{
 "metadata": {
  "name": "",
  "signature": "sha256:75cc7b8040e4dc42abacdda27c9b3915a966b17bed12362e6828e1df7d42c744"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - compatibility with Python 3\n",
      "from __future__ import print_function  # print('me') instead of print 'me'\n",
      "from __future__ import division  # 1/2 == 0.5, not 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - show figures inside the notebook\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - import common modules\n",
      "import numpy as np  # the Python array package\n",
      "import matplotlib.pyplot as plt  # the Python plotting package"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - set gray colormap and nearest neighbor interpolation by default\n",
      "plt.rcParams['image.cmap'] = 'gray'\n",
      "plt.rcParams['image.interpolation'] = 'nearest'"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - nibabel package\n",
      "import nibabel as nib"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - our rotations module, now on the PYTHONPATH\n",
      "from rotations import x_rotmat, y_rotmat, z_rotmat"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## An affine normalization"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the last notebook - [moreon_rotation](moreon_rotation.ipynb) - we undid a rotation.\n",
      "\n",
      "In that case, I told you what the rotation was.  What if I didn't tell you?  Could you work it out?\n",
      "\n",
      "This is a good job for optimization."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - the first volume of ds107_sub012_t1r2.nii\n",
      "img_4d = nib.load('ds107_sub012_t1r2.nii')\n",
      "data = img_4d.get_data()\n",
      "vol0 = data[..., 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the volume with some secret rotations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - the secretly rotated image\n",
      "rotated_img = nib.load('secret_rotated_volume.nii')\n",
      "rotated_vol0 = rotated_img.get_data()\n",
      "rotated_vol0.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "(64, 64, 35)"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Displayed side by side with the original (not-rotated) image:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - slices on z, y, and x axis from \n",
      "fig, axes = plt.subplots(3, 2, figsize=(10, 15))\n",
      "axes[0, 0].imshow(vol0[:, :, 17])\n",
      "axes[0, 1].imshow(rotated_vol0[:, :, 17])\n",
      "axes[1, 0].imshow(vol0[:, 31, :])\n",
      "axes[1, 1].imshow(rotated_vol0[:, 31, :])\n",
      "axes[2, 0].imshow(vol0[31, :, :])\n",
      "axes[2, 1].imshow(rotated_vol0[31, :, :])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.image.AxesImage at 0x10aac57d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3332dz4wJMpbJY0X5FahZ8ceP6oPxXNyfbaPexcfFec0vvPBCYTM/TxRnrdXt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CHauXNnZu/YsSOzqYWibmrSpEmD9k2NEPVMGzduzGzmAuJ7Sc+n3ujqq69WE+973/sym7mdmJfo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\n112X2fR31NbQT/D8VMdTKvHDc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       "text": [
        "<matplotlib.figure.Figure at 0x1078f4790>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You might be able to work out what the transformations are, at least roughly, but can we work them out by optimization?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first thing we need for optimization, is a mismatch metric.\n",
      "\n",
      "I suggest you use the correlation mismatch function for the metric.  You can get that from the [optimizing_space](optimizing_space.ipynb) notebook, and paste it below.  But feel free to try another mismatch metric if you like.  Remember it is a function that accepts two images and returns a scalar that is low when the images are well matched."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get the correlation mismatch metric from `optimizing_space`, paste here\n",
      "def correl_mismatch(slice0, slice1):\n",
      "    \"\"\" Negative correlation between the two images, flattened to 1D \"\"\"\n",
      "    correl = np.corrcoef(slice0.ravel(), slice1.ravel())[0, 1]\n",
      "    return -correl"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we need a function that will transform a given image by a given set of rotations.  The arguments will be:\n",
      "\n",
      "* `vol_arr` : the image that we will transform;\n",
      "* `rotations` - a vector of rotations.\n",
      "\n",
      "The function then returns a copy of `vol_arr` with those rotations applied.\n",
      "\n",
      "Specifically, the `rotations` give the *resampling transform* that gives the mapping from coordinates in a new empty copy of `vol_arr` - call this `K` - to coordinates in `vol_arr`.\n",
      "\n",
      "Our vector of rotations is length 3, containing the $r_x, r_y, r_z$, which are, respectively, the rotations about the x, y and z axis.\n",
      "\n",
      "In order to do this transformation, you will need to take the three parameters, and convert them to the corresponding rotation matrix.\n",
      "\n",
      "You then need to apply this transformation matrix to the coordinates of `K` to return a new copy of `vol_arr` with $r_x, r_y, r_z$ applied.  Of course, this will be a job for `affine_transform`:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.ndimage import affine_transform"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Your new function will look something like this:\n",
      "\n",
      "```\n",
      "def apply_rotations(vol_arr, rotations):\n",
      "    r_x, r_y, r_z = rotations\n",
      "    rotation_matrix = ?\n",
      "    # apply rotations with affine_transform to make new image\n",
      "    # return new image\n",
      "```"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make apply_rotations function, accepting `vol_arr` and `rotations` vector\n",
      "# Returning image \n",
      "def apply_rotations(vol_arr, rotations):\n",
      "    r_x, r_y, r_z = rotations\n",
      "    rotation_matrix = z_rotmat(r_z).dot(y_rotmat(r_y)).dot(x_rotmat(r_x))\n",
      "    # apply rotations to make new image\n",
      "    # return new image\n",
      "    return affine_transform(vol_arr, rotation_matrix, order=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - a quick check that 0 rotations give the same output back\n",
      "not_changed = apply_rotations(rotated_vol0, [0, 0, 0])\n",
      "assert np.allclose(not_changed, rotated_vol0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we have the function to apply the rotations, and the matching function, we can make the cost function to optimize.\n",
      "\n",
      "Use the global scope to pick up and use `rotated_vol0` and `vol0` in the function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Make a cost function, that\n",
      "# * is called 'cost_function'\n",
      "# * accepts a vector of rotations as input\n",
      "# * applies the vector of rotations to `rotated_vol0` from the global scope\n",
      "# * returns the mismatch metric for the transformed copy of `rotated_vol0` and `vol0`\n",
      "def cost_function(rotations):\n",
      "    Y_t = apply_rotations(rotated_vol0, rotations)\n",
      "    return correl_mismatch(vol0, Y_t)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - a quick check the cost function returns the current value without rotations\n",
      "current = correl_mismatch(vol0, rotated_vol0)\n",
      "redone = cost_function([0, 0, 0])\n",
      "assert np.allclose(current, redone)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we are ready to optimize.  We are going to need at least one of the cost functions from `scipy.optimize`.\n",
      "\n",
      "`fmin_powell` is a good place to start:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - get fmin_powell\n",
      "from scipy.optimize import fmin_powell"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now call `fmin_powell` with some starting guess for the rotations:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Call optimizing function and collect best estimates for rotations\n",
      "best_params = fmin_powell(cost_function, [0, 0, 0])\n",
      "best_params"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: -0.919532\n",
        "         Iterations: 5\n",
        "         Function evaluations: 318\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([-0.01003138, -0.10381244,  0.19747559])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, use these parameters to:\n",
      "\n",
      "* compile the rotation matrix from the optmized parameters.  This gives the matrix mapping from coordinates in `vol0` to coordinates in `rotated_vol0`;\n",
      "* Use `affine_transform` on `rotated_vol0` to get an un-rotated version of that image.\n",
      "\n",
      "You should be able to do this with your `apply_rotations` function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Use 'apply_rotations' and the estimated parameters to un-rotate the rotated image\n",
      "# Put the new un-rotated image into a variable `best_vol0`\n",
      "best_vol0 = apply_rotations(rotated_vol0, best_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now you can look at the original and the un-rotated image side by side:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# - slices on z, y, and x axis from \n",
      "fig, axes = plt.subplots(3, 2, figsize=(10, 15))\n",
      "axes[0, 0].imshow(vol0[:, :, 17])\n",
      "axes[0, 1].imshow(best_vol0[:, :, 17])\n",
      "axes[1, 0].imshow(vol0[:, 31, :])\n",
      "axes[1, 1].imshow(best_vol0[:, 31, :])\n",
      "axes[2, 0].imshow(vol0[31, :, :])\n",
      "axes[2, 1].imshow(best_vol0[31, :, :])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<matplotlib.image.AxesImage at 0x10c5a9510>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JIYQQovfohUgIIYQQveeYaoion1i5cmVl79ixY/CbGqJHH3102nbNhuPNjIMz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jwhMsYYY0zrsYaoT/J4M+PFzMWRa4yoX2GdINawWblyZWEzZwjj3Hl+i1qtHo6TmiHqlZq0Bhw3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\nsXHjxuIvVGOOB4PwX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vON1GrN5ffgtddea2UODzO1YB4iY3La6MNav0IUETMj4h8iYl1E\nrI2ID0XErIhYEREbIuL+iJhZ78kYY44/9mHGDIbWT4gk/S9J96WULpF0uaT1ku6QtCKltFzSAx3b\nGGMmI/ZhxgyAVk+IImKGpOtTSl+TpJTSmymlA5JulXRnZ7c7JX3qBA3RGGPGxT7MmMHR9jxESyW9\nFBF/I+kDkn4q6T9KmpdSGu7sMyxp3ngd5HqaWi6hHOpyqOupaVZIUx6cmt7ozDPPLGzm56nVJ8s1\nSMzlw3PzWOp4qBmiLqtJe8W+2Rf1ScwBQs1Xfp9qeYZ6zbNizIDo24cZY47S6hUiHZ0QXiXpz1NK\nV0l6VVhaTkd/K447Gzly5Ejxz7SPt956y98Bc6Lo24cZY47S9gnRdknbU0qPd+x/0FHnsisihiQp\nIuZL2j1eB9OnTy/+mfYxbdo0fwfMiaJvH2aMOUqrQ2YppV0RsS0ilqeUNki6SdIznX+3SfpS5/97\nxuvj5JNP7m6zTEXT6+r5cWMdy1ffGX4744wzGtvzX8wMBTEMtW/fvsaxMBzEkFseYstfVR+rL66g\nsK9aqJBhrqZx1sKQtdWcpjBYryFNY94JBuHDjDFHafWEqMPtkv42Ik6WtFHSb0maJunuiPi8pM2S\nPnPihmeMMY3YhxkzAFo/IUopPSXp58Zouul4j8UYY3rFPsyYwdB2DZExxhhjjEt39ENEpFzrw3tJ\nDUqu66GGiK+fs/2VV17huQubWp18LNT11F4hp/aJmqM33nhj3LGeffbZjX0fOnSosF999dXCphaK\nNu9TDsdN+PlQAN2klaJmiOPK7+nPfvazVqa9N1MLl+4wTbTRh3mFyBhjjDGtxxMiY4wxxrQeT4iM\nMcYY03pa/5ZZv7z11ltdXQt1JU0aImpt9u/fL+lobpzp06eP0tbUtF7U1rznPe/p9lUrWcGcRtQj\nTZ8+XYcPH+5qkVgSI9+f46QWKqWkN954o/tz6pmod2rKOzSiGXr77bd10kknjdL50K6V14gIvfXW\nW938RU1lWdh3TZdljDFmcuMVoj5pqlc2EQZZ+qEmMu4FCqknS1/SYOuIDfrzNMYYMzXwhMgYY4wx\nrccTImOMMca0Huch6gPn8TDj0cYcHmZqYf9lmmijD/OEyBhjjDGtxyEzY4wxxrQeT4iMMcYY03o8\nIeqDiLg5ItZHxHMR8cd99rU5Ip6OiJUR8ViPx34tIoYjYnX2s1kRsSIiNkTE/RExs8/+/mtEbO+M\nb2VE3HyMfS2OiAcj4pmIWBMRvzfR8TX01fPYIuKUiHg0IlZFxNqI+LOJjsuYqcgg/Venv0nhw9rg\nvzrH2YcNGGuIJkhETJP0rKSbJL0o6XFJn00prZtgf5skXZ1S2jeBY6+XdEjS/0kpXdb52Zcl7Ukp\nfbnj7M5OKd3RR3//RdIrKaWv9ji2IUlDKaVVEXGGpJ9K+pSk3+p1fA19fWaCYzstpfRaRLxH0o8k\n/aGkW3sdlzFTjUH7r06fk8KHtcV/dfq0DxsgXiGaONdIej6ltDmldETSNyT9cp99TkjVn1J6WNJ+\n/PhWSXd2tu/U0Qevn/4mNL6U0q6U0qrO9iFJ6yQtnMj4Gvqa6Nhe62yeLGmajl7zhO+bMVOId8J/\nSZPAh7XFf3X6sQ8bIJ4QTZyFkrZl9nb965d7IiRJP4iIJyLid/oa2VHmpZSGO9vDkuYNoM/bI+Kp\niPjriSzDRsR5kq6U9Gi/48v6+slExxYRJ0XEqs75H0wpPdPvuIyZIgzaf0mT34e9q/xXpx/7sAHi\nCdHEGXSs8dqU0pWSflHS73aWfQdCOhoX7Xe8/1vSUklXSNop6Su9HNxZIv6mpN9PKb3Sz/g6ff1D\np69DEx1bSuntlNIVkhZJuiEibuxnXMZMId6J7/Vk9mHvOv/VObd92ADxhGjivChpcWYv1tG/siZE\nSmln5/+XJH1LR5e0+2G4E7NWRMyXtLufzlJKu1MHSX/Vy/giYrqOOpO7Ukr39DO+rK//O9JXP2Pr\nHH9A0nclXT3RcRkzxRio/5Imtw97N/uvTh/2YQPAE6KJ84SkCyPi/2/f7lEaiKIwDL+nEVQEEcFW\nF+AObBUtrSyD7sHCXbgBGxtbSSmuwWgUQbF2ERZei7kp8+OdKZLc94EDQ8h8nATmcJhkdiNiBTgD\n+iVBEbEWERv5eB04Al4nnzVVH+jl4x5wP+G9U+ULa+SUGfuLiABugPeU0nWb/sZllfQWEdujW9MR\nsQocAoOSvqQF1Nn8gvmfYcs2v/J5zrCupZSswqK5NfwBfAFXLXL2gOdcb//NAu6Ab+CH5n8B58AW\n8Ah8Ag/AZou8C+AWGAIvNBfYzoxZB8Bv/myDXMcl/Y3JOinpDdgHnnLWDGT7ZwAAAFdJREFUELjM\nrxd/b5a1SNXV/MpZczPDaphfOc8Z1nH52L0kSaqeP5lJkqTquRBJkqTquRBJkqTquRBJkqTquRBJ\nkqTquRBJkqTquRBJkqTquRBJkqTq/QElhZYbcco1NQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bfb9f90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If you like, you can check in the file `make_rotated.py` to see what rotation I actually applied."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## If you raced ahead"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Why not try another mismatch function?\n",
      "\n",
      "And / or try another `fmin_` function from `scipy.optimize`?\n",
      "\n",
      "Is it easy for the optimization to go wrong, or is it nearly always right whatever parameter you choose?"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}