hands-on/050_convolution_complete.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Required imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-17T05:07:22.409259Z",
     "start_time": "2018-07-17T05:07:22.244395Z"
    }
   },
   "outputs": [],
   "source": [
    "from keras.datasets import mnist\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy import signal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the MNIST data set that is provided by the keras framework."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, *_), *_ = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We load the images of a 5 and a 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "five = x_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "three = x_train[7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define a function to visualize the data as a gray scale image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_img(img):\n",
    "    frame = plt.gca()\n",
    "    frame.axes.get_xaxis().set_visible(False)\n",
    "    frame.axes.get_yaxis().set_visible(False)\n",
    "    plt.imshow(img, cmap='gray')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define two kernels, one to detect diagonal features along the main diagonal, the other along the minor diagonal.  The kernels are $7 \\times 7$ pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel_main_diag = np.eye(7)/7.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel_minor_diag = np.rot90(kernel_main_diag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, the convolution of those two kernels with the images for 5 and 3 are shown."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": [
    "show_img(five)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "five_main_diag = signal.fftconvolve(five, kernel_main_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "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": [
    "show_img(five_main_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "five_minor_diag = signal.fftconvolve(five, kernel_minor_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": [
    "show_img(five_minor_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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": [
    "show_img(three)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "three_main_diag = signal.fftconvolve(three, kernel_main_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "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": [
    "show_img(three_main_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "three_minor_diag = signal.fftconvolve(three, kernel_minor_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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": [
    "show_img(three_minor_diag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the images, it is clear that these kernels could be used to detect features that are distinct for 5 and 3."
   ]
  }
 ],
 "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"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}