Smoothing in Yoon et al. (2013)

gistfile1.txt

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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Smoothing in Yoon et al. (2013)\n",
      "This notebook is a supplement to de Hollander et al. (2014) - _The subcortical cocktail problem; mixed signals from the subthalamic nucleus and substantia nigra_ and aims to show that the effect of a fwhm=2 milimeter smoothing kernel on data with a resolution of 3.4x3.4x4mm, as employed in Yoon et al. (2013) is negligible."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To make it possible to visualize, we start with the 1D-case and move up to 3D via 2D."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy as sp\n",
      "from scipy import ndimage"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 174
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 1D case"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fwhm = 2.0\n",
      "sigma = fwhm / 2.355\n",
      "\n",
      "x = np.linspace(-5, 5)\n",
      "\n",
      "pdf = sp.stats.norm(0, sigma).pdf(x)\n",
      "\n",
      "plt.plot(x, pdf, label='smoothing kernel')\n",
      "\n",
      "plt.axvline(-3.4/2, c='k', ls='--', label='bounds voxel')\n",
      "plt.axvline(3.4/2, c='k', ls='--')\n",
      "\n",
      "plt.legend()\n",
      "\n",
      "plt.xlabel('x-axis in mm')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 175,
       "text": [
        "<matplotlib.text.Text at 0x10664250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Xp3l5zeGcKLep2teSLJSURRIoEAzRuKubGdPSt7zmcIPlNndqb2WR4ZSURRKo\ncVc3wVCYWeUFTofiGtGkXKchbJGDKCmLJFB07rS6XPPJUdUDf6DU7VRSFhlOSVkkgaKJp0o95UGl\nxTlkZfiob9bwtchwSsoiCVS3sxMPMLM0z+lQXMPr8VBVlk/jrr30B4JOhyPiKqp9LWllMmsgh8Nh\n6pq7KJuaS3am3mpDVZXns7lhDw27upldUZjw11Pta0kW6imLJMjuPfvo6Q0wS/cnHyR6TjSvLHIg\nJWWRBImuLp6lRV4Hia5Gr1dSFjmAkrJIgtQN3Ier26EOVjktD6/HQ60We4kcQElZJEGiQ7Mavj5Y\nZoaP6SW51Dd3EQqHnQ5HxDWUlEUSpL65k8K8TIrys5wOxZWqyvPp7QvS0q69lUWilJQlrUxWDeSu\nnn52d/RqPnkMs8omb15Zta8lWSgpiyRAtJJXNPHIwaJ/sNSqBrbIICVlkQSoH1zkpZ7yaAY3plAN\nbJFBSsoiCVC7U3soj6cgN5PigqzBVeoioqQskhD1zZ1kZfi0h/I4qssLaO/qo6O7z+lQRFxBSVkk\nzvoDQXbs3svMMu2hPJ792ziqtywCqn0taWYyaiA37tob2UNZi7zGFZ1zr9/ZxeI5JQl7HdW+lmSh\nnrJInEXnSKu0yGtc0S0t67TYSwRQUhaJu/2VvNRTHs+0omxysnxa7CUyQElZJM7qmjvxeLSHciwi\neysX0NS6l95+7a0soqQsEkehcJj65i6ml+SRmeFzOpykMKssn3AYtrdoCFtESVkkjna197CvL6hN\nKA5B1ZDFXiLpTklZ0kqiayBH55O1yCt20bn3RC72Uu1rSRZKyiJxFL3fVnsox66yNA+f1zNYmlQk\nnSkpi8RRncprHjK/z8uMaXnUt3QRCmlvZUlvSsoicVTf3EVxQRaFuZlOh5JUZpXl09cfYmfbXqdD\nEXGUkrJInHTs7aOts1e95MMwWEREi70kzSkpi8RJdPWw5pMPXXW5amCLgGpfS5pJZA3kwUVe6ikf\nssGNKRLUU1bta0kW6imLxMn+nrKS8qHKzc5gWlE2dTs7CYe12EvSl5KySJzUNXeRnelj2pQcp0NJ\nSlVl+XTu7WeP9laWNKakLBIHff1BduzupqosH69Heygfjlla7CUS25yyMWYZcBfgA+631t427PP/\nCHwJ8ACdwGestW/FOVYR19re0k04rEVeEzG4t3JzJ8fMS9zeyiJuNm5P2RjjA+4BlgELgeXGmAXD\nmm0FzrBDBwDDAAAb/klEQVTWHgN8C/hxvAMVcTMt8pq4aLnNWvWUJY3F0lNeCmy21tYAGGMeBi4E\nNkYbWGtfHtJ+FTAzjjGKxE20/nG8V+PqdqiJm1qYRV62PyHlNhN13UXiLZY55Uqgfsjj7QPPjeaf\ngUcnEpRIsqlr7sTn9TBjmvZQPlwej4eqsnya23ro6Q04HY6II2JJyjHfn2CMOQu4CvjyYUckkmRC\noTDbm7uZXpJHhl9rJydiVnkBYaChpdvpUEQcEcvwdQNQNeRxFZHe8gGMMccA9wHLrLVt4x20tFTD\nfLHQeYpdLOfK6/XE3DZW25s76e0PcmR1cVJcLzfHuGh+KU+8Vk9rd19c4zzc6+7mc+UmOk/xE0tS\nXg0cYYyZDTQClwLLhzYwxswCHgE+Za3dHMsLt7SonN54SksLdJ5iFOu5iu5CFM/zunbTTgDKCrNc\nf73c/jNVnBP5lbRh6y6WmtK4Hfdwrrvbz5Vb6DzFJtY/XMYda7PWBoDrgL8BG4DfWGs3GmNWGGNW\nDDS7CSgGfmiMWWOMefXwwhZJPrVNkV9IVVrkNWEVJbn4fV5qmvRLXtJTTPcpW2sfAx4b9tyPhnx8\nNXB1fEMTib9ErL7d2tiBB5hdoaQ8UX6fl+ryfGqaOunrD5KZ4YvLcbXqWpKFVqWITEAwFKKmqZMZ\npXnkZGl/l3iYO6OIYChMbQJujRJxOyVlkQloaOmmtz/I3OmFToeSMubOiJzLLQ0dDkciMvmUlEUm\nYOuOSOKIJhKZuOi5jJ5bkXSipCwyAVsbo0m5yOFIUse0omwKcjPY1rjH6VBEJp2SssgEbGvsICvD\nR6UqecWNx+Nh7vRCdnf0sqer1+lwRCaVkrKklSVLFg/WQZ6ont4Ajbu6mV1RMFicQuJjcAi7MT5D\n2PG87iKJpKQscphqdnQQBuZWaj453qLTAZpXlnSjpCxymAYXeU3XfHK8zZkeuec7Xj1lkWShpCxy\nmKK37GjldfzlZmcwvSSXrTs6BktkiqQDJWWRwxAOh9m6o4PigiyKC7KcDiclzZ1RSG9fkMbd2jFK\n0oeSsshh2N2xj47uPvWSE2hwXllD2JJGVBdQ0kq8aiDvvz9ZSTlRolXStjZ2cMaxMyZ0LNW+lmSh\nnrLIYRhMyiqvmTAzy/LI9HvVU5a0oqQschi27ujA6/Ewu0JJOVF8Xi/VFQU07OpiX1/A6XBEJoWS\nssghCgRD1DZ1MrM0j6zM+GwtKCObO6OQcHj/ntUiqU5JWeQQbW/poj8Q0nzyJIgu9tqiIWxJE0rK\nIocoOsc5R0k54ebFudymiNspKUtaiUcNZO0MNXmKC7Ioys9k6wR3jFLta0kWSsoih2hrYwc5WT6m\nl+Q6HUrKi+4Y1d7VR2vHPqfDEUk4JWWRQ9C9r5+m1r3MrijE69HOUJMh3jtGibiZkrLIIdg2sAnF\nPO0MNWm0Y5SkEyVlkUOwv2iI5pMny+yKAjyopyzpQUlZ5BCovObky8nyM6M0j5qmDoKhkNPhiCSU\nal9LWplIDeRwOMzWxg6mFWVTmJcZx6hkPHOnF9LQ0k1DSzezygsO+etV+1qShXrKIjFqae+hq6df\nvWQHzKvUjlGSHpSURWKkTSicM3THKJFUpqQsEqPBpFypRV6Tbca0SJ1xrcCWVKekLBKjrTs68Hk9\nVJfnOx1K2vF6PcypKGDHrm56erVjlKQuJWWRGPQHQtTt7KSqLJ8Mv3aGcsKcGYWE2X+vuEgqUlKW\ntHK4NZDrmjsJBMNa5OWg6L3hh7NjlGpfS7JQUhaJge5Pdl703G/TYi9JYUrKIjHYpp2hHFdckEVx\nQRZbG/cQDoedDkckIZSURWKwtbGDvGw/5cU5ToeS1ubOKKRjbz+792jHKElNSsoi4+jo7qO5vYc5\n0wvxaGcoR80bGKnYPMH9lUXcSklZZBwba9sAMLOmOByJRK/Bxpo2hyMRSQzVvpa0cjg1kN+uaQVg\n0Zyp8Q5HDlF1eQF52X421LQSDodjHrlQ7WtJFuopi4whHA6zoaaVvGz/YW2EIPHl9XpYUF3M7o5e\ndrb1OB2OSNwpKYuMYWdbD60dvSyYPRWv5pNdYeHsyIjFhoERDJFUoqQsMoa3tw0MXc8udjgSiVo4\nMI0QvTYiqURJWWQM0d7YotmaT3aLsik5lE7JZlNdG8FQyOlwROJKSVlkFMFQiE11bZRNyWHaFN2f\n7CYLZ0+lpzdIzY5Op0MRiSslZUkrh1IDeduOTnp6g4PDpeIe0ZGLt2OcV1bta0kWSsoio9gwMGe5\nsFrzyW5zVHUxHvZfI5FUoaQsMooNNa14PLBAi7xcJz8ng+qKArY0drCvT/srS+pQUhYZQU9vgC2N\nHcyuKCQvO8PpcGQEi+ZMJRgKY+vanQ5FJG6UlEVGYOvbCYbCLFQv2bUWHuK8skgyUFIWGYFuhXK/\n+ZVFZPq9qoMtKUW1ryWtxFoDeUNNG5kZXuZVav9kt8rwezmyagrrt7XS1tlLcUHWqG1V+1qShXrK\nIsO0dfbSuKubI6umkOHXW8TNVHJTUo1+44gMo6Hr5BGd89+gIWxJEUrKIsMoKSePmWX5FOZmsKE2\nspWjSLJTUhYZIrJVYxuFeZlUluY5HY6Mw+vxsHD2VPZ09dGwq9vpcEQmTElZZIiGXd3s6e5j4exi\nPNqqMSks0BC2pJBxk7IxZpkxZpMx5l1jzJdH+PxRxpiXjTH7jDGfT0yYIvExXg3k/aU1NXSdLBbF\nsNhLta8lWYyZlI0xPuAeYBmwEFhujFkwrNlu4HrgewmJUGQSvT3Q21qkTSiSxtTCbKaX5GLr2gkE\ntZWjJLfxespLgc3W2hprbT/wMHDh0AbW2hZr7WqgP0ExikyKQDCErW9jeknumPe8ivssrJ5Kb3+Q\nLQ17nA5FZELGS8qVQP2Qx9sHnhNJOVsa9tDXHxq891WSx8I5kXnltzWvLEluvIpeCbvHoLS0IFGH\nTik6T7GL5Vx5vZ5R2z6+ejsApx1bmdLnPRW/t/cWZHPvH9bz7vY9I35/Y133saTiuUoEnaf4GS8p\nNwBVQx5XEektT1hLS2c8DpPSSksLdJ5iFOu5CoUif2eO1Hb1hia8Hg8VRVkpe95T+Wdq7vRC3qlv\no7a+ldxhO3uNdd1Hk8rnKp50nmIT6x8u4yXl1cARxpjZQCNwKbB8lLa6f0Rcb7QayN37+tm2o4N5\nlUXkZKkkfDJaOLuYzQ172FjbzhJTesDnVPtaksWYc8rW2gBwHfA3YAPwG2vtRmPMCmPMCgBjTIUx\nph74N+Brxpg6Y0x+ogMXiadNtW2Ew6rilcyiK+ZVB1uS2bhdAmvtY8Bjw5770ZCPmzhwiFsk6Qze\nCqWknLTmTC8kO9PH29siJTdV/EWSkSp6SdoLBEO8bpvJz8lg9nQtWElWfp+XxXOm0tzeQ93OLqfD\nETksSsqS9jbUtNK5t5+TF5Tj9+ktkcxOXVQBwMtvNzkcicjh0W8gSXsvrY/8Aj9lcbnDkchEHT2v\nhLxsP69s2EkwpOpeknyUlCWtDK+B3NMbYM27uygvzmHu9EIHI5N48Pu8LF1QTkd3HxuHFBJR7WtJ\nFkrKktbeeKeF/kCIUxdVaGFQitAQtiQzJWVJa/uHriscjkTiZV5lIaVTsnn9nRb29QWcDkfkkCgp\nS9pq6+xlU20b8yuLKJuS43Q4Eicej4dTF1XQ1x9izTu7nA5H5JAoKUvaemVDE2HgVPWSU050CPsl\nDWFLklFSlrT18vqd+LweTjqqzOlQJM7Kp+Yyd0YhG2paae/qdTockZipyK+klWgN5PrmLra3dHH8\nEdPIz8kY56skGZ26qIKtjR2s2rBTta8laainLGkpujI3OswpqWfpgjJ8Xo9WYUtSUVKWtBMKhVm1\nYSe5WX6OnV/idDiSIAW5mRw9t4S6nV00tKjspiQHJWVJO5vq2mjr7OXEo8rI8PucDkcS6JRFkSpt\nL7+90+FIRGKjpCxpJzqceZpWXae84+ZPIyfLxysbmgiFw06HIzIuJWVJK739QVbbFkoKs5k/s8jp\ncCTBMjN8LDFltHb08k5du9PhiIxLSVnSypITFvPoD67i1MXleFVWMy2ctqiCp+6/hguXneJ0KCLj\nUlKWtNLbHwS06jqdHDlrCl6Ph95AkL6B6y/iVkrKkjY6uvvoC4Tw+7xML8lzOhyZJF6Ph6xMH+Fw\nmLVbdjsdjsiYlJQlbby6cScQJitDK67TTfSav7xe9yyLuykpS9qIrLr2KCmnIb/Pi9/rZd3W3XTu\n7XM6HJFRKSlLWmjc1c22HZ1k+r14vVrglY6yMn0EQ2Fe2aB7lsW9lJQlLfzlpRoAHv7Ti6qDnIZe\nf309L696i0y/l8dX1dEf0IIvcSclZUl5dTs7WbVhJ9XlBZxw5DSnwxGHFOVlcvaSmbR19vLMmkan\nwxEZkZKypLw/Pr8NgIvPnItH9yantQ+cUk12po+/vlxDT2/A6XBEDqKkLCltc8Me3ty8iyNnFrF4\nzlSnwxGH5edksGzpLDr39vP31fVOhyNyECVlSVnhcJhHnt0CwMVnzlMvWQA476Qq8nMyePzVOrp6\n+p0OR+QASsqSsjbUtrGprp2j55ZwZNUUp8MRl8jJ8vPBU6vp6Q3y2Kpap8MROYCSsqSkA3rJZ8wd\nfH7JksUsWbLYqbDEIcOv+1nHV1JckMVTq7fT3tXrYGQiB1JSlpS05t1dbNvRyYlHlVFdUeB0OOIy\nmRk+Pvye2fQFQvzvwO1yIm6gpCwpJxQK84fntuLxwD+cPsfpcMSl3nv0dMqm5PDsm420tPc4HY4I\noKQsKWjVhp007OrmPYuna+MJGZXf5+Wi0+cQDIX58wvbnA5HBFBSlhQTCIb44wtb8Xk9fOQ9s50O\nR1xu6cJyKkvzeOntJhp2dTsdjoiSsqSW59/aQUv7Pt53XCXTpuQ4HY64nNfj4eLT5xIOwx+f3+p0\nOCL4nQ5AJF76+oP85cVtZPq9fOi06hHbqO51ehrruh93xDTmTC/kddtCTVMHsysKJzEykQOppywp\n4+k3Gmjv6uPcE6soys9yOhxJEh6Ph4+eGblt7pHn1FsWZykpS0qobergTy9uIyfLz7KTZzkdjiSZ\nhbOnsqC6mPVbW3l+rTarEOcoKUvS6+rp5z8eeJXeviCXLzPk52Q4HZIkocuXGfKy/fz8Ccvmhj1O\nhyNpSklZklowFOJHf1rPjt3dfPDUapYuKHc6JElSZcW5/L8LFxMMhbn3kXXs3qN7l2XyKSlLUvvd\nM1t4u6aNkxaW8w9DymmKHI5Fc6Zy6Vnz2dPdx388+Cr9gaDTIUmaUVKWpPXiuh088Vo900ty+fwn\nl+CNYRco1b5OT4dy3c87qYrTFlfwbn07P33MEg6HExydyH5KypKUtjZ28NDjlpwsP9d/9BjyNI8s\nceLxeLh8meGIqim8/HYTT76mfZdl8igpS9Jp7+rlnkfeIhgK8f8uXETF1FynQ5IUk+H3ceOVSynK\ny+Q3z2zm7W2tTockaUJJWZJKfyDEvY+so72rj0veN4+j55Y4HZKkqJKiHD578dH4vB5W/mk9O9v2\nOh2SpAElZUka4XCYn//NsqWxg1MWlbNsqe5HlsSaX1nEP73f0L0vwPf/Zx09vQGnQ5IUp6QsSaE/\nEOJXf3+XF9btoLqigCuWHYUnhoVdIhN1+jEzOHfJTBp3dXPX79bS1tnrdEiSwlT7WlyvuW0vP/zT\n29Q2dTK9JJfrLz6azAzfYR1Lta/T00Sv+8fPnk97dx+rNzXzjQde5ZoPL9TUiSSEesriaqs27OTm\nB1+jtqmT9x4znZsuP4mphdlOhyVpxu/z8pkLF/GP5x3Jvr4Ad/52Lb99ZjOBYMjp0CTFqKcsrtTb\nH+TXf3+X59Y2kpXp45oPL+TURRVOhyVpzOPxcM6SmcyvLGLln9bz+Ko63q1vZ8VHFmmbUIkb9ZTF\ndRp2dfPtn63mubWNzCrL5xtXnKSELK5RXVHATVecxCmLytnS2MHND77G67bZ6bAkRainLK4RCIZ4\n4a0dPPz0u/T1hzj7hEouPXs+Gf7Dmz8WSZScLD/XfGghC6qL+eUT73DvH9Zz9gmVXHT6XG2IIhOi\npCyOa+3Yx/+92chzaxvp6O4jJ8vPZ/9hIUtMmdOhiYzK4/Fw+jEzmDsjMpz99BsNPP/WDpYuKOPs\nE2YyZ3qh0yFKElJSFkeEw2E21rbxzBsNrHl3F6FwmNwsP+efVMX5J1UlbDFXtP6xVmGnl0Re98pp\neXztshN5dk0DT69p4MV1Tby4rok50ws4+4SZLF1QptEeidm4SdkYswy4C/AB91trbxuhzX8DFwB7\ngSustWviHaikhrbOXl63zTyzpoEduyMVkmaV53P2CTM5eWE5WYd5q5OIk7IyfJy/dBbnnlTFhm2t\nPP1GA2u37OInf93Ib57ezHuPmc5piyuYMS0vpo1TJH2NmZSNMT7gHuBcoAF4zRjzZ2vtxiFtPgDM\nt9YeYYw5GfghcEoCY5Yk0R8IUbuzk60Ne9jS2MGWxj20dkQKL/h9Hk5dVM5ZJ8xk3oxCFQKRlOD1\neFg8t4TFc0vY1d4zOC3z+Ko6Hl9VR26Wn7kzCpk7o5B5lUXMnVFIXrbmoGW/8XrKS4HN1toaAGPM\nw8CFwMYhbT4CPARgrV1ljJlijCm31u5MQLziMoFgiPbOXlo7e2kb+Ld7zz62NXVQt7OTQHD/tneF\nuRkcN38aR1ZN4bTFFRTmZToYuUhiTZuSwyXvm8eF753NatvC+q2tbG3cw/ptrawfssHF9JJc5k4v\npGxqLlMLsige8i87UzOM6Wa8K14JDN23bDtwcgxtZgJJk5TD4TDd+xJT03Yie7FmdvXSsbdv4EBD\njrn/4IQj/x30euEwhAkTCkeeC4chFArv/zgcJhgKEwyGCQRDBEOR/wPBMMFQiEAwxL6+4MC/APt6\nh3zcF6Szp5+2zl46uvtGjN3n9VBVls+8yiLmDfQKphVlq0csaSfD7+PURRWDt/V17u1ja2NHZPSo\nYQ/bdnTw4u6mEb82N8tPcWEWRXmZZGf6yc70Dfw78OMMvxe/z4PPO/C/z4vP68E/8L/X68HjifTk\nB//3evDC4Hsy+tYc+tgz9BMMPD7gg8jvqc69I/8eGE+ifh9kZ/rw+5Lzjt/xknKsGWX4mU2qXcF/\n9fd3eer17U6HkVQy/F6KC7KYUTJl4K/6bIoLsiJ/6RdmMaMk77BLYYqksoLcTI6dP41j508DIn8s\nN7XuZXfHPto6e2nt2Ed715DRp45eGlq6HY46uUwvyeXbV5+clJ2A8ZJyA1A15HEVkZ7wWG1mDjw3\nFk9paUFMAU6Gf/3kEv71k0ucDkMmKJafqbq62kmIxN3c9N6bLId73SfrXJWX6/YpiRivf78aOMIY\nM9sYkwlcCvx5WJs/A5cBGGNOAdo1nywiInLoxkzK1toAcB3wN2AD8Btr7UZjzApjzIqBNo8CW40x\nm4EfAdcmOGYREZGU5JnIQiQRERGJn+RcniYiIpKClJRFRERcQklZRETEJRwrF2OMuZ7IorAg8Fdr\n7ZediiUZGGM+D9wBTLPWto7XPt0YY+4APgT0AVuAK621e5yNyl1iqWOf7owxVcDPgDIi9RZ+bK39\nb2ejcq+BUsyrge3W2g87HY9bGWOmAPcDi4j8XF1lrX1lpLaO9JSNMWcRKc95jLV2MfA9J+JIFgO/\nKM4DdJPt6J4AFllrjwXeAW5wOB5XGVLHfhmwEFhujFngbFSu1A/8m7V2EZEa/p/VeRrTvxC5M0cr\nhsd2N/CotXYBcAwHlqo+gFPD158BbrXW9gNYa1sciiNZ/BfwJaeDcDNr7ZPW2tDAw1VEitjIfoN1\n7Afed9E69jKEtbbJWvvmwMddRH55znA2KncyxswEPkCkB5h8pbMmiTGmCDjdWvsARG41HmsUz6mk\nfARwhjHmFWPM/xljTnQoDtczxlxIZGjoLadjSSJXAY86HYTLjFSjvtKhWJKCMWY2cDyRP/LkYHcC\nXwRC4zVMc3OAFmPMg8aYN4wx9xljckdrnLA5ZWPMk0DFCJ+6ceB1i621pxhjTgJ+C8xNVCxuN865\nugE4f8hzafsX6Rjn6avW2r8MtLkR6LPW/mpSg3M/DS8eAmNMPvB74F8GeswyhDHmQ0CztXaNMeZ9\nTsfjcn7gBOA6a+1rxpi7gK8AN43WOCGsteeN9jljzGeARwbavWaMCRljSqy1uxMVj5uNdq6MMYuJ\n/JW11hgDkSHZ140xS621zZMYoiuM9TMFYIy5gshw2jmTElByiaWOvQDGmAzgf4BfWGv/6HQ8LnUa\n8BFjzAeAbKDQGPMza+1lDsflRtuJjHa+NvD490SS8oicWn39R+Bs4FljzJFAZrom5LFYa9cD5dHH\nxphtwBKtvj7YwMriLwJnWmv3OR2PCw3WsQcaidSxX+5oRC5kjPEAPwE2WGvvcjoet7LWfhX4KoAx\n5kzgC0rII7PWNhlj6o0xR1pr3wHOBd4erb1TSfkB4AFjzDoit7DoYsZGQ5Cj+z6QCTw5MKrwsrVW\nddgHWGsDxphoHXsf8BNr7agrQNPYe4BPAW8ZY9YMPHeDtfZxB2NKBvrdNLbrgV8ObOy0BbhytIaq\nfS0iIuISquglIiLiEkrKIiIiLqGkLCIi4hJKyiIiIi6hpCwiIuISSsoiIiIuoaQskiKMMZcbY66K\nd1sRmTy6T1lERMQlnKroJZLWjDH/Biyw1n7aREqQ/RE40VrbPazdLUTK8gWJ1K/+FJGdi+4DTiRS\nnes14HIiWzH6gJuJlIo8kkilpTXW2uuGHfdmwGet/boxZg/wbSJ7LU8HPj5Q4nVo+xrgB0PafBH4\nNJG9mW+x1v7MGPNToAVYQGQz9xuADxHZP/YFVVgTGZ+Gr0WccRdgjDHvAe4FPj1CQvYB3UT2Yj0d\nmAK8f6Cw/V+BLxBJfL+x1q5hf6nDo4Gl1trTrLXvIVIysnDY64eHtC8A3rLWnkNkn+WrR4g3DLRY\na88GXiGye9JHgH8G/m1IuzJr7YeI/GFwD3Atkb2crxghBhEZRj1lEQdYa8MDc7rPEUmqz4/QJmiM\nCRHZuCUAHAWUDHz6ZuAFIrXjzxz2pRuBXcaYvwJ/AX5rre0YJ6RnBv6vBeaP0ubFgf+3s39v5gag\naODjMPDSkOc3Rl/XGLN7oN14cYikNSVlEeeUAJ1ANQz2jP8+8LlngSeJFK5fYq3tMcb8bsjX5hLZ\ngCNz4OPBPX+ttb3AGcaY44kMH79mjHmPtbZpjFgCA/97GH3P7sCQj4NDPvaM8vzQ9sPbicgIlJRF\nHGCMyQZ+SCRpfssY8ylr7S+As4a0+QegZiAhVwOnEknUEBn+/i8iCfkuIkPOnoGvWwIsttY+BKwx\nxhwNHAEMTcpjJd/xjPZ1SroiE6Q5ZRFnfBN4xFq7GfgX4JvGmBnD2jxBZPP4F4GvA98AbjTGXA9U\nWmt/bq39EXCkMeaD7J8n3gJ81BjzojHmKaCN/UPPUUPnlMOjPD+a4W3CIzwfy3FEZBjdEiUiIuIS\n6imLiIi4hJKyiIiISygpi4iIuISSsoiIiEsoKYuIiLiEkrKIiIhLKCmLiIi4hJKyiIiIS/x/zb2g\naw5Z5foAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xe29fd90>"
       ]
      }
     ],
     "prompt_number": 175
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2D case"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x, y = np.meshgrid(np.linspace(-5, 5), np.linspace(-5, 5))\n",
      "\n",
      "\n",
      "pdf = sp.stats.multivariate_normal((0, 0),np.identity(2) * sigma).pdf(np.array([x.ravel(), y.ravel()]).T)\n",
      "\n",
      "plt.imshow(pdf.reshape(x.shape), cmap=plt.cm.jet)\n",
      "plt.colorbar()\n",
      "\n",
      "_ = plt.xticks(np.arange(0, 50, 10), np.arange(5))\n",
      "_ = plt.yticks(np.arange(0, 50, 10), np.arange(5))\n",
      "\n",
      "\n",
      "plt.xlabel('Voxels')\n",
      "plt.ylabel('Voxels')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 176,
       "text": [
        "<matplotlib.text.Text at 0x10777ad0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ryeu51ZNeQ/m6ZNcKcG6A1OzMTLdHBTy3SFOWTV7Pje9cZaxnY4wnjV6rWKfA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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10652290>"
       ]
      }
     ],
     "prompt_number": 176
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Simulation for 3D case"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Create data with a center voxel with no signal"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.ones((15, 15, 15))\n",
      "data[8,8,8] = 0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 151
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have a 2x2x2mm smoothing kernel,"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigma2 = np.array([2., 2., 2.])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 152
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\sigma = \\frac{\\text{fwhm}}{2\\sqrt{2 \\text{ln} 2}}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigma2 /= 2 * np.sqrt(2 * np.log(2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 153
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On  a voxel resolution of 3.4 x 3.4 x 4.0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigma2 /= np.array([3.4, 3.4, 4.])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 154
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "FWHM = 8mm, for comparison"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sigma8 = np.array([8., 8., 8.])\n",
      "sigma8 /= 2 * np.sqrt(2 * np.log(2))\n",
      "sigma8 /= np.array([3.4, 3.4, 4.])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 155
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data_smoothed2 = sp.ndimage.filters.gaussian_filter(data, sigma2)\n",
      "data_smoothed8 = sp.ndimage.filters.gaussian_filter(data, sigma8)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 156
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(18,6))\n",
      "import seaborn as sns\n",
      "plt.subplot(131)\n",
      "plt.title('Unsmoothed data')\n",
      "plt.imshow(data[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)\n",
      "\n",
      "plt.axis('off')\n",
      "\n",
      "plt.subplot(132)\n",
      "plt.title('Smoothed data, fwhm=2mm')\n",
      "plt.imshow(data_smoothed2[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)\n",
      "plt.axis('off')\n",
      "\n",
      "plt.subplot(133)\n",
      "plt.title('Smoothed data, fwhm=8mm')\n",
      "plt.imshow(data_smoothed8[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)\n",
      "plt.axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 178,
       "text": [
        "(-0.5, 14.5, 14.5, -0.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10657e10>"
       ]
      }
     ],
     "prompt_number": 178
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data_smoothed2[8, 8, 8], data_smoothed8[8, 8, 8]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 167,
       "text": [
        "(0.0013539699944065712, 0.92512110239154466)"
       ]
      }
     ],
     "prompt_number": 167
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "After smoothing 2mm, only approximately 0.14% of the signal in the smoothed voxel does not originate from itself.\n",
      "\n",
      "For the 8mm smoothing this is 92%"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### FSL\n",
      "gives similar results"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from nipype.interfaces import fsl\n",
      "import nibabel as nb"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 198
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "affine = np.array([3.4, 3.4, 4., 1.]) * np.identity(4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 199
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nb.save(nb.Nifti1Image(data, affine), 'data.nii.gz')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 200
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "smooth = fsl.IsotropicSmooth()\n",
      "smooth.inputs.in_file = 'data.nii.gz'\n",
      "\n",
      "smooth.inputs.fwhm = 2.0\n",
      "smooth.inputs.out_file = 'data_2.nii.gz'\n",
      "r = smooth.run()\n",
      "\n",
      "smooth.inputs.fwhm = 8.0\n",
      "smooth.inputs.out_file = 'data_8.nii.gz'\n",
      "r = smooth.run()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 208
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(18,6))\n",
      "import seaborn as sns\n",
      "plt.subplot(131)\n",
      "plt.title('Unsmoothed data')\n",
      "plt.imshow(data[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)\n",
      "\n",
      "plt.axis('off')\n",
      "\n",
      "plt.subplot(132)\n",
      "plt.title('Smoothed data, FSL, fwhm=2mm')\n",
      "plt.imshow(nb.load('data_2.nii.gz').get_data()[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)\n",
      "plt.axis('off')\n",
      "\n",
      "plt.subplot(133)\n",
      "plt.title('Smoothed data, FSL, fwhm=8mm')\n",
      "plt.imshow(nb.load('data_8.nii.gz').get_data()[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)\n",
      "plt.axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 209,
       "text": [
        "(-0.5, 14.5, 14.5, -0.5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x122401d0>"
       ]
      }
     ],
     "prompt_number": 209
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nb.load('data_2.nii.gz').get_data()[8, 8, 8], nb.load('data_8.nii.gz').get_data()[8, 8, 8]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 211,
       "text": [
        "(0.001353923580609262, 0.92512232065200806)"
       ]
      }
     ],
     "prompt_number": 211
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Fun fact: FSL crashes for fwhm of 0. This makes it harder not-to-use smoothing for the casual fMRI analyst."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "smooth.inputs.fwhm = 0.0\n",
      "smooth.inputs.out_file = 'data_0.nii.gz'\n",
      "r = smooth.run()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 214
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.title('Smoothed data, FSL, fwhm=2mm')\n",
      "plt.imshow(nb.load('data_0.nii.gz').get_data()[:, 8, :], \n",
      "           vmin=0,\n",
      "           vmax=1,\n",
      "           interpolation='nearest', \n",
      "           cmap=plt.cm.jet_r)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 215,
       "text": [
        "<matplotlib.image.AxesImage at 0x125baf10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x125bae10>"
       ]
      }
     ],
     "prompt_number": 215
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Not-a-numbers:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "nb.load('data_0.nii.gz').get_data()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 216,
       "text": [
        "array([[[ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        ..., \n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],\n",
        "\n",
        "       [[ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        ..., \n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],\n",
        "\n",
        "       [[ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        ..., \n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],\n",
        "\n",
        "       ..., \n",
        "       [[ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        ..., \n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],\n",
        "\n",
        "       [[ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        ..., \n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan]],\n",
        "\n",
        "       [[ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        ..., \n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan],\n",
        "        [ nan,  nan,  nan, ...,  nan,  nan,  nan]]])"
       ]
      }
     ],
     "prompt_number": 216
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}