Image_Loading.ipynb

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   "metadata": {},
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   "source": [
    "import os\n",
    "\n",
    "data_path = os.getcwd() + '/DATA/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from PIL import Image\n",
    "from tqdm import tqdm_notebook as tqdm\n",
    "from IPython.display import display, HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that all the images have a huge of black background. If we find the biggest figure, we will be able to reduce the amount of memory and computation needed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "top: 24, bot: 188, left: 0, right: 171\n"
     ]
    }
   ],
   "source": [
    "\n",
    "def max_extension(path, verbose = False):\n",
    "    ''' Returns the max extension of the biggest figure in the collection (i.e. the minimum pixels needed)\n",
    "    ---------\n",
    "    PARAMETERS\n",
    "    - path: string containing the dirpath to the data directory\n",
    "    ---------\n",
    "    RETURNS\n",
    "    - (top, bot, left, right)\n",
    "    \n",
    "    '''\n",
    "    # We initialize the values\n",
    "    top, bot, left, right = np.inf, 0, np.inf, 0\n",
    "    \n",
    "    # Hence we only need to read one figure of each class and rotate it in order to get the max values\n",
    "    for label in os.listdir(data_path):\n",
    "        \n",
    "        # We don't want to read hidden objects in the directory\n",
    "        if label[0] != '.':\n",
    "            # Iteration info\n",
    "            if verbose:\n",
    "                print('-' * 40)\n",
    "                print(f\"Reading figure {label}...\")\n",
    "                print('-' * 40)\n",
    "            \n",
    "            # Path to the first image of each label\n",
    "            label_path = data_path + label + '/'\n",
    "            first_image = list(os.listdir(label_path))[0]\n",
    "            first_image = label_path + first_image\n",
    "            \n",
    "            try:\n",
    "                image = Image.open(first_image).convert('L')\n",
    "                image = np.asarray(image)\n",
    "            except:\n",
    "                print(f'Failed reading image!')\n",
    "                \n",
    "            # Double loop for every image\n",
    "            top_, bot_, left_, right_ = np.inf, 0, np.inf, 0\n",
    "            \n",
    "            for i in range(200):\n",
    "                for j in range(200):\n",
    "                    if (image[i, j] != 0):\n",
    "                        if i < top_: top_ = i\n",
    "                        if i > bot_: bot_ = i\n",
    "                        if j < left_: left_ = j\n",
    "                        if j > right_: right_ = j\n",
    "            \n",
    "            if verbose:\n",
    "                print(f\"Max values: {top_}, {bot_}, {left_}, {right_}\\n\")\n",
    "            \n",
    "            # Update global values if necessary\n",
    "            if top_ < top: top = top_\n",
    "            if bot_ > bot: bot = bot_\n",
    "            if left_ < left: left = left_\n",
    "            if right_ > right: right = right_\n",
    "        \n",
    "    return (top, bot, left, right)\n",
    "                      \n",
    "top, bot, left, right = max_extension(data_path)\n",
    "\n",
    "print(f\"top: {top}, bot: {bot}, left: {left}, right: {right}\")"
   ]
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      "/Users/berges/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:9: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
      "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
      "  if __name__ == '__main__':\n"
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      "/Users/berges/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:15: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
      "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
      "  from ipykernel import kernelapp as app\n"
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       "    <tr>\n",
       "      <th>399</th>\n",
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       "      <td>3673 Peg 2M</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>6379 rows × 40001 columns</p>\n",
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      ],
      "text/plain": [
       "    0     1     2     3     4     5     6     7     8     9      ... 39991  \\\n",
       "0       0     0     0     0     0     0     0     0     0     0  ...     0   \n",
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       "4       0     0     0     0     0     0     0     0     0     0  ...     0   \n",
       "..    ...   ...   ...   ...   ...   ...   ...   ...   ...   ...  ...   ...   \n",
       "395     0     0     0     0     0     0     0     0     0     0  ...     0   \n",
       "396     0     0     0     0     0     0     0     0     0     0  ...     0   \n",
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       "399     0     0     0     0     0     0     0     0     0     0  ...     0   \n",
       "\n",
       "    39992 39993 39994 39995 39996 39997 39998 39999           40000  \n",
       "0       0     0     0     0     0     0     0     0  3005 Brick 1x1  \n",
       "1       0     0     0     0     0     0     0     0  3005 Brick 1x1  \n",
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       "3       0     0     0     0     0     0     0     0  3005 Brick 1x1  \n",
       "4       0     0     0     0     0     0     0     0  3005 Brick 1x1  \n",
       "..    ...   ...   ...   ...   ...   ...   ...   ...             ...  \n",
       "395     0     0     0     0     0     0     0     0     3673 Peg 2M  \n",
       "396     0     0     0     0     0     0     0     0     3673 Peg 2M  \n",
       "397     0     0     0     0     0     0     0     0     3673 Peg 2M  \n",
       "398     0     0     0     0     0     0     0     0     3673 Peg 2M  \n",
       "399     0     0     0     0     0     0     0     0     3673 Peg 2M  \n",
       "\n",
       "[6379 rows x 40001 columns]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "colnames = ['pixel' + str(i) for i in range(1, 4001)]\n",
    "colnames.append('label')\n",
    "\n",
    "def read_all_data(path):\n",
    "    '''\n",
    "    \n",
    "    '''\n",
    "    \n",
    "    for it, label in tqdm(enumerate(os.listdir(data_path)), total = 16):\n",
    "        if label[0] != '.':\n",
    "            label_dir = data_path + label + '/'\n",
    "            \n",
    "            count = 379 if (label == '2357 Brick corner 1x2x2') else 400\n",
    "            \n",
    "            for i, im in tqdm(enumerate(os.listdir(label_dir)), total = count):\n",
    "                \n",
    "                try:\n",
    "                    image = Image.open(label_dir + im).convert('L')\n",
    "                    image = list(np.asarray(image).flatten().astype('uint8'))\n",
    "                    image.append(label)\n",
    "\n",
    "                    if i == 0: label1 = image\n",
    "                    else: label1 = np.vstack((label1, image))\n",
    "                \n",
    "                except:\n",
    "                    print(f'Failed reading image: {im}')\n",
    "            \n",
    "            if it == 0: \n",
    "                dataframe = pd.DataFrame(label1)\n",
    "            else: \n",
    "                dataframe = dataframe.append(pd.DataFrame(label1))\n",
    "                \n",
    "    return dataframe\n",
    "        \n",
    "dataframe = read_all_data(data_path)   \n",
    "        \n",
    "dataframe   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "export = dataframe.to_csv(r'flattened.csv', index = False, header = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read the file:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def read_data():\n",
    "    # Specify dtypes\n",
    "    dtypes = {'pixel-' + str(i): 'uint8' for i in range(1, 40001)}\n",
    "    dtypes.update({'label' : 'category'})\n",
    "    \n",
    "    colnames = list(dtypes.keys())\n",
    "    \n",
    "    print('Reading data...')\n",
    "    data = pd.read_csv(\n",
    "        'flattened.csv', header = None, names = colnames, dtype = dtypes\n",
    "    )\n",
    "    print(f'train.cv file has {data.shape[0]} rows and {data.shape[1]} columns')\n",
    "    print(f'Memory usage: {round(data.memory_usage().sum() / 1024**2, 3)} Mb\\n')\n",
    "    \n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reading data...\n",
      "train.cv file has 6379 rows and 40001 columns\n",
      "Memory usage: 243.346 Mb\n",
      "\n"
     ]
    },
    {
     "data": {
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       "  </tbody>\n",
       "</table>\n",
       "<p>6379 rows × 40001 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      pixel-1  pixel-2  pixel-3  pixel-4  pixel-5  pixel-6  pixel-7  pixel-8  \\\n",
       "0           0        0        0        0        0        0        0        0   \n",
       "1           0        0        0        0        0        0        0        0   \n",
       "2           0        0        0        0        0        0        0        0   \n",
       "3           0        0        0        0        0        0        0        0   \n",
       "4           0        0        0        0        0        0        0        0   \n",
       "...       ...      ...      ...      ...      ...      ...      ...      ...   \n",
       "6374        0        0        0        0        0        0        0        0   \n",
       "6375        0        0        0        0        0        0        0        0   \n",
       "6376        0        0        0        0        0        0        0        0   \n",
       "6377        0        0        0        0        0        0        0        0   \n",
       "6378        0        0        0        0        0        0        0        0   \n",
       "\n",
       "      pixel-9  pixel-10  ...  pixel-39992  pixel-39993  pixel-39994  \\\n",
       "0           0         0  ...            0            0            0   \n",
       "1           0         0  ...            0            0            0   \n",
       "2           0         0  ...            0            0            0   \n",
       "3           0         0  ...            0            0            0   \n",
       "4           0         0  ...            0            0            0   \n",
       "...       ...       ...  ...          ...          ...          ...   \n",
       "6374        0         0  ...            0            0            0   \n",
       "6375        0         0  ...            0            0            0   \n",
       "6376        0         0  ...            0            0            0   \n",
       "6377        0         0  ...            0            0            0   \n",
       "6378        0         0  ...            0            0            0   \n",
       "\n",
       "      pixel-39995  pixel-39996  pixel-39997  pixel-39998  pixel-39999  \\\n",
       "0               0            0            0            0            0   \n",
       "1               0            0            0            0            0   \n",
       "2               0            0            0            0            0   \n",
       "3               0            0            0            0            0   \n",
       "4               0            0            0            0            0   \n",
       "...           ...          ...          ...          ...          ...   \n",
       "6374            0            0            0            0            0   \n",
       "6375            0            0            0            0            0   \n",
       "6376            0            0            0            0            0   \n",
       "6377            0            0            0            0            0   \n",
       "6378            0            0            0            0            0   \n",
       "\n",
       "      pixel-40000           label  \n",
       "0               0  3005 Brick 1x1  \n",
       "1               0  3005 Brick 1x1  \n",
       "2               0  3005 Brick 1x1  \n",
       "3               0  3005 Brick 1x1  \n",
       "4               0  3005 Brick 1x1  \n",
       "...           ...             ...  \n",
       "6374            0     3673 Peg 2M  \n",
       "6375            0     3673 Peg 2M  \n",
       "6376            0     3673 Peg 2M  \n",
       "6377            0     3673 Peg 2M  \n",
       "6378            0     3673 Peg 2M  \n",
       "\n",
       "[6379 rows x 40001 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 3min 34s, sys: 3.94 s, total: 3min 38s\n",
      "Wall time: 3min 38s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "lego = read_data()\n",
    "display(lego)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [],
   "source": [
    "# just tryin' some stuff:\n",
    "im1 = np.array(lego.iloc[0][:-1]).astype('uint8')\n",
    "im2 = np.array(lego.iloc[1][:-1]).astype('uint8')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "33796"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, ybins = list(np.histogram(image, bins = 255))\n",
    "y2, y2bins = list(np.histogram(image2, bins = 255))\n",
    "y2[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [],
   "source": [
    "def histogram_intersection(im1, im2, n_bins = 255, normalization = False):\n",
    "    ''' Histogram intersection of two gray-scale images -> it finds the number of matches at level 'L'\n",
    "    ----------\n",
    "    PARAMETERS\n",
    "    - im1, im2: flattened numpy.ndarray representing a 200x200 image (must be of the same length)\n",
    "    - n_bins: integer that defines the number of equal-width bins in the given range\n",
    "    - normalization: Boolean indicating if normalization should be performed\n",
    "    ----------\n",
    "    RETURNS\n",
    "    - intersection: returns a histogram representing the intersection\n",
    "    \n",
    "    '''\n",
    "    assert len(im1) == len(im2), \"Length of images 'im1' and 'im2' must be the same\"\n",
    "    \n",
    "    # Build the histograms from 'im1' and 'im2' espectively, with the specified number of bins\n",
    "    h1, _ = np.histogram(im1, bins = n_bins, range = (0, 255))\n",
    "    h2, _ = np.histogram(im1, bins = n_bins, range = (0, 255))\n",
    "    \n",
    "    intersection = np.minimum(h1, h2)\n",
    "    #intersect = np.true_divide(np.sum(intersect), np.sum(h2)) if normalization else np.sum(intersect)\n",
    "    \n",
    "    return intersection\n",
    "\n",
    "\n",
    "\n",
    "def divide_image(im, l):\n",
    "    ''' Split the image matrix 'im' into 2^(2L) blocks\n",
    "    ----------\n",
    "    PARAMETERS\n",
    "    - im: flattened numpy.ndarray representing a 200x200 image\n",
    "    - L: grid levels\n",
    "    ----------\n",
    "    RETURNS\n",
    "    - list with the different blocks of the image\n",
    "     \n",
    "    '''\n",
    "    assert len(im) == 40000, 'Image is not 200x200 resolution'\n",
    "    \n",
    "    nrows = 200 // (2**l)\n",
    "    im = np.reshape(im, newshape = (200, 200))\n",
    "    \n",
    "    splits = (im.reshape(200//nrows, nrows, -1, nrows)\n",
    "                .swapaxes(1, 2)\n",
    "                .reshape(-1, nrows, nrows))\n",
    "    \n",
    "    # Return the flattened split of the image\n",
    "    return [split.flatten() for split in splits]\n",
    "\n",
    "\n",
    "\n",
    "def kernel_ij(im1, im2, L, n_bins = 255, normalization = False):\n",
    "    '''\n",
    "    \n",
    "    \n",
    "    '''\n",
    "    \n",
    "    # For I_0\n",
    "    histogram = (1/2**L) * histogram_intersection(im1, im2, n_bins, normalization)    \n",
    "    \n",
    "    # For the rest:\n",
    "    for l in range(1, L + 1):\n",
    "\n",
    "        # Split images into 2^2l blocks\n",
    "        im1_split = divide_image(im1, l)\n",
    "        im2_split = divide_image(im2, l)\n",
    "\n",
    "        # Factor in the l-th iteration\n",
    "        factor = 1 / (2**(L - l + 1))\n",
    "\n",
    "        intersection = np.zeros(n_bins)\n",
    "        # Compute and add histogram intersection of every block\n",
    "        for i in range(len(im1_split)):\n",
    "            intersection += factor * histogram_intersection(im1_split[i], im2_split[i], n_bins, normalization)\n",
    "\n",
    "        histogram += intersection\n",
    "    \n",
    "    return histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True,  True,  True,  True,  True,  True,  True,  True,\n",
       "        True,  True])"
      ]
     },
     "execution_count": 208,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kernel_ij(im1, im2, n_bins = 20, L = 3) == kernel_ij(im1, im2, n_bins = 20, L = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "split_image = divide_image(image, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([  0,   0,   0, ..., 156, 154, 154], dtype=uint8),\n",
       " array([0, 0, 0, ..., 0, 0, 0], dtype=uint8),\n",
       " array([0, 0, 0, ..., 0, 0, 0], dtype=uint8),\n",
       " array([154, 154, 153, ...,   0,   0,   0], dtype=uint8)]"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "split_image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12, 8))\n",
    "plt.hist(y, bins = ybins, color = 'indianred')\n",
    "plt.hist(y2, bins = y2bins, color = 'lightblue')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PNG\n",
      "RGBA\n",
      "(200, 200)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x121106a90>"
      ]
     },
     "execution_count": 24,
     "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": [
    "from PIL import Image\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# load the image\n",
    "image = Image.open('./DATA/3005 Brick 1x1/0267.png')\n",
    "# summarize some details about the image\n",
    "print(image.format)\n",
    "print(image.mode)\n",
    "print(image.size)\n",
    "#show the image\n",
    "plt.imshow(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "float32\n",
      "(200, 200, 4)\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": [
    "from matplotlib import image\n",
    "\n",
    "data = image.imread('./DATA/3005 Brick 1x1/0267.png')\n",
    "print(data.dtype)\n",
    "print(data.shape)\n",
    "\n",
    "plt.imshow(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 200)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img = Image.open('./DATA/3005 Brick 1x1/0267.png').convert('L')\n",
    "data = np.asarray(img)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x10f357110>"
      ]
     },
     "execution_count": 39,
     "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(data, cmap = 'gray', vmin = 0, vmax = 255)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}