notebooks/Segmentation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Segmentation Network Example\n",
    "\n",
    "Builds a unet segmentation neural network with TensorFlow 2.0 eager execution ([code](../examples/color/segmentation.py))\n",
    "\n",
    "### Code Overview:\n",
    "1. Import libraries\n",
    "2. Import data for training and testing \n",
    "3. Define Model\n",
    "4. Define Loss function\n",
    "5. Define Training procedure\n",
    "6. Run Model code \n",
    "    a. Train model\n",
    "    b. Test model\n",
    "7. Plot accuracy of results\n",
    "\n",
    "## Example Code\n",
    "\n",
    "import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import absolute_import, division, print_function\n",
    "import os\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'\n",
    "\n",
    "import numpy as np\n",
    "import tensorflow as tf \n",
    "from tensorflow import keras\n",
    "from tensorflow.keras.layers import Conv2D, Conv2DTranspose, MaxPooling2D, Flatten, Dense, Dropout, BatchNormalization, concatenate\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define DataGenerator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import cairo\n",
    "\n",
    "WIDTH = 128\n",
    "HEIGHT = 128\n",
    "CHANNELS = 3\n",
    "\n",
    "class DataGenerator:\n",
    "\n",
    "    def __init__(self):\n",
    "        self.size = 1000\n",
    "        self.ratio = 0.8\n",
    "        self.threshold = [128, 0, 0]\n",
    "\n",
    "        self.WIDTH = WIDTH\n",
    "        self.HEIGHT = HEIGHT\n",
    "        self.CHANNELS = CHANNELS\n",
    "\n",
    "        self.generate();\n",
    "\n",
    "    def generate_image(self):\n",
    "        ''' Randomly generates an image with random boxes '''    \n",
    "\n",
    "        data = np.zeros( (HEIGHT,WIDTH, 4), dtype=np.uint8 ) \n",
    "        surface = cairo.ImageSurface.create_for_data( data, cairo.FORMAT_ARGB32, WIDTH, HEIGHT )\n",
    "        ctx = cairo.Context( surface )\n",
    "\n",
    "        ctx.scale (WIDTH, HEIGHT) # Normalizing the canvas\n",
    "        ctx.set_source_rgb(0, 0, 0)\n",
    "        ctx.rectangle (0, 0, 1, 1)  # Rectangle(x0, y0, x1, y1) \n",
    "        ctx.fill()\n",
    "\n",
    "        # Create random colored boxes\n",
    "        for _ in range(50):\n",
    "            rc = np.random.rand(3)\n",
    "            ctx.set_source_rgb(rc[0], rc[1], rc[2])\n",
    "\n",
    "            r = np.random.rand(2)\n",
    "            ctx.translate (r[0], r[1])      # Changing the current transformation matrix\n",
    "            ctx.rectangle (0, 0, 0.1, 0.1)  # Rectangle(x0, y0, x1, y1)\n",
    "            ctx.fill()\n",
    "            ctx.translate (-r[0], -r[1])    # Changing the current transformation matrix\n",
    "\n",
    "        # Create a randomly placed red box\n",
    "        ctx.set_source_rgb(0, 0, 1)\n",
    "        r = np.random.rand(2)\n",
    "        ctx.translate (r[0], r[1])      # Changing the current transformation matrix\n",
    "        ctx.rectangle (0, 0, 0.1, 0.1)  # Rectangle(x0, y0, x1, y1)\n",
    "        ctx.fill()\n",
    "        ctx.translate (-r[0], -r[1])\n",
    "\n",
    "        img = data[:,:,0:3]\n",
    "        return img;\n",
    "\n",
    "    def whiten_data(self, features):\n",
    "        \"\"\" whiten dataset - zero mean and unit standard deviation \"\"\"\n",
    "        features = np.reshape(features, (self.size, WIDTH * HEIGHT * CHANNELS))\n",
    "        features = (np.swapaxes(features,0,1) - np.mean(features, axis=1)) / np.std(features, axis=1)\n",
    "        features = np.swapaxes(features,0,1)\n",
    "        features = np.reshape(features, (self.size, WIDTH, HEIGHT, CHANNELS))\n",
    "        #features = (features - np.mean(features, axis=0)) / np.std(features, axis=0)\n",
    "        return features\n",
    "\n",
    "    def unwhiten_img(self, img): \n",
    "        \"\"\" remove whitening for a single image \"\"\" \n",
    "        img = np.reshape(img, (WIDTH * HEIGHT * CHANNELS))\n",
    "        img = (img - np.min(img)) / (np.max(img) - np.min(img)) \n",
    "        img = np.reshape(img, (WIDTH, HEIGHT, CHANNELS))\n",
    "        return img\n",
    "\n",
    "    def generate(self):\n",
    "        ''' Generates a randomly generated dataset '''\n",
    "        img = self.generate_image()\n",
    "        self.data = np.stack( (img, self.generate_image()))\n",
    "        for _ in range(self.size - 2):\n",
    "            img = self.generate_image()\n",
    "            self.data = np.concatenate( (self.data, img[None,:]), axis=0)\n",
    "        \n",
    "        # Generate truth data\n",
    "        self.label = np.all(np.greater_equal(self.data, self.threshold), axis=3) * 1.0;\n",
    "        self.label = np.reshape(self.label, (self.size, WIDTH, HEIGHT, 1))\n",
    "        self.label = np.concatenate( (1 - self.label, self.label), axis=3) # Index 0: Incorrect, Index 1: Correct\n",
    "\n",
    "        # Setup data \n",
    "        self.data = self.whiten_data(self.data)\n",
    "\n",
    "        # Split data into test/training sets\n",
    "        index = int(self.ratio * len(self.data)) # Split index\n",
    "        self.x_train = self.data[0:index, :].astype(np.float32)\n",
    "        self.y_train = self.label[0:index].astype(np.float32)\n",
    "        self.x_test = self.data[index:,:].astype(np.float32)\n",
    "        self.y_test = self.label[index:].astype(np.float32)\n",
    "    \n",
    "        # Data lengths\n",
    "        self.train_length = self.x_train.shape[0]\n",
    "        self.test_length = self.x_test.shape[0]\n",
    "\n",
    "    def show(self, index):\n",
    "        ''' Show a data slice at index'''\n",
    "        img = self.unwhiten_img( self.data[index] )\n",
    "        plt.imshow(img)\n",
    "        plt.show()\n",
    "\n",
    "    def show_label(self, index):\n",
    "        ''' Show a truth data slice at index'''\n",
    "        img = self.label[index]\n",
    "        plt.imshow(img[:,:,0], cmap='gray')\n",
    "        plt.show()  \n",
    "        plt.imshow(img[:,:,1], cmap='gray')\n",
    "        plt.show()  \n",
    "\n",
    "    def print(self):\n",
    "        print(\"Data Split: \", self.ratio)\n",
    "        print(\"Train => x:\", self.x_train.shape, \" y:\", self.y_train.shape)\n",
    "        print(\"Test  => x:\", self.x_test.shape, \" y:\", self.y_test.shape)\n",
    "\n",
    "    def next_batch(self, batch_size):\n",
    "        ''' Retrieves the next batch for a given batch size '''\n",
    "        length = self.x_train.shape[0]\n",
    "        indices = np.random.randint(0, length, batch_size) # Grab batch_size values randomly\n",
    "        return [self.x_train[indices], self.y_train[indices]]\n",
    "\n",
    "    def batch_count(self, batch_size):\n",
    "        return math.floor(self.train_length / batch_size)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data Split:  0.8\n",
      "Train => x: (800, 128, 128, 3)  y: (800, 128, 128, 2)\n",
      "Test  => x: (200, 128, 128, 3)  y: (200, 128, 128, 2)\n"
     ]
    }
   ],
   "source": [
    "# Generate Dataset\n",
    "data = DataGenerator()\n",
    "data.print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set Training and Network Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Training Parameters\n",
    "num_epochs = 10\n",
    "display_step = 1\n",
    "batch_size = 16\n",
    "\n",
    "# Network Parameters\n",
    "WIDTH = data.WIDTH; HEIGHT = data.HEIGHT; CHANNELS = data.CHANNELS\n",
    "NUM_INPUTS = WIDTH * HEIGHT * CHANNELS\n",
    "NUM_OUTPUTS = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Unet Model Architecture\n",
    "def Model():\n",
    "\n",
    "    def down_block(x, filters):\n",
    "        x = Conv2D(filters, (3, 3), padding=\"same\", activation=tf.nn.relu, kernel_initializer='he_normal')(x)\n",
    "        x = Conv2D(filters, (3, 3), padding=\"same\", activation=tf.nn.relu, kernel_initializer='he_normal')(x)\n",
    "        x = BatchNormalization(axis=-1, momentum=0.95, epsilon=0.001)(x)\n",
    "        #x = Dropout(rate=0.0)(x)\n",
    "        return x\n",
    "\n",
    "    def max_pool(x):\n",
    "        return MaxPooling2D(padding=\"same\", strides=(2, 2), pool_size=(2, 2))(x)\n",
    "\n",
    "    def up_block(x, filters, skip_connect):\n",
    "        x = Conv2DTranspose(filters, (3, 3), strides=2, padding=\"same\", activation=tf.nn.relu)(x)\n",
    "        x = concatenate([x, skip_connect], axis=3)\n",
    "        x = Conv2D(filters, (3, 3), padding=\"same\", activation=tf.nn.relu, kernel_initializer='he_normal')(x)\n",
    "        x = Conv2D(filters, (3, 3), padding=\"same\", activation=tf.nn.relu, kernel_initializer='he_normal')(x)\n",
    "        x = BatchNormalization(axis=-1, momentum=0.95, epsilon=0.001)(x)\n",
    "        #x = Dropout(rate=0.0)(x)\n",
    "        return x \n",
    "\n",
    "    def unet():\n",
    "        fn = [32, 64, 128, 256, 512]\n",
    "        fdepth = len(fn)\n",
    "\n",
    "        x_stack = []\n",
    "        xin = keras.Input(shape=(HEIGHT, WIDTH, CHANNELS), name='img')\n",
    "\n",
    "        x = xin\n",
    "        for idx in range(fdepth):\n",
    "            x = down_block(x, fn[idx])\n",
    "\n",
    "            if(idx < fdepth - 1):\n",
    "                x_stack.append(x)\n",
    "                x = max_pool(x)\n",
    "\n",
    "        for idx in range(fdepth - 1):\n",
    "            idx = fdepth - idx - 2\n",
    "            x = up_block(x, fn[idx], x_stack.pop())\n",
    "\n",
    "        xout = Conv2D(NUM_OUTPUTS, (1, 1), padding=\"same\", activation=tf.nn.softmax)(x)\n",
    "        return tf.keras.Model(inputs=xin, outputs=xout)\n",
    "\n",
    "    return unet()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define Train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def train(model, inputs, outputs):\n",
    "    with tf.GradientTape() as tape:\n",
    "        predictions = model(inputs, training=True)\n",
    "        loss_value = loss(predictions, outputs)\n",
    "    grads = tape.gradient(loss_value, model.variables)\n",
    "    optimizer.apply_gradients(zip(grads, model.variables))\n",
    "    train_loss(loss_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "@tf.function\n",
    "def test(model, inputs, outputs):\n",
    "    predictions = model(inputs)\n",
    "    test_accuracy(outputs, predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set Losses and Optimizers "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"model\"\n",
      "__________________________________________________________________________________________________\n",
      "Layer (type)                    Output Shape         Param #     Connected to                     \n",
      "==================================================================================================\n",
      "img (InputLayer)                [(None, 128, 128, 3) 0                                            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d (Conv2D)                 (None, 128, 128, 32) 896         img[0][0]                        \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_1 (Conv2D)               (None, 128, 128, 32) 9248        conv2d[0][0]                     \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization (BatchNorma (None, 128, 128, 32) 128         conv2d_1[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "max_pooling2d (MaxPooling2D)    (None, 64, 64, 32)   0           batch_normalization[0][0]        \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_2 (Conv2D)               (None, 64, 64, 64)   18496       max_pooling2d[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_3 (Conv2D)               (None, 64, 64, 64)   36928       conv2d_2[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_1 (BatchNor (None, 64, 64, 64)   256         conv2d_3[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "max_pooling2d_1 (MaxPooling2D)  (None, 32, 32, 64)   0           batch_normalization_1[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_4 (Conv2D)               (None, 32, 32, 128)  73856       max_pooling2d_1[0][0]            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_5 (Conv2D)               (None, 32, 32, 128)  147584      conv2d_4[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_2 (BatchNor (None, 32, 32, 128)  512         conv2d_5[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "max_pooling2d_2 (MaxPooling2D)  (None, 16, 16, 128)  0           batch_normalization_2[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_6 (Conv2D)               (None, 16, 16, 256)  295168      max_pooling2d_2[0][0]            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_7 (Conv2D)               (None, 16, 16, 256)  590080      conv2d_6[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_3 (BatchNor (None, 16, 16, 256)  1024        conv2d_7[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "max_pooling2d_3 (MaxPooling2D)  (None, 8, 8, 256)    0           batch_normalization_3[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_8 (Conv2D)               (None, 8, 8, 512)    1180160     max_pooling2d_3[0][0]            \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_9 (Conv2D)               (None, 8, 8, 512)    2359808     conv2d_8[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_4 (BatchNor (None, 8, 8, 512)    2048        conv2d_9[0][0]                   \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_transpose (Conv2DTranspo (None, 16, 16, 256)  1179904     batch_normalization_4[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "concatenate (Concatenate)       (None, 16, 16, 512)  0           conv2d_transpose[0][0]           \n",
      "                                                                 batch_normalization_3[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_10 (Conv2D)              (None, 16, 16, 256)  1179904     concatenate[0][0]                \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_11 (Conv2D)              (None, 16, 16, 256)  590080      conv2d_10[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_5 (BatchNor (None, 16, 16, 256)  1024        conv2d_11[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_transpose_1 (Conv2DTrans (None, 32, 32, 128)  295040      batch_normalization_5[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "concatenate_1 (Concatenate)     (None, 32, 32, 256)  0           conv2d_transpose_1[0][0]         \n",
      "                                                                 batch_normalization_2[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_12 (Conv2D)              (None, 32, 32, 128)  295040      concatenate_1[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_13 (Conv2D)              (None, 32, 32, 128)  147584      conv2d_12[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_6 (BatchNor (None, 32, 32, 128)  512         conv2d_13[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_transpose_2 (Conv2DTrans (None, 64, 64, 64)   73792       batch_normalization_6[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "concatenate_2 (Concatenate)     (None, 64, 64, 128)  0           conv2d_transpose_2[0][0]         \n",
      "                                                                 batch_normalization_1[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_14 (Conv2D)              (None, 64, 64, 64)   73792       concatenate_2[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_15 (Conv2D)              (None, 64, 64, 64)   36928       conv2d_14[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_7 (BatchNor (None, 64, 64, 64)   256         conv2d_15[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_transpose_3 (Conv2DTrans (None, 128, 128, 32) 18464       batch_normalization_7[0][0]      \n",
      "__________________________________________________________________________________________________\n",
      "concatenate_3 (Concatenate)     (None, 128, 128, 64) 0           conv2d_transpose_3[0][0]         \n",
      "                                                                 batch_normalization[0][0]        \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_16 (Conv2D)              (None, 128, 128, 32) 18464       concatenate_3[0][0]              \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_17 (Conv2D)              (None, 128, 128, 32) 9248        conv2d_16[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "batch_normalization_8 (BatchNor (None, 128, 128, 32) 128         conv2d_17[0][0]                  \n",
      "__________________________________________________________________________________________________\n",
      "conv2d_18 (Conv2D)              (None, 128, 128, 2)  66          batch_normalization_8[0][0]      \n",
      "==================================================================================================\n",
      "Total params: 8,636,418\n",
      "Trainable params: 8,633,474\n",
      "Non-trainable params: 2,944\n",
      "__________________________________________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Setup Unet model\n",
    "model = Model()\n",
    "model.summary()\n",
    "\n",
    "# Set Losses and Optimizers \n",
    "loss = tf.keras.losses.CategoricalCrossentropy()\n",
    "optimizer = tf.keras.optimizers.Adam()\n",
    "train_loss = tf.keras.metrics.Mean(name='train_loss')\n",
    "test_accuracy = tf.keras.metrics.CategoricalAccuracy(name='test_accuracy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch  0: training loss=1.75705 test accuracy=0.91617\n",
      "Epoch  1: training loss=0.35460 test accuracy=0.98287\n",
      "Epoch  2: training loss=0.23441 test accuracy=0.98769\n",
      "Epoch  3: training loss=0.22768 test accuracy=0.98708\n",
      "Epoch  4: training loss=0.18005 test accuracy=0.98906\n",
      "Epoch  5: training loss=0.17037 test accuracy=0.98868\n",
      "Epoch  6: training loss=0.16304 test accuracy=0.98892\n",
      "Epoch  7: training loss=0.14469 test accuracy=0.99070\n",
      "Epoch  8: training loss=0.14379 test accuracy=0.99158\n",
      "Epoch  9: training loss=0.13169 test accuracy=0.99156\n"
     ]
    }
   ],
   "source": [
    "epochs = range(num_epochs)\n",
    "for epoch in epochs:\n",
    "\n",
    "    for _ in range(data.batch_count(batch_size)):\n",
    "        x_train, y_train = data.next_batch(batch_size)\n",
    "        train(model, x_train, y_train)\n",
    "        test(model, data.x_test, data.y_test)\n",
    "    \n",
    "    if(epoch % display_step == 0):\n",
    "        print('Epoch %2d: training loss=%2.5f test accuracy=%2.5f' % \n",
    "            (epoch, train_loss.result(), test_accuracy.result()))\n",
    "\n",
    "    # Reset the metrics for the next epoch\n",
    "    train_loss.reset_states()\n",
    "    test_accuracy.reset_states()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot Results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = model(data.x_test)\n",
    "\n",
    "index = 0\n",
    "input_data = data.unwhiten_img(data.x_test[index])\n",
    "truth_data = data.y_test[index][:,:,1] \n",
    "segmentation = np.greater(predictions[index,:,:,1], predictions[index,:,:,0]) * 1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show Original Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fee204be6d8>"
      ]
     },
     "execution_count": 11,
     "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(input_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show Truth Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fee20553ac8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p5gSvOtpkCpiKiNF0/yBFKNTdHh8CXo6IVyPiLeAp4P3U3x6t5mqD2t+7Let93BOp71+2Hk0IgWeBgTT7u4JiQdPDVW9UxelcjwETEfFQy48OA0Pp9hDFXEFlImJPRKyLiA0Uf/s3IuIe4DhwV431+AFwVtJ7UtGtFF8dX2t7UAwDtkq6Kr1GM/WotT1mmasNDgMfS3sJtgJvzgwbqqCL633cEZev97FT0hWSNrLY9T6qnORZxATIdorZ+e8CD9S0zQ9SdJmeB/4zXbZTjMePAafT9eoa2+FmLu4d2JReyEngK8AVNWz/N4Cx1Cb/DKzqRXsAfwG8BJwA/pFi1ruW9gD2U8xFvEXxH3bXXG1A0Q3/2/S+fQEYrLgekxRj/5n36xdaHv9Aqscp4LbFbMuHDZtlrgnDATPrIYeAWeYcAmaZcwiYZc4hYJY5h4BZ5hwCZpn7fzVftIbviLJTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(truth_data, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show Prediction Results "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fee2040dc18>"
      ]
     },
     "execution_count": 14,
     "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(segmentation, cmap='gray')"
   ]
  },
  {
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}