR1tbW5oo7+P59G3ZMeJtP/bmfPo3nwg8caZnLOf1+v5LsajweV2SUSDoaDAZz371P/j2PfiyKouIG4XN0uP4mJ6nK3S3j8ThMXMVyk59jXh+UIzFZovCEVe4WSSnhvvvuA3BbLrl48SKuXLkCALh8+XJ5/rnUwdJWTp0sEiWV8ohIlka8jZd5//yzKIozr93ZJvQGLoQQLUUPcCGEaCl6gAshREuRBn4XwNnzmLrivlGEInA7AtMLwm5sbJQap+vP3W63PBYXeXB9lIsQ+zbexrY/7ntUACE/hyhikrPy8T6iDIa53dD7xLq6nxfbDlnnz4/PY+d6dlTouK4gcj4Wg8Eg/A0hZzQalTozW/bcKujb7u7uViJVuV+Rzp9bRPf29srvrHH7dx+foijmdG7ehzg8egMXQoiWoge4EEK0FEkodzE+VW6yIHKE5fXr1wHcLt5w69at0rrm0+NerzcnFzh5YYOUUkUi4AjHvIYmMB/F6dvmxQy4LZI1WMJgCYmjPIH5yEg/H5dTxuNxZb2iKCrnzUm8HK6JyfVEvf8e5crb+bkWRVGRuYqiKLd1OcvMymhGl7vG43Epobhtc2dnp1JYhIt0+KfvdzweV+SS8XhckUYmk0nZJpnkZNEbuBBCtBQ9wIUQoqVIQhGN8NTap8geybe5uVlKCP7JsghHU+b5qff39ytulSiasSiKipPEzMrpfZ4ki7fldnZ+NCXv8mNxFGQeaTgYDCp5uTn3OB/Tl7O84mMVSUxRFKdvyw4f33Y0GpVt7Phoch1xXnCXR9gZEskkvo73hSWSKOe5OB30Bi6EEC1FD3AhhGgpeuF7w00AABPRSURBVIALIURLkQYuDoxb1HZ2dkprmrcB1fqSg8GgUoeSMySyfTG3G3a73bBeZK6Bm1mpxbrGDMxbD+tgrTrKzpdnBWQLJNv6uC/elkdd8m8Evl+OcGR9Pi/8wDZCrmvJkay+P9+3L9vd3Z2rJwlM60tevXoVQKxz5xGT4/FYmQJXjKXfwM2sa2Z/aGa/Mfv3w2b2aTN7zsw+YmaDk+umEEKInINIKD8G4Fn6988A+LmU0psAXAXwvuPsmBBCiGaWklDM7CEAfxPAvwLwEzad5307gL83W+VJAD8N4OdPoI9ixXDr2Y0bN8riDj7tHo1GpVWQIz1dYnFrGlvxPDJwNBpVIix5yu4SwWg0KiUZn973+/2KTBJN91NKlQIRk8mkItNwAQo/H5ZNXKaJCmRwVGje9/39/VA6crxvw+GwHDM/R7Zy+rY7Oztlm0sj29vbc9GyAHDt2jVsb28DuH0NJpNJRUKZTCaV8RGry7Jv4P8OwD8F4Ff2fgDXUkpuNn0RwOuOuW9CCCEaWPgAN7PvBXA5pfRZbg5WDX/dMLPHzOxpM3v6kH0UQggRsIyE8k4A32dm7wawDuACpm/kW2bWm72FPwTgpWjjlNITAJ4AADPTT9h3EHt7e+UUfXNzE8A00jKSKFw24HzSLoO4JNPtduccJMBteYW35eRPLEO4xOFywGAwCCMxcwfLYDAo3TReX5LrZeb1PL2vvF921ThRjm120HjbeDwuxyDan69369atUhrxz729vfK752vf3d0tk1jxpx/Da5sWRaHc3C1n4Rt4SuknU0oPpZTeCOC9AP5nSumHAXwSwPfPVnsUwMdOrJdCCCEqHCWQ5/2Y/qD5PKaa+AePp0tCCCGW4UCBPCmlTwH41Oz7lwG8/fi7JIQQYhkUiSkOzc2bN0vt1CMDB4NBqWNz5jzXcaMoSYf1Ydd/R6NRRbNm7dYLSnChBC4a4Vq2f66trZXbuD1wY2OjbPNP18S73W6luAQXhWAtPC/ywOfH2n9eSIPP0cdxb2+v1Ky9bXd3t9S5eT3/znq3r8dWRD+uj8Xm5uZckQrRPpQLRQghWooe4EII0VIkoYhDMxqNyim613LkggCRlMA1L/27yxaTyaSSTGp/f78SncmFHxyuk+myxvr6erk/lktyWYWTbfk+2L6YJ66K6mp2u91KrUsfIz83YCp9cBSlL3NJiOUS/+77YAnFP3d2dsr9+XifO3euUkhiNBqV48JFOPy6eV9Eu9AbuBBCtBQ9wIUQoqVIQhGHJqVUcUWMx+NK/ux+v19xnHDNx7w2pi8HpjKIyx8+9efISc7Hna/X7/fLNmcymVSOx3UyHZcb2IXCzhOOogSmzhiXOvxcObe2LxuNRuVyH7vxeFwZx+FwWKl1ORqNKk6b9fX1Sk1KlmQ8QpZlH+/T7u5uKRU1JdgSq4vewIUQoqXoAS6EEC1FD3AhhGgp0sDFkfDov/vvvx/AvO7rOnWkq3K2PS6Y4LY216fX19fn9F5fxpkEgak+7fvjKErXw3n93E4HzEdKArcjGP2YfB5cFMLbWPt3/bkoilKzdg18PB6XOjev58eNilBwjc08M2JKac6a6ct8XDj60s/FdW8+rhd72N7eVlRmi9AbuBBCtBQ9wIUQoqVIQhFHwhMu+SdPvzkKMo90ZCsg15fME031er2KDNLtdivRlJFc0u12y+++P27z9c2slDXypFJcFILrVbr8wdGmuaxSFEVl2/39/UrE5v7+/lzBCd9Hbl9kmaiJyWRSjgsfgwtdAFOpyW2GLoHt7e1VtmWZKJJ4xNmhN3AhhGgpeoALIURLkYQiDow7Ifr9fqU25MbGRllXcmtrC8A0GjCfvrMMwpIGR1v6slzyYCeJf0bukk6nU+7HYeeFJ3BiRwzX3QTmXSi+HUc6cpvLCywzcHSpH8vHj6NT8zqZLMlwPc1c1uAI0kg64tzsPhbuQhmNRpX854PBoOIa4j7l8g+7jsTpozdwIYRoKXqACyFES9EDXAghWoo0cFGBNWHXUnu9XtiWR0SeP3++1FPZwuc2Po4k5KyBQBx1aWaVjIJsGeTCBd4/1qU9ojLSnZ2oQARr634edds6UU1O18rz7IW8XkRKqbI/1qC5T/l593q9ipbf6/UqRSjW19fL8WENPM9uyNp+roFHhSy4qIc4WfQGLoQQLUUPcCGEaCmSUO5SWIbgwgv+7yiqMZ+CezuvVye/5ImtIqtbt9sNIw0jKcGn+d42HA7L/fH0PSok4dv4emY2l/SJP0ejUZlgK5I8WC7JC1R0Op3K8c2sHAO2CeZtdbVAOVIzP7+oL06n06nUBy2KorQU+vXZ2Nio2Bd57PLvkazCBTzYbihZ5fjRG7gQQrSUpd7AzewFADcATACMU0pvM7P7AHwEwBsBvADgB1NKV0+mm0IIIXIOIqH89ZTSX9C/HwfwiZTSB8zs8dm/33+svROHIs8ZzRGT3MbySP6ZywU8Jc+TLPH34XAYyir5lL7X61UiF1kO4MhIz6XN8gG7T5x8yr+/v1+JEuS+RJGLnLjJ8e+cPzw/ViQrRbU2eV2uUZnXq4wSbE0mk3IsOPlVLnlMJpMwUjOPmuX84s7W1lZZnzM610jOypexrMKumfw6j0YjySpH5CgSyiMAnpx9fxLAe47eHSGEEMuy7AM8AfhtM/usmT02a3swpXQJAGafr4k2NLPHzOxpM3v66N0VQgjhLCuhvDOl9JKZvQbAx83sT5Y9QErpCQBPAICZKZmwEEIcE0s9wFNKL80+L5vZRwG8HcDLZnYxpXTJzC4CuHyC/RQBHB3Jtj+25fmyXJdmW5nD/861UTMrtUtfjwsRuJY5Ho8r9STX1tbm7IPAvHWO7XKu8XqBCLbOeZ+41mRku2M7G2dOzM8tsvt5/9ym2O12Sy2a95HD9kDvW/QbAev3fF55hGWkDXMmQx5vrq2Zb8t2w1yX5v25nfDq1auV/kXH588oAjU/VhSxyRGj0sUPx0IJxcw2zewe/w7guwB8AcBTAB6drfYogI+dVCeFEEJUWeYN/EEAH53937UH4JdTSv/dzD4D4FfN7H0AvgrgB06um0IIIXIWPsBTSl8G8Oag/RUA7zqJTonb09GoYAEXO+ACCd7GMslhaYrCY+tYHmk4HA4rUkJKqZwWexQgW9WuXbsGYHrOHB0JTKfUuWWQIzbZGhdJPD4+LNfk8hAns8qlHrbueQEIryPJ/eRtOHEV98WXRRJKPp51clYkbUXWPj8PH+eiKEpZiqWo/LhcgMLbctmEie6x6Bz5O49FLrVwFCdLQyoaEaNITCGEaCl6gAshREvRA1wIIVqKshGeMWY2V/gAiIsd9Pv9cnlkT4u000Vt0XJf57D7LYqi1Izdfnfr1q2y7ebNm+X5+HfXP30d3reZlZnyXB/njIWsjebZEjudTkXTjvrPRRHysPROp1M5bv77QL5fp9vtVkLa2Y7JOrvDNsH8ukTnGl0rtvuxLdLbXBff3d3F9evXAaC0fnJovmvQUeg9j3GUdqFJA8/HOl/m7fz7Bdsmgem9VXcd7ib0Bi6EEC1FD3AhhGgpklBOAc4O6DKITw9ZGmF74GHhKfWybfnUPypEUFcPMi8wcO3atTICk62DLA8B87UmfarOFjLOGJgXb4iiQrnN+xKdx6KIQF/m/R2Px+V18fPZ3d0tZZ0o6pLb8mk+H79JAuh2u+XxeL0mayiPWS7dRAU5UkqlnOFte3t7pcRy48aNuf2ur69Xonw5ojfqW2SBjGyJHImaX7PJZFIe15etr6/PySkAKrU87wb0Bi6EEC1FD3AhhGgpklCOiTxpEssGPgXnKWgU1eZEkoe3A7H7g6Pxmtry7SIiBwRv426R0WhUST6VUqpMaS9cuIB77713ru8crcdyRZ7UyfvPbTz1d6LiCTyOHGmZS1RFUVTqc3KiKz8P7+dwOJyTFXj/+fHz5FQc9cnSSC4rRLUu2aHRtC27UKKx4DHhoht+/nnSLj+mO1WYwWBQjgtHA/sx+Drl1yzqJ/fF4XuRI2q9n+xWie7HOxm9gQshREvRA1wIIVqKHuBCCNFSpIEfAtfy3Ep27ty5Ugt1PS6KlgTiAr5NejPrmpHtL9d48+VNy+oiMQFULFrD4bDUFV0LjRLvR3ola5Oul7L+yjqlj6OTUiq1zkjP5GX52EaRg5wZMcramEddcvZCHwsu8uD9TSlVChMzHH2Y2wij4/M14/1G2/oYREUw2O7Huj4wvRaeYZH74PfwMvDvIHyu/rfBtsP8fmObZXQfN2U/jK43Z5/06zKZTMpzvBMzGuoNXAghWooe4EII0VIkoTTQ6XTKqZgn8d/c3AxlkiZbXpNUEW3bZBNctF7d/psi+Hxq7dLIzs5O+f0w0W0+pc6TIQGxtZGtlZwkKd+mSerp9/uNUhTvI7ezTSaT0JboyyJLnssvPj0/f/58ubxJSqmrvxkluMrrjTKcWCuSJiIrXmRp9LH381hfXw9lp4MwmUzKRGV8/FxWGQwGlWtWF7nZlBwrklX8b7QoirnvwLwc2Hb0Bi6EEC1FD3AhhGgpklBm9Hq9MlrwnnvuAbD8r/HLTjEjmWPZxFHHdWz/3N7eLmtRHmcSIHZAsKMij+4bDoeV6NWNjY1KX/Lt+DjAvOSQt0V5sXm8eYqeuzt4yh7lsc7lod3d3fJ+4X3kkZWcozxKehVFYEYuFXb45NuaWSXndl3tSsfdQTdu3KhECx9HNOP+/n4p0zjsVuFozjxSlsenKdq0Tl7JpbrBYIBz584BQMVZ1Tb0Bi6EEC1FD3AhhGgpeoALIURLues0cNfcHnjgAQDVyL+DcBCt+iT2sWhbt/Ndvnz5VDU+P67rjEVRlFqja7ODwaBi3QPmrXDAfPY+1rFzfTjaVxStB8Tabp2VkzMzcgRnbu3jiE0+fm5jjLImclsUNZsXqqg77yZdnMeRx44teN52lIIiB4Hthv65vr5e3jd+blyMgn/fWMaCCKByjhwVyr+/cA1X4Hj+vk8avYELIURL0QNcCCFaip1mwnMz+38AdgD8xakd9PC8Gqvfzzb0EVA/jxv183hpQz+/PqX0QN54qg9wADCzp1NKbzvVgx6CNvSzDX0E1M/jRv08XtrSzwhJKEII0VL0ABdCiJZyFg/wJ87gmIehDf1sQx8B9fO4UT+Pl7b0s8Kpa+BCCCGOB0koQgjRUk7tAW5m321mXzKz583s8dM67iLM7PVm9kkze9bMvmhmPzZr/2kz+79m9rnZf+9egb6+YGafn/Xn6VnbfWb2cTN7bvb5qjPu4zfSmH3OzK6b2Y+vwnia2YfM7LKZfYHawvGzKf9+dr/+kZm99Qz7+G/M7E9m/fiomW3N2t9oZrs0pr9wGn1s6GftNTazn5yN5ZfM7G+ccT8/Qn18wcw+N2s/s/E8NB5ufJL/AegC+DMA3wBgAOAZAN98Gsdeom8XAbx19v0eAH8K4JsB/DSAf3LW/cv6+gKAV2dt/xrA47PvjwP4mbPuZ3bdvwbg61dhPAF8G4C3AvjCovED8G4AvwXAALwDwKfPsI/fBaA3+/4z1Mc38norMJbhNZ79PT0DYA3Aw7NnQfes+pkt/7cA/vlZj+dh/zutN/C3A3g+pfTllNIIwIcBPHJKx24kpXQppfQHs+83ADwL4HVn26sD8QiAJ2ffnwTwnjPsS867APxZSukrZ90RAEgp/Q6AK1lz3fg9AuA/pym/B2DLzC6eRR9TSr+dUvLkK78H4KGT7sciasayjkcAfDilNEwp/R8Az2P6TDhxmvpp04QpPwjgV06jLyfBaT3AXwfgz+nfL2IFH5Jm9kYAbwHw6VnTj86mrR86a2liRgLw22b2WTN7bNb2YErpEjD9nxGA15xZ76q8F/N/HKs2nkD9+K3qPfsPMZ0ZOA+b2R+a2f8ys289q04R0TVe1bH8VgAvp5Seo7ZVG89GTusBbkHbStlfzOw8gF8D8OMppesAfh7AXwLwLQAuYTrVOmvemVJ6K4DvAfAjZvZtZ92hOsxsAOD7APzXWdMqjmcTK3fPmtlPARgD+KVZ0yUAb0gpvQXATwD4ZTO7cFb9Q/01XrmxnPFDmH/BWLXxXMhpPcBfBPB6+vdDAF46pWMvxMz6mD68fyml9OsAkFJ6OaU0SSntA/hPOKUpXxMppZdmn5cBfBTTPr3sU/vZ5+Wz6+Ec3wPgD1JKLwOrOZ4z6sZvpe5ZM3sUwPcC+OE0E2xnksQrs++fxVRb/stn1ceGa7xSYwkAZtYD8HcAfMTbVm08l+G0HuCfAfAmM3t49mb2XgBPndKxG5npYB8E8GxK6WepnfXOvw3gC/m2p4mZbZrZPf4d0x+2voDpOD46W+1RAB87mx5WmHu7WbXxJOrG7ykA/2DmRnkHgG2XWk4bM/tuAO8H8H0ppVvU/oCZdWffvwHAmwB8+Sz6OOtD3TV+CsB7zWzNzB7GtJ+/f9r9y/gOAH+SUnrRG1ZtPJfitH4txfRX/T/F9P9qP3XWv95Sv/4qptO5PwLwudl/7wbwXwB8ftb+FICLZ9zPb8D0l/xnAHzRxxDA/QA+AeC52ed9KzCm5wC8AuBeajvz8cT0fyiXABSYvhW+r278MJ32/8fZ/fp5AG87wz4+j6mG7PfnL8zW/buze+EZAH8A4G+d8VjWXmMAPzUbyy8B+J6z7Oes/RcB/KNs3TMbz8P+p0hMIYRoKYrEFEKIlqIHuBBCtBQ9wIUQoqXoAS6EEC1FD3AhhGgpeoALIURL0QNcCCFaih7gQgjRUv4/rdd5wuWTS/UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sinogram = np.stack([p[1] for p in projections])\n",
    "plt.imshow(sinogram, cmap=\"gray\", aspect = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pretty, isn't it? This image is commonly called _a sinogram_ because it appears to be an overlapping of sinusoids (and there is some neat signal processing math explaining why that is the case), and sometimes people talk of sinogram as the raw data that comes into a CT scanner after the analog signal has been sampled.\n",
    "\n",
    "But how do we get an image out of this?\n",
    "\n",
    "Remember, that \"C\" in \"CT\" stands for _Computed_ and that's where computation comes in. \n",
    "\n",
    "The basic computation is quite simple. We take each projection and \"smear\" all the aggregated intensity values that have been captured by it across a reconstructed image. Let's do this for one of those projections:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "bp = np.zeros((im.width, im.height))\n",
    "\n",
    "for y in range(sinogram.shape[1]):\n",
    "    bp[:, y] = projections[0][1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f8aa5c9d0>"
      ]
     },
     "execution_count": 38,
     "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.imshow(bp, cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From here, we do this for all other projections, and then stack them all together, remembering the angle from which the projection was taken!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "bp = np.zeros((im.width, im.height))\n",
    "\n",
    "for p in projections:\n",
    "    \n",
    "    # Smear the projection\n",
    "    img = np.zeros(bp.shape)\n",
    "    for y in range(img.shape[1]):\n",
    "        img[:, y] = p[1]\n",
    "        \n",
    "    # Rotate the projection back\n",
    "    img = nd.rotate(img, -p[0], reshape = False)\n",
    "    \n",
    "    bp += img"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f8aab48e0>"
      ]
     },
     "execution_count": 40,
     "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.imshow(bp, cmap =\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can you see our original image here? It is a bit blurry, but this is exactly what happens with the actual CT images reconstructed through backprojection. Next step, to get a nice and crisp image out of it would be running image through a sharpening filter and obtaining what radiologists usually see at their workstation - a _filtered backprojection_.\n",
    "\n",
    "There are many ways to construct that filter, and sometimes you will see in the CT imaging datasets (to which we will get later in the course) various metdata items referring to convolutions - these parameters have to do with varoius scanner settings available to the operator, which control the filters applied to unfiltered backprojections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TASK: There is a slice of a brain CT in the same directory as our phantom.bmp, named sample_brain.png. \n",
    "# Similar to what was dome above, simulate a set of parallel-beam projections at every 1 degree, plot a sinogram, \n",
    "# and plot an unfiltered backprojection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f88fda9d0>"
      ]
     },
     "execution_count": 41,
     "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": [
    "# SOLUTION (TODO)\n",
    "\n",
    "# Load and display the image\n",
    "b_im = Image.open(\"sample_brain.png\").convert(\"L\")\n",
    "plt.imshow(b_im, cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<PIL.Image.Image image mode=L size=512x512 at 0x20F899A5400>\n"
     ]
    }
   ],
   "source": [
    "print(b_im)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Obtain the sinogram\n",
    "\n",
    "b_projections = []\n",
    "for angle in range(0, 180, 1):\n",
    "    p = []\n",
    "    im_r = b_im.rotate(angle)\n",
    "    for x in range(0, b_im.width):\n",
    "        p.append(np.sum(np.array(im_r)[x]))\n",
    "    b_projections.append((angle, p))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f8902ea30>"
      ]
     },
     "execution_count": 43,
     "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.imshow(np.stack([p[1] for p in b_projections]), cmap=\"gray\", aspect = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reconstruct through backprojection\n",
    "\n",
    "b_bp = np.zeros((b_im.width, b_im.height))\n",
    "\n",
    "for p in b_projections:\n",
    "    \n",
    "    # Smear the projection\n",
    "    img = np.zeros(b_bp.shape)\n",
    "    for y in range(b_bp.shape[1]):\n",
    "        img[:, y] = p[1]\n",
    "        \n",
    "    # Rotate the projection back\n",
    "    img = nd.rotate(img, -p[0], reshape = False)\n",
    "    \n",
    "    b_bp += img"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x20f897ec070>"
      ]
     },
     "execution_count": 45,
     "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": [
    "# Display result\n",
    "\n",
    "plt.imshow(b_bp, cmap =\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "We have gone through the basic process of obtaining a sinogram from detector signal, and reconstructing an image using a process called _backprojection_. You have seen that the image that is obtained after this process is not yet quite crisp, and additional filtering pass is required. \n",
    "\n",
    "Note that there are a few differences between the simulated process here and how actual CT scans are obtained. We will cover those in a video that follows.\n",
    "\n",
    "If you want to dig deeper into sinograms and backprojections, here's a cool simulator of CT scanner operation: http://xrayphysics.com/ctsim.html"
   ]
  }
 ],
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   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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