hands-on/050_convolution_lazy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Required imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "five = x_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "kernel_main_diag = np.eye(7)/7.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_img(five)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "five_main_diag = signal.fftconvolve(five, kernel_main_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_img(five_main_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "five_minor_diag = signal.fftconvolve(five, kernel_minor_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_img(five_minor_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_img(three)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "three_main_diag = signal.fftconvolve(three, kernel_main_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "show_img(three_main_diag)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "three_minor_diag = signal.fftconvolve(three, kernel_minor_diag, mode='same')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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."
   ]
  }
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