BMEN4460_NB1_simple_cell_segmentation_with_single_layered_perceptrons.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Cell Segmentation with Single-Layered Perceptrons.\n",
    "Nanyan \"Rosalie\" Zhu and Chen \"Raphael\" Liu.\n",
    "\n",
    "This notebook belongs to this repository [\"RnR-2018/BMEN4460-NB1-simple_cell_segmentation_with_a_single_layered_perceptron\"](https://github.com/RnR-2018/BMEN4460-NB1-simple_cell_segmentation_with_a_single_layered_perceptron) and its parent repository [\"RnR-2018/Deep-learning-with-PyTorch-and-GCP\"](https://github.com/RnR-2018/Deep-learning-with-PyTorch-and-GCP)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Import the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from helper import rescaling, extract_patches_given_center, extract_all_patches, grouper"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the random seed to ensure reproducibility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.manual_seed(20200202)\n",
    "np.random.seed(20200202)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Load a sample microscopy cell image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "cell_image_path = './data/sample_cell_img.tif'\n",
    "cell_image = plt.imread(cell_image_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max intensity: 4095 \n",
      "Mean intensity: 248.141166556145 \n",
      "Min intensity: 120\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": [
    "plt.imshow(cell_image, cmap = 'gray')\n",
    "plt.axis('off');\n",
    "print('Max intensity: %s \\nMean intensity: %s \\nMin intensity: %s' % (cell_image.max(), cell_image.mean(), cell_image.min()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Adjust the image to satisfy our human eyes.\n",
    "Also it is generally a good practise to rescale the image intensity to between 0 and 1 if these pixel values are going to be fed as inputs to a neural network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max intensity: 1.0 \n",
      "Mean intensity: 0.09958455 \n",
      "Min intensity: 0.0\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": [
    "adjusted_cell_image = rescaling(np.float32(cell_image), lower_fraction = 0.001, upper_fraction = 0.999, out_range = (0, 1))\n",
    "plt.imshow(adjusted_cell_image, cmap = 'gray')\n",
    "plt.axis('off');\n",
    "print('Max intensity: %s \\nMean intensity: %s \\nMin intensity: %s' % (adjusted_cell_image.max(), adjusted_cell_image.mean(), adjusted_cell_image.min()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Note that this image is fairly easy to segment semantically. A simple thresholding will do the job."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "segmented_cell_image = np.int16(adjusted_cell_image > adjusted_cell_image.mean())\n",
    "plt.imshow(segmented_cell_image, cmap = 'gray')\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Crop out a small patch with one single cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "single_cell_image = adjusted_cell_image[0:50, 210:260]\n",
    "segmented_single_cell_image = segmented_cell_image[0:50, 210:260]\n",
    "plt.imshow(single_cell_image, cmap = 'gray')\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now we are going to use a single-layered perceptron to perform a semantic segmentation task.\n",
    "Credit to [this Medium Post](https://medium.com/@tomgrek/building-your-first-neural-net-from-scratch-with-pytorch-56b0e9c84d54).\n",
    "\n",
    "### Perceptron Candidate One! Single input single output.\n",
    "\n",
    "This is probably the easiest neural network that you will ever see. It has the simplest structure and does the simplest function. It consists of 1 single layer, 1 single neuron/node, and the input/output pair each consists of 1 tensor of size 1 (aka, a scalar). It is supposed to map the pixel intensity in the cell image to the segmentation result for that pixel (whether or not the pixel belongs to a cell). It only uses the information on each specific pixel itself without looking at any of the surroundings or the global picture.\n",
    "\n",
    "We used a sigmoid activation function because the task is a binary classification task.\n",
    "\n",
    "- Input: A scalar representing the pixel intensity.\n",
    "- Output: A scalar representing the likelihood for the corresponding input scalar to belong to a cell.\n",
    "\n",
    "<img src=\"data/perceptron_single_input.PNG\" width=\"1200\" align=\"center\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Build our perceptron candidate 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class perceptron_candidate1(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(perceptron_candidate1, self).__init__()\n",
    "        self.fc1 = nn.Linear(1, 1, bias = True)\n",
    "    def forward(self, x):\n",
    "        x = torch.sigmoid(self.fc1(x))\n",
    "        return x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define the loss function (for all our perceptrons)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_function(out, label):\n",
    "    return (label - out)**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### How do we train our percepron?\n",
    "\n",
    "We can select the pixels from the cell image as the input, and the corresponding pixels in the segmented (by simple thresholding) as the ground truth to guide the training. We are going to use the pixels in the single-cell image that we just cropped out recently as our test set. **We need to make sure not to use the data in the test set to train our perceptron.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Crop out a certain region, that doesn't contain the test image, for training.\n",
    "# adjust_cell_image_subset_for_training and segmented_cell_image_subset_for_training are both 100x100 images.\n",
    "adjust_cell_image_subset_for_training = adjusted_cell_image[100:200, 0:100]\n",
    "segmented_cell_image_subset_for_training = segmented_cell_image[100:200, 0:100]\n",
    "\n",
    "# training_input and ground_truth are both of length 10000, as they are flattened versions of the corresponding 100x100 images.\n",
    "training_input = adjust_cell_image_subset_for_training.flatten()\n",
    "ground_truth = segmented_cell_image_subset_for_training.flatten()\n",
    "\n",
    "# Reshape the horizonal arrays to vertical arrays. Now they become 10000x1 vectors.\n",
    "training_input = np.reshape(training_input, (len(training_input), 1))\n",
    "ground_truth = np.reshape(ground_truth, (len(ground_truth), 1))\n",
    "\n",
    "# Stack them together\n",
    "training_data = np.hstack((training_input, ground_truth))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.06533262, 0.        ],\n",
       "       [0.05624202, 0.        ],\n",
       "       [0.0595477 , 0.        ],\n",
       "       ...,\n",
       "       [0.02731738, 0.        ],\n",
       "       [0.02401171, 0.        ],\n",
       "       [0.02483813, 0.        ]], dtype=float32)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# training_data consists of 2 columns: pixel value and segmentation ground truth (0 or 1).\n",
    "training_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perceptron_candidate1(\n",
      "  (fc1): Linear(in_features=1, out_features=1, bias=True)\n",
      ")\n",
      "Epoch 0 - loss: 0.3928207755088806\n",
      "Epoch 1 - loss: 0.14258016645908356\n",
      "Epoch 2 - loss: 0.09995075315237045\n",
      "Epoch 3 - loss: 0.08058656752109528\n",
      "Epoch 4 - loss: 0.06964526325464249\n",
      "Epoch 5 - loss: 0.06264661252498627\n",
      "Epoch 6 - loss: 0.05779075622558594\n",
      "Epoch 7 - loss: 0.05421843007206917\n",
      "Epoch 8 - loss: 0.05147183686494827\n",
      "Epoch 9 - loss: 0.04928478226065636\n"
     ]
    }
   ],
   "source": [
    "# Initialize our perceptron.\n",
    "our_perceptron_candidate1 = perceptron_candidate1()\n",
    "print(our_perceptron_candidate1)\n",
    "\n",
    "# Define the optimizer.\n",
    "candidate1_optimizer = optim.SGD(our_perceptron_candidate1.parameters(), lr = 0.01, momentum = 0.5)\n",
    "\n",
    "# Train for 10 epochs.\n",
    "for epoch in range(10):\n",
    "    # Create a list to store the losses over every epoch.\n",
    "    Epoch_loss_list = []\n",
    "    # enumerate the training data.\n",
    "    for iteration, training_input_GT_pair in enumerate(training_data):\n",
    "        # isolate the training input and ground truth from the training data.\n",
    "        training_input, GT = iter(training_input_GT_pair)\n",
    "        # redefine the training input and ground truth and PyTorch tensors.\n",
    "        training_input, GT = Variable(torch.FloatTensor([training_input])), \\\n",
    "                             Variable(torch.FloatTensor([GT]))\n",
    "        # reset the gradient for the optimizer.\n",
    "        candidate1_optimizer.zero_grad()\n",
    "        # use the current model to predict the output from the input.\n",
    "        outputs = our_perceptron_candidate1(training_input)\n",
    "        # compute the loss (metric of goodness) between the prediction and the ground truth.\n",
    "        loss = loss_function(outputs, GT)\n",
    "        # backpropogate the gradient\n",
    "        loss.backward()\n",
    "        # update the weights using the gradient with the optimizer\n",
    "        candidate1_optimizer.step()\n",
    "        \n",
    "        # append the current loss value to the loss list for this epoch.\n",
    "        Epoch_loss_list.append(loss.data[0])\n",
    "\n",
    "        # print the current loss every 1000 iterations.\n",
    "        if (iteration % 1e4 == 0):\n",
    "            print(\"Epoch {} - loss: {}\".format(epoch, np.mean(Epoch_loss_list)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What's the probability for a cell image pixel with value 0.1 to belong to a cell?  0.31709003\n",
      "What's the probability for a cell image pixel with value 0.2 to belong to a cell?  0.66944\n",
      "What's the probability for a cell image pixel with value 0.5 to belong to a cell?  0.99408394\n"
     ]
    }
   ],
   "source": [
    "print(\"What's the probability for a cell image pixel with value 0.1 to belong to a cell? \", \\\n",
    "      our_perceptron_candidate1(Variable(torch.Tensor([[[0.1]]]))).cpu().detach().numpy()[0][0][0])\n",
    "\n",
    "print(\"What's the probability for a cell image pixel with value 0.2 to belong to a cell? \", \\\n",
    "      our_perceptron_candidate1(Variable(torch.Tensor([[[0.2]]]))).cpu().detach().numpy()[0][0][0])\n",
    "\n",
    "print(\"What's the probability for a cell image pixel with value 0.5 to belong to a cell? \", \\\n",
    "      our_perceptron_candidate1(Variable(torch.Tensor([[[0.5]]]))).cpu().detach().numpy()[0][0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's try it out on our test image (the single-cell cropped-out image)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "candidate1_predicted_segmentation = np.zeros(single_cell_image.shape)\n",
    "\n",
    "for current_row in range(candidate1_predicted_segmentation.shape[0]):\n",
    "    for current_column in range(candidate1_predicted_segmentation.shape[1]):\n",
    "        current_pixel_value = single_cell_image[current_row, current_column]\n",
    "        candidate1_predicted_segmentation[current_row, current_column] = \\\n",
    "        our_perceptron_candidate1(Variable(torch.Tensor([[[current_pixel_value]]]))).cpu().detach().numpy()[0][0][0]\n",
    "        \n",
    "# Although we used a sigmoid activation function, the output is still not going to be exactly 0 or 1. We need to binarize the output anyway.\n",
    "candidate1_predicted_segmentation = np.int16(candidate1_predicted_segmentation > 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [18, 10]\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.imshow(single_cell_image, cmap = 'gray'); plt.axis('off'); plt.title('Our input cell image');\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.imshow(segmented_single_cell_image, cmap = 'gray'); plt.axis('off'); plt.title('Ground truth using thresholding');\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.imshow(candidate1_predicted_segmentation, cmap = 'gray'); plt.axis('off'); plt.title('What our perceptron candidate 1 says');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perceptron Candidate Two! Multi input single output. (Training a convolutional kernel.)\n",
    "\n",
    "*Anything beyond this point is not necessary for this task, because the image-to-segmentation mapping is a simple monotonic relationship that can be even achieved by a simple thresholding. However, this might be a good practice in case you face slightly more complicated cases in the future. Well of course you can go after more powerful tools then and give up on perceptrons altogether...*\n",
    "\n",
    "Now we have upgraded our perceptron. Same as before, it consists of 1 single layer, 1 single neuron/node, and the output consists of 1 tensor of size 1 (aka, a scalar). But the difference is that for this one it takes in multiple inputs. It still maps the pixel intensity in the cell image to the segmentation result for that pixel (whether or not the pixel belongs to a cell), but this time it starts taking the surrounding pixels into consideration.\n",
    "\n",
    "- Input: Conceptually, it is a 3$\\times$3 tensor/matrix representing the pixel intensity in a 3$\\times$3 region. In reality, this tensor/matrix needs to be flattened into a 9$\\times$1 vector to be fed into the perceptron as the input.\n",
    "- Output: A scalar representing the likelihood for the corresponding center of the 3$\\times$3 region to belong to a cell.\n",
    "\n",
    "The idea of looking at a 3$\\times$3 neighborhood of the pixel under inspection is somewhat similar to the notion of convolution. **What we are doing here is effectively training a single convolutional feature-extraction kernel.** You will probably get a better understanding on what we are doing and why we are doing this when you study convolutional neural networks (CNN) in the future lectures.\n",
    "\n",
    "<img src=\"data/perceptron_multi_input.PNG\" width=\"1200\" align=\"center\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Build our perceptron candidate 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class perceptron_candidate2(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(perceptron_candidate2, self).__init__()\n",
    "        self.fc1 = nn.Linear(9, 1, bias = False)\n",
    "        self.fc2 = nn.Linear(1, 1, bias = True)\n",
    "    def forward(self, x):\n",
    "        x = self.fc1(x)\n",
    "        x = self.fc2(x)\n",
    "        x = torch.sigmoid(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Crop out a certain region, that doesn't contain the test image, for training.\n",
    "adjust_cell_image_subset_for_training = adjusted_cell_image[100:200, 0:100]\n",
    "segmented_cell_image_subset_for_training = segmented_cell_image[100:200, 0:100]\n",
    "\n",
    "# training_patches_3x3_matrix is a 100x100x3x3 tensor. training_patches_3x3_matrix[x, y, :, :] is a 3x3 matrix\n",
    "# who corresponds to the 3x3 neighborhood of the pixel adjust_cell_image_subset_for_training[x, y].\n",
    "training_patches_3x3_matrix = extract_all_patches(adjust_cell_image_subset_for_training, patch_x = 3, patch_y = 3)\n",
    "\n",
    "# training_patches_3x3_array is a 10000x3x3 tensor. training_patches_3x3_matrix[index, :, :] is a 3x3 matrix\n",
    "# who corresponds to the 3x3 neighborhood of the pixel adjust_cell_image_subset_for_training.flatten()[index].\n",
    "training_patches_3x3_array = training_patches_3x3_matrix.reshape(-1, training_patches_3x3_matrix.shape[-2], training_patches_3x3_matrix.shape[-1])\n",
    "\n",
    "ground_truth = segmented_cell_image_subset_for_training.flatten()\n",
    "\n",
    "# Reshape the horizonal arrays to vertical arrays.\n",
    "# training_input now becomes a 10000x9 array. Each 1 of the 10000 element is a flattened vector of length 9.\n",
    "# ground_truth has a shape 10000x1.\n",
    "training_input = np.reshape(training_patches_3x3_array, (len(training_patches_3x3_array), 9))\n",
    "ground_truth = np.reshape(ground_truth, (len(ground_truth), 1))\n",
    "\n",
    "# Stack the training input and the ground truth together.\n",
    "# training_data is now a 10000x10 tensor, with the first 9 columns being inputs and the last column being the ground truth.\n",
    "training_data = np.hstack((training_input, ground_truth))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.02483813, 0.18433684, 0.17194058, ..., 0.05210993, 0.04301933,\n",
       "        0.        ],\n",
       "       [0.18433684, 0.17194058, 0.1959067 , ..., 0.04301933, 0.04467217,\n",
       "        0.        ],\n",
       "       [0.17194058, 0.1959067 , 0.25623524, ..., 0.04467217, 0.03144947,\n",
       "        0.        ],\n",
       "       ...,\n",
       "       [0.02979664, 0.01987962, 0.03144947, ..., 0.6157272 , 0.5950667 ,\n",
       "        0.        ],\n",
       "       [0.01987962, 0.03144947, 0.0281438 , ..., 0.5950667 , 0.552093  ,\n",
       "        0.        ],\n",
       "       [0.03144947, 0.0281438 , 0.24135971, ..., 0.552093  , 0.06533262,\n",
       "        0.        ]], dtype=float32)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# training_data consists of 9 columns: 3x3 neighborhood of each image pixel, and segmentation ground truth for that image pixel (0 or 1).\n",
    "training_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perceptron_candidate2(\n",
      "  (fc1): Linear(in_features=9, out_features=1, bias=False)\n",
      "  (fc2): Linear(in_features=1, out_features=1, bias=True)\n",
      ")\n",
      "Epoch 0 - loss: 0.18687285482883453\n",
      "Epoch 0 - loss: 0.1960943043231964\n",
      "Epoch 0 - loss: 0.17227518558502197\n",
      "Epoch 0 - loss: 0.1500333845615387\n",
      "Epoch 1 - loss: 0.43374332785606384\n",
      "Epoch 1 - loss: 0.08683376014232635\n",
      "Epoch 1 - loss: 0.07898493111133575\n",
      "Epoch 1 - loss: 0.07292558997869492\n",
      "Epoch 2 - loss: 0.4911710321903229\n",
      "Epoch 2 - loss: 0.058062635362148285\n",
      "Epoch 2 - loss: 0.05312006175518036\n",
      "Epoch 2 - loss: 0.050607822835445404\n",
      "Epoch 3 - loss: 0.5444408655166626\n",
      "Epoch 3 - loss: 0.046687252819538116\n",
      "Epoch 3 - loss: 0.04240851104259491\n",
      "Epoch 3 - loss: 0.040953390300273895\n",
      "Epoch 4 - loss: 0.5915493965148926\n",
      "Epoch 4 - loss: 0.04062025994062424\n",
      "Epoch 4 - loss: 0.03659557178616524\n",
      "Epoch 4 - loss: 0.03556350618600845\n"
     ]
    }
   ],
   "source": [
    "# Initialize our perceptron.\n",
    "our_perceptron_candidate2 = perceptron_candidate2()\n",
    "print(our_perceptron_candidate2)\n",
    "\n",
    "# Define the optimizer.\n",
    "optimizer = optim.SGD(our_perceptron_candidate2.parameters(), lr = 0.001, momentum = 0.5)\n",
    "\n",
    "# Train for 5 epochs.\n",
    "for epoch in range(5):\n",
    "    # Create a list to store the losses over every epoch.\n",
    "    Epoch_loss_list = []\n",
    "    # enumerate the training data.\n",
    "    for iteration, training_input_GT_pair in enumerate(training_data):\n",
    "        # isolate the training input and ground truth from the training data.\n",
    "        training_input, GT = grouper(9, iter(training_input_GT_pair))\n",
    "        # redefine the training input and ground truth and PyTorch tensors.\n",
    "        training_input, GT = Variable(torch.FloatTensor(training_input)), \\\n",
    "                             Variable(torch.FloatTensor(GT))\n",
    "        # reset the gradient for the optimizer.\n",
    "        optimizer.zero_grad()\n",
    "        # use the current model to predict the output from the input.\n",
    "        outputs = our_perceptron_candidate2(training_input)\n",
    "        # compute the loss (metric of goodness) between the prediction and the ground truth.\n",
    "        loss = loss_function(outputs, GT)\n",
    "        # backpropogate the gradient\n",
    "        loss.backward()\n",
    "        # update the weights using the gradient with the optimizer\n",
    "        optimizer.step()\n",
    "\n",
    "        # append the current loss value to the loss list for this epoch.\n",
    "        Epoch_loss_list.append(loss.data[0])\n",
    "        \n",
    "        # print the current loss every 1000 iterations.\n",
    "        if (iteration % 3e3 == 0):\n",
    "#            print(training_input)\n",
    "            print(\"Epoch {} - loss: {}\".format(epoch, np.mean(Epoch_loss_list)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's try it out on our test image (the single-cell cropped-out image)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "candidate2_predicted_segmentation = np.zeros(single_cell_image.shape)\n",
    "\n",
    "for current_row in range(candidate2_predicted_segmentation.shape[0]):\n",
    "    for current_column in range(candidate2_predicted_segmentation.shape[1]):\n",
    "        current_pixel_neighborhood = extract_patches_given_center(single_cell_image, current_row, current_column, patch_x = 3, patch_y = 3)\n",
    "        current_pixel_neighborhood = np.reshape(current_pixel_neighborhood, (1, 9))\n",
    "        candidate2_predicted_segmentation[current_row, current_column] = \\\n",
    "        our_perceptron_candidate2(Variable(torch.tensor(current_pixel_neighborhood))).cpu().detach().numpy()[0][0]\n",
    "        \n",
    "# Although we used a sigmoid activation function, the output is still not going to be exactly 0 or 1. We need to binarize the output anyway.\n",
    "candidate2_predicted_segmentation = np.int16(candidate2_predicted_segmentation > 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [18, 10]\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.imshow(single_cell_image, cmap = 'gray'); plt.axis('off'); plt.title('Our input cell image');\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.imshow(segmented_single_cell_image, cmap = 'gray'); plt.axis('off'); plt.title('Ground truth using thresholding');\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.imshow(candidate2_predicted_segmentation, cmap = 'gray'); plt.axis('off'); plt.title('What our perceptron candidate 2 says');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perceptron Candidate Three! The simplest CNN perceptron. (Actually using the convolutional operation.)\n",
    "\n",
    "This time we are re-implementing the idea behind perceptron candidate 2, except that we are going to do it in a more elegant and more succinct manner. Just as what we have said before, perceptron candidate 2 basically re-invented the concept of a convolutional kernel. Now we will see how people will build a convolutional neural network, or in our case a perceptron with 1 single layer and 1 single convolutional kernel, in real life.\n",
    "\n",
    "- Input: A 3$\\times$3 tensor/matrix representing the pixel intensity in a 3$\\times$3 region. This 3$\\times$3 region will remain this shape when fed into the perceptron.\n",
    "- Output: A scalar representing the likelihood for the corresponding center of the 3$\\times$3 region to belong to a cell.\n",
    "\n",
    "This is a 3$\\times$3 -> 1$\\times$1 mapping.\n",
    "\n",
    "<img src=\"data/perceptron_CNN.PNG\" width=\"1200\" align=\"center\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_channel = 1; output_channel = 1\n",
    "\n",
    "class perceptron_candidate3(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(perceptron_candidate3, self).__init__()\n",
    "        self.conv = nn.Conv2d(input_channel, output_channel, kernel_size=3, stride = 1, padding = 1)\n",
    "        self.maxpool = nn.MaxPool2d(kernel_size = 3, stride = 1)\n",
    "    def forward(self, x):\n",
    "        x = self.conv(x)\n",
    "        x = self.maxpool(x)\n",
    "        x = torch.sigmoid(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Crop out a certain region, that doesn't contain the test image, for training.\n",
    "adjust_cell_image_subset_for_training = adjusted_cell_image[100:200, 0:100]\n",
    "segmented_cell_image_subset_for_training = segmented_cell_image[100:200, 0:100]\n",
    "\n",
    "# training_patches_3x3_matrix is a 100x100x3x3 tensor. training_patches_3x3_matrix[x, y, :, :] is a 3x3 matrix\n",
    "# who corresponds to the 3x3 neighborhood of the pixel adjust_cell_image_subset_for_training[x, y].\n",
    "training_patches_3x3_matrix = extract_all_patches(adjust_cell_image_subset_for_training, patch_x = 3, patch_y = 3)\n",
    "\n",
    "# training_patches_3x3_array is a 10000x3x3 tensor. training_patches_3x3_matrix[index, :, :] is a 3x3 matrix\n",
    "# who corresponds to the 3x3 neighborhood of the pixel adjust_cell_image_subset_for_training.flatten()[index].\n",
    "training_patches_3x3_array = training_patches_3x3_matrix.reshape(-1, training_patches_3x3_matrix.shape[-2], training_patches_3x3_matrix.shape[-1])\n",
    "\n",
    "ground_truth = segmented_cell_image_subset_for_training.flatten()\n",
    "\n",
    "# Reshape the horizonal arrays to vertical arrays.\n",
    "# training_input now becomes a 10000x9 array. Each 1 of the 10000 element is a flattened vector of length 9.\n",
    "# ground_truth has a shape 10000x1.\n",
    "#training_input = np.reshape(training_patches_3x3_array, (len(training_patches_3x3_array), 9))\n",
    "training_input = training_patches_3x3_array\n",
    "ground_truth = np.reshape(ground_truth, (len(ground_truth), 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "perceptron_candidate3(\n",
      "  (conv): Conv2d(1, 1, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1))\n",
      "  (maxpool): MaxPool2d(kernel_size=3, stride=1, padding=0, dilation=1, ceil_mode=False)\n",
      ")\n",
      "Epoch 0 - loss: 0.30111783742904663\n",
      "Epoch 0 - loss: 0.1483122706413269\n",
      "Epoch 0 - loss: 0.1103004738688469\n",
      "Epoch 0 - loss: 0.0910266861319542\n",
      "Epoch 1 - loss: 0.44225919246673584\n",
      "Epoch 1 - loss: 0.045957885682582855\n",
      "Epoch 1 - loss: 0.04098516330122948\n",
      "Epoch 1 - loss: 0.03990384563803673\n",
      "Epoch 2 - loss: 0.5059212446212769\n",
      "Epoch 2 - loss: 0.037163447588682175\n",
      "Epoch 2 - loss: 0.032997436821460724\n",
      "Epoch 2 - loss: 0.032919805496931076\n",
      "Epoch 3 - loss: 0.5580415725708008\n",
      "Epoch 3 - loss: 0.03327879309654236\n",
      "Epoch 3 - loss: 0.029407305642962456\n",
      "Epoch 3 - loss: 0.029606349766254425\n",
      "Epoch 4 - loss: 0.6007249355316162\n",
      "Epoch 4 - loss: 0.030984608456492424\n",
      "Epoch 4 - loss: 0.027280451729893684\n",
      "Epoch 4 - loss: 0.02757955715060234\n"
     ]
    }
   ],
   "source": [
    "# Initialize our perceptron.\n",
    "our_perceptron_candidate3 = perceptron_candidate3()\n",
    "print(our_perceptron_candidate3)\n",
    "\n",
    "# Define the optimizer.\n",
    "optimizer = optim.SGD(our_perceptron_candidate3.parameters(), lr = 0.01, momentum = 0.5)\n",
    "\n",
    "# Train for 5 epochs.\n",
    "for epoch in range(5):\n",
    "    # Create a list to store the losses over every epoch.\n",
    "    Epoch_loss_list = []\n",
    "    # \"zip\", unlike when we use \"iter\" or \"grouper\", cannot be re-used and thus we need to put that inside the loop.\n",
    "    training_data = zip(training_input, ground_truth)\n",
    "    # enumerate the training data.\n",
    "    for iteration, training_input_GT_pair in enumerate(training_data):\n",
    "        # isolate the training input and ground truth from the training data.\n",
    "        our_input, our_GT = iter(training_input_GT_pair)\n",
    "        # redefine the training input and ground truth and PyTorch tensors.\n",
    "        our_input, our_GT = Variable(torch.FloatTensor(our_input)), \\\n",
    "                             Variable(torch.FloatTensor(our_GT))\n",
    "        \n",
    "        # For the CNN, we need to reshape the input to [num_batch, num_channel, x_dimension, y_dimension]\n",
    "        our_input = our_input[np.newaxis, np.newaxis, :, :]\n",
    "        # reset the gradient for the optimizer.\n",
    "        optimizer.zero_grad()\n",
    "        # use the current model to predict the output from the input.\n",
    "        outputs = our_perceptron_candidate3(our_input)\n",
    "        # compute the loss (metric of goodness) between the prediction and the ground truth.\n",
    "        loss = loss_function(outputs, our_GT)\n",
    "        # backpropogate the gradient\n",
    "        loss.backward()\n",
    "        # update the weights using the gradient with the optimizer\n",
    "        optimizer.step()\n",
    "\n",
    "        # append the current loss value to the loss list for this epoch.\n",
    "        Epoch_loss_list.append(loss.data[0])\n",
    "        \n",
    "        # print the current loss every 1000 iterations.\n",
    "        if (iteration % 3e3 == 0):\n",
    "            print(\"Epoch {} - loss: {}\".format(epoch, np.mean(Epoch_loss_list)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's try it out on our test image (the single-cell cropped-out image)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "candidate3_predicted_segmentation = np.zeros(single_cell_image.shape)\n",
    "\n",
    "for current_row in range(candidate3_predicted_segmentation.shape[0]):\n",
    "    for current_column in range(candidate3_predicted_segmentation.shape[1]):\n",
    "        current_pixel_neighborhood = extract_patches_given_center(single_cell_image, current_row, current_column, patch_x = 3, patch_y = 3)\n",
    "        current_pixel_neighborhood = np.reshape(current_pixel_neighborhood, (1, 1, 3, 3))\n",
    "        candidate3_predicted_segmentation[current_row, current_column] = \\\n",
    "        our_perceptron_candidate3(Variable(torch.tensor(current_pixel_neighborhood))).cpu().detach().numpy()[0][0]\n",
    "        \n",
    "# Although we used a sigmoid activation function, the output is still not going to be exactly 0 or 1. We need to binarize the output anyway.\n",
    "candidate3_predicted_segmentation = np.int16(candidate3_predicted_segmentation > 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = [18, 10]\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.imshow(single_cell_image, cmap = 'gray'); plt.axis('off'); plt.title('Our input cell image');\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.imshow(segmented_single_cell_image, cmap = 'gray'); plt.axis('off'); plt.title('Ground truth using thresholding');\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.imshow(candidate3_predicted_segmentation, cmap = 'gray'); plt.axis('off'); plt.title('What our perceptron candidate 3 says');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Some closing remarks\n",
    "\n",
    "Of course, in a more comprehensive case, when we use a convolutional neural network (CNN), we wouldn't chop up the images into small 3$\\times$3 patches for training and evaluation. The common practice is to train with images of the size that you would expect your test images to have. For example, if our desired test image is of dimension 50$\\times$50, we would most likely build a CNN such that:\n",
    "\n",
    "1) it can accomodate the 50$\\times$50 input image, and\n",
    "\n",
    "2) it generates the segmentation mask of dimension 50$\\times$50.\n",
    "\n",
    "We are quite sure you will soon see how real-life CNNs are implemented, and this tutorial is just to give you a bit of the taste as well as shed some lights on the philosophies behind the essential concepts of perceptrons and CNNs."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "[RR (python3.7)]",
   "language": "python",
   "name": "rr"
  },
  "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": 4
}