{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Understanding DCT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import fftpack\n",
    "from scipy.misc import bytescale\n",
    "import matplotlib.image as mpimg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fc6d4be7588>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FK0lJLFhJSrKeJxqsxYEAu3btqu0DB4MB/f5e17htzKRmm9RcYLZxTWq2Sc0F9WVb1GcH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc6cea12e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# loading a simple Z character image (8x8)\n",
    "img = bytescale(mpimg.imread('i/z_char_8x8.png'))\n",
    "img_h = 8\n",
    "gray_img = img[:,:,0]\n",
    "\n",
    "plt.imshow(img, cmap='gray', interpolation='nearest')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All pixel's value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[255, 255, 255, 255, 255, 255, 255, 255],\n",
       "       [255, 165,   0,   0,   0,  22, 255, 255],\n",
       "       [255, 252, 251, 221,  22,  88, 255, 255],\n",
       "       [255, 255, 250,  59,  28, 238, 255, 255],\n",
       "       [255, 255, 125,  13, 218, 255, 255, 255],\n",
       "       [255, 187,   0,  96, 218, 206, 255, 255],\n",
       "       [255, 171,   0,   0,   0,   0, 255, 255],\n",
       "       [255, 255, 255, 255, 255, 255, 255, 255]], dtype=uint8)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.set_printoptions(precision=1, linewidth=140, suppress=True)\n",
    "gray_img"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# All coefficient's value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1533.1,   -57.3,   450.2,    49.7,   -39.4,    21.9,   -77.6,    14. ],\n",
       "       [   13.6,    47.2,     7.7,   -85.3,   -37.5,    49.5,    25.4,   -14.8],\n",
       "       [   59.4,    14.5,   -98.6,   -45. ,    94.5,    42.7,   -46.3,    -2.4],\n",
       "       [  -19. ,   -95.4,   -21.9,   172. ,    71.9,   -98.6,   -44.8,    27.3],\n",
       "       [  293.4,    22.1,  -200.3,    25.4,   -98.1,   -81.2,   122.9,    11.7],\n",
       "       [   -3.7,    45.9,    23.6,   -88.7,   -43.5,    59.6,    30.2,   -22.1],\n",
       "       [  251. ,    30.1,  -223.6,   -30.1,    25.9,     6.6,    28.1,   -41.6],\n",
       "       [   23.3,    38.6,   -12.8,   -51.8,     5.7,     2.1,   -22.9,    20.7]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# transform: 2D DCT\n",
    "z_dct = fftpack.dct(fftpack.dct(gray_img.T, norm='ortho').T, norm='ortho')\n",
    "\n",
    "np.set_printoptions(precision=1, linewidth=140, suppress=True)\n",
    "z_dct"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DCT basis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fc6cea166a0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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RokWefvzxxz0d24TBVch5A0yssglvSuDNKqy5ijkQbpphIhWgi24j1g5X8Y5V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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc6cee2a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dct_basis = bytescale(mpimg.imread('i/dct_basis.png'))\n",
    "plt.imshow(dct_basis, cmap='gray', interpolation='nearest')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reconstructed images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "partial_z_idct = []\n",
    "partial_z_dct = []\n",
    "\n",
    "for ii in range(img_h*img_h):\n",
    "    dct_copy = np.copy(z_dct)\n",
    "    frequency_counter = 0 \n",
    "    \n",
    "    for u in range(img_h):\n",
    "        for v in range(img_h):\n",
    "            if frequency_counter > ii:\n",
    "                dct_copy[u,v] = 0\n",
    "            frequency_counter += 1\n",
    "            \n",
    "    partial_z_dct.append(dct_copy)\n",
    "    \n",
    "    partial_img_idct = fftpack.idct(fftpack.idct(dct_copy.T, norm='ortho').T, norm='ortho')\n",
    "    partial_z_idct.append(partial_img_idct)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/ipykernel/__main__.py:7: DeprecationWarning: using a non-integer number instead of an integer will result in an error in the future\n"
     ]
    },
    {
     "data": {
      "image/png": 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4h2xW7nlf0l34zYtsHm7MKTrY532lsqyK4G+8Teey3wF/kczDybZDk+23t+12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\nROcj8f4Ln9Q2+6KEa/GKO/fOdcwHbwNLtdifq8X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7nlv4zL1y2K10PlrVSd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\n+e7bcZsOiX9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc6cea1f7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# shows each coefficient evolution towards the image formation\n",
    "# here you can see how each DCT basis constributes to the image formation\n",
    "# try to visualize them as a summation of the basis throughout the 64 elements \n",
    "fig = plt.figure(figsize=(16, 16))\n",
    "for ii in range(img_h*img_h):\n",
    "    plt.subplot(8, 8, ii + 1)\n",
    "    plt.title(partial_z_dct[ii][ii / 8, ii % 8])\n",
    "    plt.imshow(partial_z_idct[ii], cmap='gray', interpolation='nearest')\n",
    "    plt.grid(False);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);"
   ]
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
