Dilated Convolution

dilatedConvolution.ipynb

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    "%matplotlib inline\n",
    "import sys\n",
    "sys.path.insert(0, '/home/auviz23/Repos/caffe/python')\n",
    "import caffe\n",
    "import numpy as np"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Caffe Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
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   "source": [
    "net = caffe.Net('dilatedConv_deploy.prototxt', caffe.TEST)\n",
    "src = net.blobs['data']\n",
    "dst = net.blobs['conv1']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
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   "outputs": [],
   "source": [
    "x = np.arange(9*9).reshape(1, 1, 9, 9)\n",
    "#y = np.ones((1, 1, 3, 3))\n",
    "y = np.arange(3*3).reshape(1, 1, 3, 3)\n",
    "\n",
    "src.data[...] = x\n",
    "net.params['conv1'][0].data[...] = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Blob:  data (1, 9, 9)\n",
      "Blob:  conv1 (1, 3, 3)\n",
      "Filter:  conv1 (1, 3, 3)\n"
     ]
    }
   ],
   "source": [
    "for key in net.blobs.keys():\n",
    "    print \"Blob: \", key, net.blobs[key].data[0].shape\n",
    "    \n",
    "for key in net.params.keys():\n",
    "    print \"Filter: \", key, net.params[key][0].data[0].shape\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
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     "text": [
      "Input: \n",
      "[[  0.   1.   2.   3.   4.   5.   6.   7.   8.]\n",
      " [  9.  10.  11.  12.  13.  14.  15.  16.  17.]\n",
      " [ 18.  19.  20.  21.  22.  23.  24.  25.  26.]\n",
      " [ 27.  28.  29.  30.  31.  32.  33.  34.  35.]\n",
      " [ 36.  37.  38.  39.  40.  41.  42.  43.  44.]\n",
      " [ 45.  46.  47.  48.  49.  50.  51.  52.  53.]\n",
      " [ 54.  55.  56.  57.  58.  59.  60.  61.  62.]\n",
      " [ 63.  64.  65.  66.  67.  68.  69.  70.  71.]\n",
      " [ 72.  73.  74.  75.  76.  77.  78.  79.  80.]] \n",
      "\n",
      "Filter: \n",
      "[[0 1 2]\n",
      " [3 4 5]\n",
      " [6 7 8]] \n",
      "\n",
      "Output: \n",
      "[[ 1584.  1620.  1656.]\n",
      " [ 1908.  1944.  1980.]\n",
      " [ 2232.  2268.  2304.]] \n",
      "\n"
     ]
    }
   ],
   "source": [
    "out = net.forward()\n",
    "print \"Input: \\n\", src.data[0, 0], \"\\n\"\n",
    "print \"Filter: \\n\", y[0, 0], \"\\n\"\n",
    "print \"Output: \\n\", dst.data[0, 0], \"\\n\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary : Idea is very simple. There is a new **dilation** parameter in the convolution kernel in caffe. By default, **dilation = 1**. It denotes our normal convolution.\n",
    "\n",
    "Now if **dilation = 2**, it **fills one zero** in between filter elements. For example, 3x3 kernel becomes 5x5 (because one zero between all the filter elements). Then do the convolution with this new 5x5 kernel.\n",
    "\n",
    "If **dilation = 3**, it **fills two zeros** in between filter elements. So 3x3 kernel becomes 7x7 kernel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vanilla Python Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weights :\n",
      "[[ 0.  0.  0.  1.  0.  0.  2.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 3.  0.  0.  4.  0.  0.  5.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  0.  0.  0.]\n",
      " [ 6.  0.  0.  7.  0.  0.  8.]]\n",
      "Output : \n",
      "[[ 1584.  1620.  1656.]\n",
      " [ 1908.  1944.  1980.]\n",
      " [ 2232.  2268.  2304.]]\n"
     ]
    }
   ],
   "source": [
    "from scipy.signal import correlate2d  # Use correlation for straight convolution\n",
    "\n",
    "# A function to do 2D convolution without stride\n",
    "def convolution(img, wts, pad = 0, dilation = 1):\n",
    "    wr, wc = wts.shape\n",
    "    newX = wr+(wr-1)*(dilation-1)\n",
    "    newWts = np.zeros((newX, newX))\n",
    "    newWts[::dilation, ::dilation] = wts\n",
    "    print \"Weights :\\n\", newWts\n",
    "    return correlate2d(img, newWts, mode='valid')\n",
    "\n",
    "result = convolution (x[0, 0], y[0, 0], dilation = 3)\n",
    "print  \"Output : \\n\", result"
   ]
  }
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