Edge_Detection.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.3"
    },
    "colab": {
      "name": "Edge_Detection.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Isra1997/EdgeDetection/blob/master/Edge_Detection.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0NjS3ekeddxT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from PIL import  Image\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "#function used to Calculate the LoG function\n",
        "def LoG_Function(X,Y,Sigma):\n",
        "    return (-1/(math.pi*Sigma**4))*(1-((X**2+Y**2)/(2*Sigma**2)))* math.exp(-1*((X**2+Y**2)/(2*Sigma**2)))\n",
        "\n",
        "#function used to Calculate the LoG mask\n",
        "def CalculateKernal(Sigma,size):\n",
        "    Result_Matrix=np.zeros([size,size])\n",
        "    for i in range(size):\n",
        "        for j in range(size):\n",
        "            Result_Matrix[i,j]=round(260*LoG_Function(i-(size-1)/2,j-(size-1)/2,Sigma))\n",
        "    return Result_Matrix\n",
        "\n",
        "\n",
        "def prewitt(image,Sigma,Threshold):\n",
        "    \n",
        "    width=image.shape[0]\n",
        "    height=image.shape[1]\n",
        "    \n",
        "    sumOfVertical=0\n",
        "    sumOfHorizontal=0\n",
        "    \n",
        "    #prewitt operators\n",
        "    H1=[[1,1,1],\n",
        "        [0,0,0],\n",
        "        [-1,-1,-1]]\n",
        "    \n",
        "    H2=[[-1,0,1],\n",
        "        [-1,0,1],\n",
        "        [-1,0,1]]\n",
        "    \n",
        "    #Intializing empty numpy array\n",
        "    Thresholding_array=np.zeros(image.shape)\n",
        "    magnitude_array=np.zeros(image.shape)\n",
        "    LoG_array=np.zeros(image.shape)\n",
        "    \n",
        "    #Getting the horizontal edges\n",
        "    for i in range(width-2):\n",
        "        for j in range(height-2):\n",
        "            sumOfHorizontal=np.sum(np.multiply(H1,image[i:i+3,j:j+3]))\n",
        "            sumOfVertical=np.sum(np.multiply(H2,image[i:i+3,j:j+3]))\n",
        "            magnitude_array[i,j]=math.sqrt(sumOfHorizontal**2+sumOfVertical**2)\n",
        "            \n",
        "    #Calculating the size of kernal  \n",
        "    size=(2*math.ceil(3*Sigma)+1)\n",
        "    #Calculating the LoG  kernal\n",
        "    LoG_kernal=CalculateKernal(Sigma,size)\n",
        "    \n",
        "    #Calculating the LoG image\n",
        "    for i in range(width-size-1):\n",
        "        for j in range(height-size-1):\n",
        "            LoG_array[i,j]=np.sum(np.multiply(LoG_kernal,image[i:i+size,j:j+size]))\n",
        "    \n",
        "            \n",
        "    #Thresholding the image\n",
        "    for i in range(width):\n",
        "        for j in range(height):\n",
        "            if((magnitude_array[i,j]>Threshold*255 and LoG_array[i,j]<=0)):\n",
        "                Thresholding_array[i,j]=1\n",
        "            else:\n",
        "                Thresholding_array[i,j]=0\n",
        "                \n",
        "    return Thresholding_array\n",
        "             \n",
        "\n",
        "# def main():\n",
        "#     openImg=Image.open(\"/Users/israragheb/Desktop/Assignment2CV/Cameraman.tif\").convert('L')  \n",
        "#     testing0=prewitt(np.array(openImg),2,0.1)\n",
        "#     testing1=prewitt(np.array(openImg),3,0.1)\n",
        "#     testing2=prewitt(np.array(openImg),4,0.1)\n",
        "\n",
        "#     plt.imshow(testing0,cmap='gray')\n",
        "#     plt.imshow(testing1,cmap='gray')\n",
        "#     plt.imshow(testing2,cmap='gray')\n",
        "\n",
        "    \n",
        "# if __name__==\"__main__\":\n",
        "#     main()\n",
        "    \n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zUaSjUJNddxa",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "openImg=Image.open(\"Cameraman.tif\").convert('L')  "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cgx4_s-Dddxh",
        "colab_type": "code",
        "colab": {},
        "outputId": "9d0f6a66-ba74-49c2-93a6-161995a6e6e6"
      },
      "source": [
        "testing0=prewitt(np.array(openImg),2,0.1)\n",
        "plt.imshow(testing0,cmap='gray')\n",
        "plt.savefig(\"LoG_2.jpg\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TFJ_xJ4Wddxm",
        "colab_type": "code",
        "colab": {},
        "outputId": "c8c5cdb7-228e-4de3-f317-4ea627eba7dc"
      },
      "source": [
        "testing1=prewitt(np.array(openImg),3,0.1)\n",
        "plt.imshow(testing1,cmap='gray')\n",
        "plt.savefig(\"LoG_3.jpg\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KlrqXdbcddxq",
        "colab_type": "code",
        "colab": {},
        "outputId": "9dcb8e84-e31f-4948-9b97-e3f7ba820ce7"
      },
      "source": [
        "testing2=prewitt(np.array(openImg),4,0.1)\n",
        "plt.imshow(testing2,cmap='gray')\n",
        "plt.savefig(\"LoG_4.jpg\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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HYhvYc2N6PhZ1JDoHd2L4Jl1PlEbqOVIGot1ntQZwTPH42mq1KtZWVFLF68YTQvlzznPUYuMVg80SlEJNarkOteEmesyNqK0catWTsq0qZQo3JcaiFYN0oGyDEpAy1WGiGCnt2gG+nvBZHbnjrafr6yLGQESTCKEWQ5yp/d9UepKv1hiKXU+pS6ExhgDbpBR6mTg1mcJq8B1K8hEL7Ia2HyX1h8apL2bmxodyx3oXj127L2pp8dlGuMMz3N64r6yvvjkUa2uFkHvCEpCdsnTdjlgZiVLg6uVky6ELxTAlm24t2Lgn6Oyf7veAfJDNpWhb3LuU4GFswoYmu52nNqmWiIStcCV68ktb0/o6Ww1syRZpzs5EjXsf2mqsuUpz5TmXofWZE2BLLIacg0HKdEi2LWvU7fu+xO2Mjamco+Yp7lqrhWDjLIZtsg5yiPVPj31nyxw6sFbaRmnZXOshZA3MxcYphh4Hdk/MGR/IbZuL7tdUCKHYyRwrd+lZkxr905Vi0NV+PlqvTjXvqyQekVpX7ORlKE9talxfqUXVVYxBlUIZvfXfkpSNyxRmvGSXI4ca2/RdKYYSYttJGniMIx1Ipea1NGAXeuAo9p3vDIGUKZRsz2dsunIlSui1gzeRGuZ7bFuS+ymVxU3TsZHOxigGjU/kM6U1Veto8xR7+RIkD1JN7fLUaG9RikGyLeQ7Q77t5E6e2pPOtRa4+n1tuvfWp2SmdB2k40xyrFqKROmUjvmuFAO3TRPaTuIG0Fhm24hFsmttFabgW80kkX73OlJWRskYqB1PKamj5ABeq7He7WPXuaubW3ZblETuwZ/aB4W4ujlcReZaEWOekj19X/u5R6olyqpzlvnYtX0DcgZsD0pubqbogxruhe0GuPWNaSkPOElPGEp3rTgrtaYlFms/1AbnUrn5Q8pVQjeKgbsBudtNqiAu4fPLW7cZ20kYJ74vEMkNeskhJEl6KG9K/7Q4tJWTt4XC6kYxhAZw6emvTSdlOy+1L31xHIk8qduMsXwxt0I6qUufbdgGulEMI/bN1y3IODX6p8YEtuHiBjUI1VXqTvQ41uZc2Lo4+ej7F3XA5afYJJ9tp2X/SOsptfRyiCkNzi11r0PaX6GTmDmk7KCM80T6yZapBy3p7kpwq01su2oDIsbJcNcfC2Jx/ZSzdVejTOrhnNT8NYj1j3t9qbsooWvy7dSkYrWxzF0J4PLOLdmq2mZquwa5cCuypIwkmOjb5vRZnT6k8RLp9ykxDsn30gWy9rZzd4rBR4o1sA3WgkuO+Z5rLaTIJGmDUyCSeAK3zRmSJZUUCym2hVhC6ngv3aoEOlQMKX6dj5IOWQq5blPpilJrgkkGe842JKc0Uvf7ud99yqjEhZWWk4xn12oqHf/dKQabFO3LDYZNVw4jc7gHpXv99v3ilIA9GXOIbXNywUWf9RGyStzxVkPenO85eWy5UulGMXAXkBpskq4UPVJTkXEBMUngLyZfLVzlIvXLJflCLkZoNZUEt33psWCudGFz8+fES2rF5bpRDL4LjgWWYuXHOpagHHII+ZM5cYdQOyVuhDQW4MvDlUl1NXyru6swfG1xfeC7rtTxJp3QtSyLGN0ohhC+XQqAH/y+G9izcsiVzR2YoUBUCa1M5FbEFBk3oSULTyimwN0LibLw3Tc3vVVgmaN7xRDrTN8+8hKVQw1amPxjvVIl48YOQma4i9Sktttxf4/JyNUbmoCh4Gmq2xCLffjyS3cmalmJ0ZOPRHSAiL5FRE8S0RNE9JEh/SoiepiInh5+XjmkExF9nojOEtEZIrop1sahQ4de+d2Yy/+tWuhvRtbg3279S8UXqJNer1Q5+gZxiXJ1ZXXvrZ1nTPddX0xZSdxTO8jJpXPKkRtnXN4Ud6jURag9riVHol8C8DFjzB8DuAXA3UR0A4DjAE4bYw4COD38DQC3Azg4fI4BuDfWwN7eHoB17eh2eKjzOaURMyWXriBCgzSUJ6V+u19jitlXBwe3Ekpkdd1K10oskWmsj7tWbpxxSs29Fp9C9V03J1upIs4hqhiMMReMMd8ffv8VgCcB7AdwBMDJIdtJAHcMvx8BcL9Z8R0AbySifaE2RotBaoZxCsLNJx28S1YOvknrKkffNcbMballxn0XUgghl86V113NOdl8q66vndB1pUwkn2VhX4crZyivTzaJ6+ZbIHLHd9JDVET0ZgBvB/BdANcaYy4AK+UB4Joh234Az1vFzg1p0jbYdKk74dZTywRuzVSKLMeNiH3ncw9ycS2VMW2sO6V+aV5OAdl1cOMp5Opy1q6bJ6effG4LJ3PJfRArBiJ6PYCvAvioMeaXoaxM2pqERHSMiHaJaPfFF1+8lNHT2b6ODmlt38qyJlzBjdo2QquqdOWTKH+3Ta6+EkUfs5ZCcZtQOteOzzW2y8TGMadYpNeTg2hXgohejZVS+LIx5mtD8gtEtM8Yc2FwFS4O6ecAHLCKXwfgvFunMeYEgBND/a9clTsIYjfAHWxcea6+kJLo2bLgGK8xtoqE0n11Skg12e38PmUhdRVy4cZF6n3n+n1M5+Tk+jSkSH1l3PhKqP5cJLsSBOCLAJ40xnzW+uoUgKPD70cBPGSlf4BW3ALgF6PL4cN+HwPnH/s0pK1hQ8rEVRqxzlua5eAbbDF/P6VOSVwhtX7pvXbbqqW4Q1aBLZc9vlw5ObcnNpFDcnCWg5sWs8zccjlILIZbAbwfwGNE9OiQ9gkAnwbwIBHdBeAnAN47fPcNAIcBnAXwawAflAgSM8O4/CFlYN80n4bl6pkLyQ0MTVZ7oLp5alyfxEXgCPU9ly9WX2gilMYefDL48rortfszVEYqW8hijlmFJdZvVDEYY/4TfNwAAP6cyW8A3J0qSGzguPm49BFOQ+cMnt7h+qzW9aWYw76ynFXgw64/1kZt89lehWN1u3lH2X3WmatsOOUTW+Ck+JR2jnLo5g1O3AoP+DtzKLeWL2YheNpnB0NKh+aUSSW0CqVep+97uy3f37FVP3TPfPnd9t300muLleXadNNCbXJjT9q2T/lI5AjNDaaOZb3B6dChQ1FN6Vv9YxNRurpJ88fqaaUgJGajLYtkMHN1SQaanWbn5SZGzH9PSUtRTL7vU9qMKRvOGgrJytUX6tPQtcTkLF3wu3gZrI3dMb7OHdOknZgahClxO+y25rLGarTrc8HsIBjXnlRBcfhWRJ9r4pYNfZ+D1LqSlA3FCjgFO6b7XBSJnKnj3qYrxRC7ubVvvFSmXHJckVZIZQmtPLZ/zeWN1SWV0Wfac0rJLeurZ6wrdaL48sfMejedG7uS/pP2dax8Kl3FGJy0tXyu2SS5aal+tSRfC2KDNsdVSPVVY75uTZM+9L1Ettx6U/puxB53bvlQmxL3K1XGHBYfY7A7PuZTu79zpAxmrqydv1XswG1vJHfQxPpH0q++umL3xs0r+T4lLsBNypgbw+UJTdiQ++pbrLh6uHEXU0pjPt91+K6xBd24ErGOGwmZaz7fN1RGUvcc+MzmKSy8Gm1zE8uuu7RO7m+uXqlyDLmxKea8W0cNd8D+aSupcc6E+jeXrlyJmhpQala6SE1vX/kW1FglpgiI+mSTpPtW+PE7IL59KXUTYnm5snb7knZ9ZaQWRAqcVeEZm2JXoguLYXzsOjtQwmjNsT77u5SJLF0dWhMyK8e0ltTosxy3MGRZ+KwRN93+xKyNEDH3KdVlk1oQ0r7nrIoSKwXoJMZgIwnuxPx/3yAqUTyhGz215ZB7TSl53XhCS3/WV3cNEzxHFq58isURc12lsnF974thjGlcPCWHLiyGEXtltzU9p+251SGm2VPh2vDlq9l27fpig0MSVCuRJdS+L4DIDXwuJlRiFfqu26ekpLGRWKxibFsiK9c/obprxaS6ijEMvydfTKgzQj5dbEKEblxq7EJKrN4c31S6UtX2eXPLhFZnnz8fshp96TE5U+MQobq5OECoLk5WXznJdQwsM8YA5G0Lhvw2qU+XM5BruhApFoLbR7Vk8Q06+6eP2GrqrvzuKh9yj2Kuk3RFDdUrsZpKsMegbeWErJZQ34diKzXoQjEA6wOQu1huQHFlUoM2nBwpcpdaCKUD0B1INQkp1ZTB6fOJfXXn4LsXMVeGkyE2KUPB0VB99vexe+8qk5iCtNNzXCubbhSDxNS3O8gXeZW4CykytSRm/rmrbK7fL1E+IQUnGWTuJIkp8JJ7FIv1cOk+YhMsZH34ytawPkqVfKnS7SbGAPi35mquKDFNzskRSs+1OlJW4PG7WPuSvsrtT+n9KI0v2GmAf2BLvi8dP6VjL2bJ+uSrfR8XG2MA/KaYpINy27DTYyuH216sjKTOVNldxeHWI3EnShVZrI2Ua4vVI13pXcuqFinuGScDZ/67YyNnLITKbVSMwQ4+5nZQLjG/TepjStuyB1ts5Q3JyqXXWq2lMoVcjxQllWtmc+XdtJrjw23fNw5Ck53rQ7e/UpRFrnsZo7sDTnO4NqHJwXV8jjntDt6SmEGIVOWQ4opIJ13JpGzhqtRGen2SeEdoYZrzOruwGHLhgmI1TCmfVve16SK5odyKaq9AKddkrzqpVkhJf/lkDLUTs7QkfeerIzU9F8m4S2kvR7aa18PRncXAEQvQxNyBFLgJy9WfG9uQWCdunpyVSZqvpO98/cJZRC1N+9h3tVdeybiTKriYMo/J0IpuLIaUVUQatU1pI1e2GFyA0P7OXXVarjS59UsslpHSoHGLlXDKtlJICW7GqG01d6MYcvziVJOUi2RzgbKQ9k+ZXFydnDXiRrFLLIBYfk7JlrbD1RlzHez+CPU9V74kQG27anPHKkoCvyFydzpsulEMQDjaz61ekl2EFqtCjvnXQq7a1xZyoVLKuttxEvPft+LZ5XMUMtdervkea7MkluGLL43f1Qh0ptCVYojdNKmGzbk5U6we7oDPCTDapAYaY3AWVUrZVOXnWkqcHD75YrKkyFGCG/hNcQ/ca3bHP2fZ+ALTta+xG8UQuzCficmZorkBtdp+WqwdySDyTR4uj03qJHIHWI2AmFReSTzIvdel96ekfMxFLFGwNj4roEVQ16UbxQDIOtEeHK3MwrHukAyl5NThm0A1rz9F+dRsI2YNuStqTkwqlpZbX4q7k6rcSl3WXLpRDNKbLXE3JB3vGywSq6FWcJAzE0MycRZGDaUgHaAhH1haj29lLY3Qp7ZdgxxLzVYgPmst1oZUtqL+nDsyCwDkeRkstxrWXiFjprNEptw2OSQrdg/3zGbsE/enNL+dVlsuQH6OJLcN6dgtbQeQ33tO8WBpD1H5XgYbUgo+H9T+m/tdQs7ETSHXBWrlNnG0DOBywTSJe5EDN6ZauEXS+IqL1Erg7n1oDpSOky4Ug5RQUNEXlCn14yTuQAlSJVF7QMfI9eHtFdQHFyyOmeW2ue1zFzk3qyQwmxIvkNQTcxVd+WJB2pAyKg3Sdq8YfBpVesE1ouu5eXP8vNAKMrULIZnc7sQMRcnd6/DFGEKTmVsAQv1jx0ZSKelvbvW2J7yrHDkZXaUhCYjnWi4uXSkGTkP6bnaqRSDR/jnyScpyq5xvIMQi6DWuQ4rEkuImpiRoK7UQcmTj8rZQqinyunliFm9qG67S2ShXQhJ448qUuguS77k8odUxVmfuYI2tgC0CXhKZUsvX7Js5g7G+iRuKj+X0V6ic20bKoukjqhiI6AARfYuIniSiJ4joI0P6PUT0UyJ6dPgctsp8nIjOEtFTRPTuVKFCJidHrYFRErD0EVsFUnFvfi0kvnhKoMwt7/ZtrnmfQsxHr9kGNyF91lSKUk+RuZYbAcgeu34JwMeMMd8nojcA2COih4fvPmeM+Ts7MxHdAOBOAG8D8AcA/oOI/sgY87JUqLFD7Z9D3WtpEnJMq5oTTyJz7Nq4fsihdt+FTF0uGOz7u1ROrqzbX5L+T4W7JyXX7at/aqIWgzHmgjHm+8PvvwLwJID9gSJHADxgjPmNMebHAM4CuDlVMFc5jGn2Tx+x6K2UkshuLJDkElot3EFbMlhikyMkt9Tdik3CHLeNQ7ry1mpPUj5lrEhjU9L0nDZ8JMUYiOjNAN4O4LtD0oeJ6AwR3UdEVw5p+wE8bxU7B0aRENExItolot29vR3mV18AAARgSURBVL1Qm+Kb5hvAbkfGfEHuu1AHl/rivjySFShGiSkaS3eDqalySNN8xO6Pz5Vo6cbUjI2E7kdMwefIYyNWDET0egBfBfBRY8wvAdwL4K0AbgRwAcBnxqxM8TXpjDEnjDE7xpgd+2WwTp4qHS2tJ9USkZbj6nE/rZDECex8Of2dYiXEBm1osucGM+08uTGaHMUXyy+599LFyc5Tw/0QKQYiejVWSuHLxpivAYAx5gVjzMvGmN8B+AIuuQvnABywil8H4HyxpJdkSf7evQEpFkioo3MHSyu/UTJwWlockvIpVljMJYhZCamKJ0TO6h5yRSXKNNUlduNQRdgCch+sLID7Afy9k77P+v2vsIorAKug4w8AvBbA9QCeBXBFpA2jH/3op/lnNzbfx49kV+JWAO8H8BgRPTqkfQLA+4joxqHB5wB8CACMMU8Q0YMAfojVjsbdJmFHQlGU+enl6coXAfwvgJ/NLYuAq7EMOYHlyKpy1oeT9Q+NMW+SFO5CMQAAEe0a4SOhc7IUOYHlyKpy1qdU1q6ORCuK0geqGBRFWaMnxXBibgGELEVOYDmyqpz1KZK1mxiDoij90JPFoChKJ8yuGIjoNlo9nn2WiI7PLY8LET1HRI/R6tHy3SHtKiJ6mIieHn5eGaungVz3EdFFInrcSmPlohWfH/r4DBHd1IGs91Cjx/YL5PS9YqCrfg3IWa9PpSehWnwAXAHgGQBvAfAarE5M3jCnTIyMzwG42kn7WwDHh9+PA/ibGeR6B4CbADwekwvAYQD/itUp1lsAfLcDWe8B8NdM3htw+cnZZxA5OVtRzn0Abhp+fwOAHw3ydNWvATmr9encFsPNAM4aY541xvwWwANYPbbdO0cAnBx+PwngjqkFMMZ8G8DPnWSfXEcA3G9WfAfAG4lo3zSSemX1UeWx/RyM/xUDXfVrQE4fyX06t2IQPaI9MwbAN4loj4iODWnXGmMuAKubBOCa2aS7HJ9cvfZz9mP7raHLXzHQbb86cgKV+nRuxSB6RHtmbjXG3ATgdgB3E9E75hYogx77ueix/ZbQ+isGvFmZtMlkZeSs1qdzK4amj2jXwBhzfvh5EcDXsTLBXhhNxuHnxfkkvAyfXN31s5npsf0Y3CsG0GG/tn4VwtyK4REAB4noeiJ6DVbvijw1s0yvQESvo9V7LkFErwPwLgCPYyXj0SHbUQAPzSPhGj65TgH4wBBFvwXAL0bTeC4cX/w9WPUrsJL1TiJ6LRFdD+AggO9NJBMB+CKAJ40xn7W+6qpffXJW7dMpoqiRCOthrKKqzwD45NzyOLK9Bato7g8APDHKB+D3AZwG8PTw86oZZPsKVubi/2G1ItzlkwsrU/Ifhj5+DMBOB7L+0yDLmWHg2u/3+OQg61MAbp9Qzj/FysQ+A+DR4XO4t34NyFmtT/Xko6Ioa8ztSiiK0iGqGBRFWUMVg6Ioa6hiUBRlDVUMiqKsoYpBUZQ1VDEoirKGKgZFUdb4f5KHGGh5IEBmAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1ZPsRYl8ddxu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}