akiross/Convolutional Arithmetic.ipynb

## Convolutional Arithmetic.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Convolution Arithmetics with TensorFlow\n",
    "A practical introduction to convolution with TF.\n",
    "\n",
    "Size and padding policies of TF are described in:\n",
    "https://www.tensorflow.org/api_docs/python/nn.html#convolution\n",
    "\n",
    "Animated GIFs comes from: https://github.com/vdumoulin/conv_arithmetic\n",
    "and I suggest reading their article: https://arxiv.org/abs/1603.07285"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ed35dea58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import tensorflow as tf\n",
    "from matplotlib import pyplot as plt # Used to plot stuff\n",
    "plt.set_cmap('viridis') # Specify the color mapping (value -> color)\n",
    "\n",
    "def show_pixel_image(*images, width=2, height=2, show_text=False, int_values=True):\n",
    "    '''Plot the data wihout interpolation, optionally displaying\n",
    "    the values over the cells'''\n",
    "    from itertools import product\n",
    "    # Scale image size\n",
    "    plt.figure(figsize=(width * len(images), height))\n",
    "    # Plot each figure in a row\n",
    "    for i, data in enumerate(images, 1):\n",
    "        plt.subplot(1, len(images), i)\n",
    "        plt.axis('off') # Hide axis\n",
    "        plt.imshow(data, interpolation='nearest')\n",
    "        if show_text:\n",
    "            if int_values:\n",
    "                for y, x in product(range(data.shape[0]), range(data.shape[1])):\n",
    "                    plt.text(x, y, int(data[y,x]), va='center', ha='center')\n",
    "            else:\n",
    "                for y, x in product(range(data.shape[0]), range(data.shape[1])):\n",
    "                    plt.text(x, y, data[y,x], va='center', ha='center')\n",
    "\n",
    "def conv2d(image, kernel, strides, padding):\n",
    "    '''Prepare tf.nn.conv2d op for the given input.\n",
    "    Strides shall be a (height, width) tuple/list.'''\n",
    "    c_batch = tf.constant(image, dtype=tf.float32)\n",
    "    img = tf.reshape(c_batch, (1, image.shape[0], image.shape[1], 1))\n",
    "    c_kern = tf.constant(kernel, dtype=tf.float32)\n",
    "    ker = tf.reshape(c_kern, (kernel.shape[0], kernel.shape[1], 1, 1))\n",
    "    return tf.nn.conv2d(img, ker, strides=(1,)+strides+(1,), padding=padding)\n",
    "\n",
    "def conv2d_t(image, kernel, out_shape, strides, padding):\n",
    "    '''Prepare tf.nn.conv2d_transpose op for the given input.'''\n",
    "    c_batch = tf.constant(image, dtype=tf.float32)\n",
    "    img = tf.reshape(c_batch, (1, image.shape[0], image.shape[1], 1))\n",
    "    c_kern = tf.constant(kernel, dtype=tf.float32)\n",
    "    ker = tf.reshape(c_kern, (kernel.shape[0], kernel.shape[1], 1, 1))\n",
    "    shape = tf.pack((1,)+out_shape+(1,))\n",
    "    return tf.nn.conv2d_transpose(img, ker, shape, strides=(1,)+strides+(1,), padding=padding)\n",
    "\n",
    "def show_conv2d(image, kernel, strides, padding, **kwargs):\n",
    "    '''Run conv2d and shows the images'''\n",
    "    with tf.Session() as sess:\n",
    "        out = conv2d(image, kernel, strides, padding).eval()\n",
    "        out = out.reshape(out.shape[1], out.shape[2])\n",
    "        show_pixel_image(image, kernel, out, show_text=True, **kwargs)\n",
    "\n",
    "def show_conv2d_any_pad(image, kernel, strides, padding=[(0, 0), (0, 0)], **kwargs):\n",
    "    '''Like show_conv2d, but uses tf.pad to add custom padding to height or width of the input image.\n",
    "    The VALID method is used.'''\n",
    "    with tf.Session() as sess:\n",
    "        c_batch = tf.constant(image, dtype=tf.float32)\n",
    "        img = tf.reshape(c_batch, (1, image.shape[0], image.shape[1], 1))\n",
    "        p_img = tf.pad(img, [(0, 0)] + padding + [(0, 0)])\n",
    "        c_kern = tf.constant(kernel, dtype=tf.float32)\n",
    "        ker = tf.reshape(c_kern, (kernel.shape[0], kernel.shape[1], 1, 1))\n",
    "        op = tf.nn.conv2d(p_img, ker, strides=(1,) + strides + (1,), padding='VALID')\n",
    "        _, i_h, i_w, _ = p_img.get_shape()\n",
    "        _, o_h, o_w, _ = op.get_shape()\n",
    "        show_pixel_image(p_img.eval().reshape(i_h, i_w), kernel, op.eval().reshape(o_h, o_w), **kwargs)\n",
    "\n",
    "def compute_out_and_padding(in_size, filter_size, stride, method):\n",
    "    '''This function returns output size and padding along a single dimension\n",
    "    according to the tensorflow policies.'''\n",
    "    from math import ceil\n",
    "    \n",
    "    if method == 'VALID':\n",
    "        out_size = ceil((in_size - filter_size + 1) / stride)\n",
    "        return out_size, 0\n",
    "    elif method == 'SAME':\n",
    "        out_size = ceil(in_size / stride)\n",
    "        padding = ((out_size - 1) * stride + filter_size - in_size) / 2\n",
    "        return out_size, padding\n",
    "    else:\n",
    "        return None\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecfb0a4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Few images that we will use to explore the operations\n",
    "image2_diag = np.array([[0, 1], [1, 0]])\n",
    "\n",
    "image3_vert = np.array([[0, 1, 0], [0, 1, 0], [0, 1, 0]])\n",
    "image3_cent = np.array([[0, 0, 0], [0, 1, 0], [0, 0, 0]])\n",
    "image3_cros = np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])\n",
    "image3_diag = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n",
    "\n",
    "image4_dots = np.array([[1,0,1,0], [0,1,0,1], [1,0,1,0], [0,1,0,1]])\n",
    "image4_squa = np.array([[1,1,0,0], [1,1,0,0], [0,0,1,1], [0,0,1,1]])\n",
    "image4_ring = np.array([[1,1,1,1], [1,0,0,1], [1,0,0,1], [1,1,1,1]])\n",
    "\n",
    "show_pixel_image(image2_diag, image3_vert, image3_cent, image3_cros, image3_diag, image4_dots, image4_squa, image4_ring, show_text=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No padding, no strides ![no padding, no strides](https://github.com/vdumoulin/conv_arithmetic/raw/master/gif/no_padding_no_strides.gif)\n",
    "\n",
    "Using the VALID padding, strides will be always zero, and the output size will be 2, because, according to [tensorflow convolution arithmetic](https://www.tensorflow.org/api_docs/python/nn.html#convolution), we have\n",
    "\n",
    "    out_size = ceil((in_size - filter_size + 1) / stride)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 0)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_out_and_padding(4, 3, 1, 'VALID')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we use a 3x3 kernel with 1 just in the center and 0 elsewhere. Using VALID padding, conv2d will consider only the 4 centermost pixels, it will just copy them to a new image, because the corner pixels will be weighted 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ed08f70f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAC3CAYAAAChWnyPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkrJcSJKkpP4PLTCKcndcWJgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ef4519c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAC3CAYAAAChWnyPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nLgCAov4HMRUrXlhuC6IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec95fc5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_conv2d(image4_dots, image3_cent, (1, 1), 'VALID')\n",
    "show_conv2d(image4_squa, image3_cent, (1, 1), 'VALID')\n",
    "show_conv2d(image4_ring, image3_cent, (1, 1), 'VALID')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now try with a different kernel: a vertical line. With VALID, it will consider only the pixels in the 4x4 image, without padding it. The output pixel will copy the values of the top, center and bottom pixels. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec93db5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Z8M9LDklS4wo9cyFJktKzXEiSpKQsF5IkKSnLhSRJSspyIUmSkrJcSJKkpCwXkiQpKcuF\nJElKynIhSZKSslxIkqSkLBeSJCmpEO987aQkSVICnlxIkqSkLBeSJCkpy4UkSUrKciFJkpKyXEiS\npKQsF5IkKSnLhSRJSspyIUmSkrJcSJKkpCwXkiQpKcuFJElKynIhSZKSslxIkqSkLBeSJCkpy4Uk\nSUrKciFJkpKyXEiSpKQsF5IkKSnLhSRJSspyIUmSkrJcSJKkpCwXkiQpKcuFJElKynIhSZKSslxI\nkqSkLBeSJCkpy4UkSUrKciFJkpKyXEiSpKT+HynwWm6HF4CdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9339908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAC3CAYAAAChWnyPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJWW5kCRJSf0/lAGHQva8aiMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9626828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_conv2d(image4_dots, image3_vert, (1, 1), 'VALID')\n",
    "show_conv2d(image4_squa, image3_vert, (1, 1), 'VALID')\n",
    "show_conv2d(image4_ring, image3_vert, (1, 1), 'VALID')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Half (same) padding, no strides ![half padding, no strides](https://github.com/vdumoulin/conv_arithmetic/raw/master/gif/same_padding_no_strides.gif)\n",
    "\n",
    "In this case, we do the same thing as we did earlier, but using the SAME padding: the kernel is now allowed to go outside the input image, and values outside it are padded with zeroes, but the center pixel of the kernel will always match a pixel of the input image. The output image will get larger, because now we can apply the kernel to every pixel of it, instead of the central ones.\n",
    "\n",
    "According to TF arithmetics, we have an output image of 4, and a padding of 1: the 3x3 kernel will get one pixel outside the input image on both sides (1 extra pixel top, left, bottom and right)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1.0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_out_and_padding(4, 3, 1, 'SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As far as I know, there are no arbitrary or full paddings in tensorflow.\n",
    "\n",
    "Note how, using `image3_cent`, we just copy the input to the output, because paddings and neighbors are ignored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec94f2668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAC3CAYAAABOmBexAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecd794c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAC3CAYAAABOmBexAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhlcjY+47dcoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecdaa3cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_conv2d(image4_dots, image3_cent, (1, 1), 'SAME')\n",
    "show_conv2d(image4_squa, image3_cent, (1, 1), 'SAME')\n",
    "show_conv2d(image4_ring, image3_cent, (1, 1), 'SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use `image3_vert` instead, we will go outside the figure and have a padded input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zOfQBeXWSUltoo0IP17nSuFYUBde5QhfrEyZbnex7sQUWqNDNILvNYY4VK/0dixxOgOd0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\n0TgsJElSNP8PhvIWuHiudx0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9376390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec94efa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9Sj/76aaXG9lAiWZeYyeVtJx1tAsaGa2ypreRxx9ZRJJkneY/V6/rLcXCHQspckfoZxnd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\n8/86zqW+rp0vCAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec94e34e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_conv2d(image4_dots, image3_vert, (1, 1), 'SAME')\n",
    "show_conv2d(image4_squa, image3_vert, (1, 1), 'SAME')\n",
    "show_conv2d(image4_ring, image3_vert, (1, 1), 'SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Let's see now what happens using strides with the VALID padding.\n",
    "\n",
    "![no padding, with strides](https://github.com/vdumoulin/conv_arithmetic/raw/master/gif/no_padding_strides.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 0)\n",
      "(2, 0)\n",
      "(1, 0)\n"
     ]
    }
   ],
   "source": [
    "print(compute_out_and_padding(4, 2, 1, 'VALID'))\n",
    "print(compute_out_and_padding(4, 2, 2, 'VALID'))\n",
    "print(compute_out_and_padding(4, 2, 3, 'VALID'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ed08f70b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JUmIxkCRJicVAkiQlFgNJkpT4giNJkpR4x0CSJCUWA0mSlFgMJElSYjGQJEmJxUCSJCUW\nA0mSlFgMJElSYjGQJEmJxUCSJCUWA0mSlFgMJElSYjGQJEmJxUCSJCUWA0mSlFgMJElSYjGQJEmJ\nxUCSJCUWA0mSlFgMJElSYjGQJEmJxUCSJCUWA0mSlFgMJElSYjGQJEmJxUCSJCUWA0mSlFgMJElS\nYjGQJEmJxUCSJCX/C9qJCljmm1nNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec921db70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAADJCAYAAAAZ3PqmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRjkDQDHKGQCKUc4AUMz/ASzyQgUQe7lTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9441eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_conv2d(image4_dots, image2_diag, strides=(1, 1), padding='VALID')\n",
    "show_conv2d(image4_dots, image2_diag, (1, 2), 'VALID')\n",
    "show_conv2d(image4_dots, image2_diag, (1, 3), 'VALID') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With SAME padding and strides"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 0.5)\n",
      "(2, 0.0)\n",
      "(2, 0.5)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec91b5940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9563a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecdae4358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(compute_out_and_padding(4, 2, 1, 'SAME'))\n",
    "print(compute_out_and_padding(4, 2, 2, 'SAME'))\n",
    "print(compute_out_and_padding(4, 2, 3, 'SAME'))\n",
    "show_conv2d(image4_dots, image2_diag, strides=(1, 1), padding='SAME')\n",
    "show_conv2d(image4_dots, image2_diag, (1, 2), 'SAME')\n",
    "show_conv2d(image4_dots, image2_diag, (1, 3), 'SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the **first case**, note how the kernel starts from the top-left corner and moves right 4 times before stopping: the last time, half of the kernel is outside the image and the value 0 is used where there are no pixels. Note that the computed value for the padding is 0.5, meaning that there is no padding on the left (top), but there will be padding of 1 at the right (bottom).\n",
    "\n",
    "In the **second case**, the kernel starts as before on the top-left corner and it moves just once, without overflow on the right side of the image. Two values are computed and there is no need for padding (computed padding is, in fact, 0).\n",
    "\n",
    "In the **third case**, the computed padding is again 0.5 and, in fact, the kernel overflows the input of 1 pixel on the right.\n",
    "\n",
    "In general, having a `int(n) + 0.5` computed padding means that the overflow will be of `n` pixels on left (top) side, but there will be a `n+1` overflow of the kernel on the right (bottom) side.\n",
    "\n",
    "With a kernel of size 3, it may happen that the computed padding value is of 1.0, meaning that the kernel will overflow 1 pixel on the left (top) and right (bottom) sides, as shown below in the first and third examples, where the kernel is centered in the top-left corner (and, therefore, it overflows of 1 pixels on the left and top sides, which are padded with 0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 1.0)\n",
      "(2, 0.5)\n",
      "(2, 1.0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9532710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecd7ef908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Mlifnrdw0/e76FHbSprQLOYV5QFoziW0jjzLMe5SKLjro4iyjVFmkj8HY0W5rZrbK2PjC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\nZclLkpQpS16SpExZ8pIkZcqSlyQpU/8LYjr+h7942JEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecd8e7240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(compute_out_and_padding(4, 3, 1, 'SAME'))\n",
    "print(compute_out_and_padding(4, 3, 2, 'SAME'))\n",
    "print(compute_out_and_padding(4, 3, 3, 'SAME'))\n",
    "show_conv2d(image4_dots, image3_vert, strides=(1, 1), padding='SAME')\n",
    "show_conv2d(image4_dots, image3_vert, (1, 2), 'SAME')\n",
    "show_conv2d(image4_dots, image3_vert, (1, 3), 'SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a kernel size of 4, we may in fact obtain a computed padding of 1.5, meaning that 1 pixel will overflow on the left (top), but 2 pixels will overflow on the right (bottom)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 1.5)\n",
      "(2, 1.0)\n",
      "(2, 1.5)\n"
     ]
    },
    {
     "data": {
      "image/png": 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HkkMQxzH7922mqdjJzFnp/nYO8Lutuyn3Hqf9sS+mvvaFxvqP0fvMk1QmxsnlCyz81P0U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\nSZIS838A0BQekDSLNSoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecdade780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(compute_out_and_padding(4, 4, 1, 'SAME'))\n",
    "print(compute_out_and_padding(4, 4, 2, 'SAME'))\n",
    "print(compute_out_and_padding(4, 4, 3, 'SAME'))\n",
    "show_conv2d(image4_dots, image4_ring, strides=(1, 1), padding='SAME')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transposed convolution (\"deconvolution\")\n",
    "\n",
    "A transposed convolution (a.k.a fractionally strided convolution, backward convolution or deconvolution) swaps the sizes of the input and the output of a regular convolution: if you convolve an input of size 4x4 with a kernel 3x3 and method VALID, you get a 2x2 output. The transpose of this convolution takes a 2x2 input and applies a 3x3 kernel to produce a 4x4 output.\n",
    "\n",
    "Let's start by seeing how it is done in TF. The `tf.nn.conv2d_transpose` operation is used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec93e8630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qlCtR2jFSkQtyFGjkKmNzr0VRxFXGKNKcYjJJUhL8KWSVDhy8Qm/PelpLeSYmq3x0eILP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\nKTYWC0mSFBuLhSRJio3FQpIkxeb/ASAYsc/JvH3rAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec96794e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Regular convolution: 4x4 input, 3x3 kernel, 2x2 output\n",
    "show_conv2d(image4_dots, image3_diag, strides=(1, 1), padding='VALID')\n",
    "\n",
    "# Transposed convolution: 2x2 input, 3x3 kernel, 4x4 output\n",
    "with tf.Session() as sess:\n",
    "    in_img = image2_diag * 3.0\n",
    "    op = conv2d_t(in_img, image3_diag, (4, 4), (1, 1), 'VALID')\n",
    "    show_pixel_image(in_img, image3_diag, op.eval().reshape(4, 4), show_text=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note how, in the transposed convolution, the kernel fits in the output: with a 2x2 input, there are 2x2 positions of the kernel in the output image. If you multiply the kernel for the input value corresponding to the input position and you sum all the products, you get the final image. To make it more explicit, let's apply it using some negative weights in the kernel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ex+s7k4+3Uw6AsBligL6EF4vTcJFHIZ20jbhuL0GqzRd51dzIe+Z2+szkn5xH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\n0inL6cA3s4zuXXXxZaZp0r3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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9335978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "if True: # try setting this to False to see the same output as the conv2d_transpose above\n",
    "    kernel = image2_diag - 0.5 # form -0.5 to 0.5\n",
    "else:\n",
    "    kernel = image2_diag\n",
    "\n",
    "out_img = np.zeros((4, 4))\n",
    "out_img[0:3,0:3] += image3_diag * kernel[0, 0] ; pos1 = out_img.copy()\n",
    "out_img[1:4,0:3] += image3_diag * kernel[1, 0] ; pos2 = out_img.copy()\n",
    "out_img[0:3,1:4] += image3_diag * kernel[0, 1] ; pos3 = out_img.copy()\n",
    "out_img[1:4,1:4] += image3_diag * kernel[1, 1]\n",
    "show_pixel_image(pos1, pos2, pos3, out_img, show_text=True, int_values=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is possible to visualize better how the transposed convolution works by explicitly setting the padding of the input image, in fact it is always possible to transform any transposed convolution into a regular convolution.\n",
    "\n",
    "In our case, to produce a 4x4 output image, it is necessary to pad the 2x2 input image with 2 empty pixels on the left, right, top and bottom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAApC8AMAUBCCHwCAghD8AAAUhOAHAKAgBD8AAAUh+AEAKAjBDwBAQQh+AAAKQvADAFCQ\n/wLHkD8Rd1zMaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec94a25f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_conv2d_any_pad(image2_diag, image3_diag, (1, 1), [(2, 2), (2, 2)], show_text=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some more examples of transposed convolution with the equivalent convolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jPu6xkCTNKS9PyFTKZaaGR0g+f8RocniE+PgQNQ0NLGlpTi1HXuaRlxzVWCwkSXPKyxMy\n8cAgJ155deb12JtvMQasuGMLNz76SGo58jKPvOSoxmIhSaoqD0/I1K/rorPnpUwzTMvDPPKUYy7u\nsZAkScFYLCRJUjAWC0mSFIzFQpIkBWOxkCRJwVgsJElSMBYLSZIUjMVCkiQFY7GQJEnBWCwkSVIw\nFgtJkhRMNP1rcZIkSQvlioUkSQrGYiFJkoKxWEiSpGAsFpIkKRiLhSRJCsZiIUmSgrFYSJKkYCwW\nkiQpGIuFJEkKxmIhSZKCsVhIkqRgLBaSJCkYi4UkSQrGYiFJkoKxWEiSpGAsFpIkKRiLhSRJCsZi\nIUmSgrFYSJKkYCwWkiQpGIuFJEkKxmIhSZKCsVhIkqRgLBaSJCkYi4UkSQrGYiFJkoKxWEiSpGAs\nFpIkKRiLhSRJCuZ/ATrkaRYRI9ZYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec949f550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecd8b89e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    op = conv2d_t(image2_diag, image3_cros, (4, 4), (1, 1), 'VALID')\n",
    "    show_pixel_image(image2_diag, image3_cros, op.eval().reshape(4, 4), show_text=True)\n",
    "# Or equivalently\n",
    "show_conv2d_any_pad(image2_diag, image3_cros, (1, 1), [(2, 2), (2, 2)], show_text=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAC3CAYAAABOmBexAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFpIkKZn/B/EiiWaRpbHAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecda1d828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAC3CAYAAADzTzw1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecd7f4a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    op = conv2d_t(image2_diag, image3_vert, (4, 4), (1, 1), 'VALID')\n",
    "    show_pixel_image(image2_diag, image3_vert, op.eval().reshape(4, 4), show_text=True)\n",
    "# Or equivalently\n",
    "show_conv2d_any_pad(image2_diag, image3_vert, (1, 1), [(2, 2), (2, 2)], show_text=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec955c6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AADiOCFRHal2dmwhUADCPCFQHal2d24ZELQAoBESgOlDr6tz5FoEKALaKZDGfSFuqUOXk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\nwHEs5gAAOO7/AC+9xibuIJ1CAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec9263b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    op = conv2d_t(image3_diag, image4_ring, (6, 6), (1, 1), 'VALID')\n",
    "    show_pixel_image(image3_diag, image4_ring, op.eval().reshape(6, 6), show_text=True)\n",
    "# Or equivalently\n",
    "show_conv2d_any_pad(image3_diag, image4_ring, (1, 1), [(3, 3), (3, 3)], show_text=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider now when the stride is greater than one.\n",
    "\n",
    "![no padding, strides, transposed](https://github.com/vdumoulin/conv_arithmetic/raw/master/gif/no_padding_strides_transposed.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ccW60r19uV7cisZjmlZUGlsVEju27Luvjlp/V8v4iFcYcXeodkySVFEcUjc5hWaWBLKbG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ed08f70b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    op = conv2d_t(image3_diag, image4_ring, (8, 8), (2, 2), 'VALID')\n",
    "    show_pixel_image(image3_diag, image4_ring, op.eval().reshape(8, 8), show_text=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To create an equivalent form, we have to change the input and pad some zeroes *within* the input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXEAAAC7CAYAAACTg67CAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nE3GAMBEHCBNxgDARBwgTcYCwBxxoIJ9gu5qjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ecdae0d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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enbhDv/vaKC62J1BeFkBN9Z3NLHTZN3vpExG5T2TB16Xfu93f+eJCAk+9GIFhAIYBvP5W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\nLPhEREQ+8P8VFjw6JBSifwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ec921def0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "spaced_in = np.zeros((5, 5))\n",
    "spaced_in[::2,::2] = image3_diag\n",
    "show_pixel_image(image3_diag, spaced_in) # This is how the input is transformed\n",
    "show_conv2d_any_pad(spaced_in, image4_ring, (1, 1), [(3, 3), (3, 3)], show_text=True)"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}