Unconstrained Image Manipulation

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   "source": [
    "import numpy as np\n",
    "import scipy.ndimage.filters as filter\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import matplotlib.image as mpimg\n",
    "import scipy\n",
    "from scipy.signal import sepfir2d\n",
    "from scipy.signal import cspline2d\n",
    "import numpy.matlib\n",
    "from numpy.linalg import inv\n",
    "import math"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation of convmtx2"
   ]
  },
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   "cell_type": "code",
   "execution_count": 7,
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   "source": [
    "def my_convmtx2(kernel, patch_size):\n",
    "    s = kernel.shape\n",
    "    m = patch_size - s[0] + 1\n",
    "    n = patch_size - s[1] + 1\n",
    "    mtx = np.zeros((m * n, patch_size ** 2))\n",
    "\n",
    "    k = 0\n",
    "    for i in xrange(0, m):\n",
    "        for j in xrange(0, n):\n",
    "            for p in xrange(0, s[0]):\n",
    "                l1 = (i + p) * patch_size + j\n",
    "                l2 = l1 + s[1]\n",
    "                mtx[k, l1:l2] = kernel[p, :]\n",
    "            k += 1\n",
    "    return mtx\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "f = mpimg.imread('photo3.png')[:,:,0].astype(np.float32)\n",
    "shape = f.shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://dl.dropboxusercontent.com/u/46105572/ucim/orig.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "source": [
    "kernel = np.array([[1.,1.,1.],[1.,1.,1.],[1.,1.,1.]], dtype=np.float)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": [
    "H = my_convmtx2(kernel, shape[0])\n",
    "\n",
    "# Flattened Image to Vector\n",
    "f_vec = f.flatten()\n",
    "\n",
    "# Size of Image vector\n",
    "shqrt = math.sqrt(f_vec.size)\n",
    "\n",
    "\n",
    "# THE BLURRING OPERATION\n",
    "hf = np.dot(H,f_vec)\n",
    "\n",
    "# Putting the blurered vec into a matrix\n",
    "hf = np.reshape(hf, (shqrt-2, shqrt-2))\n",
    "\n",
    "\n",
    "# Adding noise to get G\n",
    "g = hf + 0.04*hf.std()*np.random.random(hf.shape)\n",
    "z = g\n",
    "# Putting G into a vector\n",
    "g_vec = g.flatten()\n",
    "\n",
    "# Pseudo Inverse\n",
    "inver = np.linalg.pinv(H)\n",
    "\n",
    "# Inverse * g\n",
    "hG = np.dot(inver,g_vec)\n",
    "\n",
    "# Putting the restored vector into a matrix\n",
    "res = np.reshape(hG, (shqrt, shqrt))\n",
    "\n",
    "print res.shape\n",
    "\n",
    "plt.subplot(121),plt.imshow(z, cmap = 'gray')\n",
    "plt.subplot(122),plt.imshow(res, cmap = 'gray')\n",
    "plt.title('Output'), plt.xticks([]), plt.yticks([])\n",
    "plt.savefig('f0.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distorted Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://dl.dropboxusercontent.com/u/46105572/ucim/g.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Restored Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://dl.dropboxusercontent.com/u/46105572/ucim/res.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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