{
 "metadata": {
  "name": "random_fields"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Thresholding with random field theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can read this notebook without knowing any Python programming, by skipping over the code, but reading the code will often help understand the ideas.\n",
      "\n",
      "I based the notebook on my understanding of the 1992 paper by Keith Worsley (see refs below). For me, this paper is the most comprehensible paper on random fields in neuroimaging. Please refer to this paper and the Worsley 1996 paper for more detail.\n",
      "\n",
      "An earlier version of this notebook became the [Random fields introduction](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch14.pdf) chapter in the book [Human Brain Function second edition](http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Most statistics packages for functional imaging data create statistical parametric maps. These maps have a value for a certain statistic at each voxel in the brain, which is the result of the statistical test done on the scan data for that voxel, across scans.  $t$ values and $F$ values are the most common.\n",
      "\n",
      "For the sake of simplicity, I'll assume that we have $Z$ values instead of $t$ or $F$ values.  $Z$ values are values from the standard normal distribution.  The same sort of arguments apply to $t$ and $F$ values, just with slightly different formulae.\n",
      "\n",
      "The null hypothesis for a particular statistical comparison probably will be that there is no change anywhere in the brain. For example, in a comparison of activation against rest, the null hypothesis would be that there are no differences between the scans in the activation condition, and the scans in the rest condition. This null hypothesis implies that the whole brain volume full of statistic values for the comparison will be similar to a equivalent set of values from a random distribution."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The multiple comparison problem"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given we have a brain full of $Z$ values, how do we decide whether some of the $Z$ values are larger (more positive) than we would expect in a similar volume of random numbers?  So, in a typical brain volume, we have, say, 200000 voxels and therefore 200000 $Z$ scores. Because we have so many $Z$ scores, even if the null hypothesis is true, we can be confident that some of these $Z$ scores will appear to be significant at standard statistical thresholds for the the individual $Z$ scores. For example, $p$ value thresholds such as $p<0.05 $ or $p<0.01 $ correspond to $Z = 1.64 $ and $Z = 2.33 $ respectively."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats\n",
      "normal_distribution = scipy.stats.norm()\n",
      "# The inverse normal CDF\n",
      "inv_n_cdf = normal_distribution.ppf\n",
      "inv_n_cdf([0.95, 0.99])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "array([ 1.64485363,  2.32634787])"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, if we threshold our brain $Z$ scores at $2.33 $ or above, we would expect a number of false positives, even if the null hypothesis is true. So, how high should we set our $Z$ threshold, so that we can be confident that the remaining peak $Z$ scores are indeed too high to be expected by chance? This is the multiple comparison problem.\n",
      "\n",
      "We could call all the $Z$ scores in the brain a \"family\" of tests.  We want to find a threshold so that we can correct for a whole \"family\" of tests.  For this reason, these multiple comparison correction methods are often known as *family-wise* correction methods."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Why not a Bonferroni correction?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The problem of false positives with multiple statistical tests is an old one. One standard method for dealing with this problem is to use the Bonferroni correction. For the Bonferroni correction, you set your p value threshold for accepting a test as being significant as $alpha$ / (number of tests), where $alpha$ is the false positive rate you are prepared to accept. $alpha$ is often 0.05, or one false positive in 20 repeats of your experiment. Thus, for a statistical map with 200000 voxels, the Bonferroni corrected p value would be 0.05 / 200000 = [equivalent Z] 5.03. We could then threshold our Z map to show us only Z scores higher than 5.03, and be confident that all the remaining Z scores are unlikely to have occurred by chance. For some functional imaging data this is a perfectly reasonable approach, but in most cases the Bonferroni threshold will be considerably too conservative. This is because, for most stastistic maps, the Z scores at each voxel are highly correlated with their neighbours."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial correlation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Functional imaging data usually have some spatial correlation. By this, we mean that data in one voxel are correlated with the data from the neighbouring voxels. This correlation is caused by several factors: \n",
      "\n",
      "* With low resolution imaging such as PET, data from an individual voxel will contain some signal from the tissue around that voxel;\n",
      "* Unmodeled brain activation signal, which is very common, will tend to cover several voxels and induce correlations between them;\n",
      "* Resampling of the images during preprocessing causes some smoothing across voxels;\n",
      "* Most neuromaging statistical analyses work on smoothed images, and this creates strong spatial correlation. Smoothing is often used to improve signal to noise according to the matched filter theorem (the signal we are looking for is almost invariably spread across several voxels).\n",
      "\n",
      "The reason this spatial correlation is a problem for the Bonferroni correction is that the Bonferroni correction assumes that you have performed some number of *independent* tests. If the voxels are spatially correlated, then the $Z$ scores at each voxel are not independent. This will make the correction too conservative."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Spatial correlation and independent observations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "An example can show why the Bonferroni correction is too conservative with non-independent tests. Let us first make an example image out of random numbers. We generate 16384 random numbers, and then put them into a 128 by 128 array. This results in a 2D image of spatially independent random numbers. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.kernel.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Constants for image simulations etc\n",
      "shape = [128, 128] # No of pixels in X, Y\n",
      "n_voxels = np.prod(shape) # Total pixels\n",
      "s_fwhm = 8 # Smoothing in number of pixels in x, y\n",
      "seed = 1939 # Seed for random no generator\n",
      "alpha = 0.05 # Default alpha level\n",
      "\n",
      "# Image of independent random nos\n",
      "np.random.seed(seed) # Seed the generator to get same numbers each time\n",
      "test_img = np.random.standard_normal(shape)\n",
      "plt.figure()\n",
      "plt.imshow(test_img)\n",
      "plt.set_cmap('bone')\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Image 1 - array of independent random numbers')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x47b6950>"
       ]
      },
      {
       "output_type": "display_data",
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Go8ETn/hEnv70p9/hmiuvvJKbbrrpHgfuBz/4QU6ePMnCwgI/9VM/xZvf/Gae9rSnTd97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//f7D919b34+N7eZ54//st0kj0UxlcdbEnUlztShyHrzyiMNHR6iNIr4X97i7mvD+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w9+4QOKrOTu9R3D6RC/77G4XhLvYnlDdl36hwMG4z5+zyMKYpnGDbuE25DrlzdQN7gdl91i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\nA2QkK9VvRgfQAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x376f210>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this picture, whiter pixels are more positive, darker pixels more negative. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Bonferroni correction is the right one for this image, because the image is made up of 128*128 = 16384 random numbers from a normal distribution. Therefore, from the Bonferroni correction ($\\alpha / N = 0.05 / 16384$ = [Z equivalent] 4.52), we would expect only 5 out of 100 such images to have one or more random numbers in the whole image larger than 4.52."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Bonferroni threshold for this image\n",
      "bonf_thresh = inv_n_cdf(1 - (alpha / n_voxels))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The situation changes if we add some spatial correlation to this image. We can take our image above, and perform the following procedure:\n",
      "\n",
      "* Break up the image into 8 by 8 squares;\n",
      "* For each square, calculate the mean of all 64 random numbers in the square;\n",
      "* Replace the 64 random numbers in the square by the mean value.\n",
      "\n",
      "(In fact, we have one more thing to do to our new image values. When we take the mean of 64 random numbers, this mean will tend to zero. We have therefore to multiply our mean numbers by 8 to restore a variance of 1. This will make the numbers correspond to the normal distribution again).\n",
      "\n",
      "The following is the image that results from the procedure above applied to our first set of random numbers:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Divide into FWHM chunks and fill square from mean value\n",
      "sqmean_img = test_img.copy()\n",
      "tarr = np.ones((s_fwhm, s_fwhm)) * s_fwhm # mutliply up to unit variance\n",
      "for i in range(0, shape[0], s_fwhm):\n",
      "    i_slice = slice(i, i+s_fwhm)\n",
      "    for j in range(0, shape[1], s_fwhm):\n",
      "        j_slice = slice(j, j+s_fwhm)\n",
      "        vals = sqmean_img[i_slice, j_slice]\n",
      "        sqmean_img[i_slice, j_slice] = tarr * vals.mean()\n",
      "plt.figure()\n",
      "plt.imshow(sqmean_img)\n",
      "plt.set_cmap('bone')\n",
      "# axis xy\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Taking means over %s by %s elements from image 1' % (s_fwhm, s_fwhm))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<matplotlib.text.Text at 0x4915f50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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BJ9kNi9XCZKdGVNTVNMLQ2S4apxXJeX0IM0ZyGanJSElOQG5uRrvajSX4M7lT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\nTzAFsQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4795b90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We still have 16384 numbers in our image. However, it is clear that we now have only (128 / 8) * (128 / 8) = 256 independent numbers. The appropriate Bonferroni correction would then be ($\\alpha / N$ = 0.05 / 256 = [$Z$ equivalent] 3.55). We would expect that if we took 100 such mean-by-square-processed random number images, then only 5 of the 100 would have a square of values greater than 3.55 by chance. However, if we took the original Bonferroni correction for the number of pixels rather than the number of independent pixels, then our $Z$ threshold would be far too conservative."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Smoothed images and independent observations"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The mean-by-square process we have used above is a form of smoothing. In the mean-by-square case, the averaging takes place only within the squares, but in the case of smoothing with a smoothing kernel, the averaging takes place in a continuous way across the image. We can smooth our first random number image with a Gaussian kernel of FWHM 8 by 8 pixels.  (As for the mean-by-square example, the smoothing reduces the variance of the numbers in the image, because an average of random numbers tends to zero. In order to return the variance of the numbers in the image to one, to match the normal distribution, the image must be multiplied by a scale factor. The derivation of this scaling factor is rather technical, and not relevant to the discussion here)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# smooth random number image\n",
      "import scipy.ndimage as spn\n",
      "sd = s_fwhm / np.sqrt(8.*np.log(2)) # sigma for this FWHM\n",
      "stest_img = spn.filters.gaussian_filter(test_img, sd, mode='wrap')\n",
      "\n",
      "def gauss_2d_varscale(sigma):\n",
      "    \"\"\" Return variance scaling for smoothing with 2D Gaussian of sigma `sigma`\n",
      "\n",
      "    The code in this function isn't important for understanding the rest of the tutorial\n",
      "    \"\"\"\n",
      "    # Make a single 2D Gaussian using given sigma\n",
      "    limit = sigma * 5 # go to limits where Gaussian will be at or near 0\n",
      "    x_inds = np.arange(-limit, limit+1)\n",
      "    y_inds = x_inds # Symmetrical Gaussian (sd same in X and Y)\n",
      "    [x,y] = np.meshgrid(y_inds, x_inds)\n",
      "    # http://en.wikipedia.org/wiki/Gaussian_function#Two-dimensional_Gaussian_function\n",
      "    gf    = np.exp(-(x*x + y*y) / (2 * sigma ** 2))\n",
      "    gf    = gf/np.sum(gf)\n",
      "    # Expectation of variance for this kernel\n",
      "    AG    = np.fft.fft2(gf)\n",
      "    Pag   = AG * np.conj(AG) # Power of the noise\n",
      "    COV   = np.real(np.fft.ifft2(Pag))\n",
      "    return COV[0, 0]\n",
      "\n",
      "# Restore smoothed image to unit variance\n",
      "svar = gauss_2d_varscale(sd)\n",
      "scf = np.sqrt(1 / svar)\n",
      "stest_img = stest_img * scf\n",
      "\n",
      "# display smoothed image\n",
      "plt.figure()\n",
      "plt.imshow(stest_img)\n",
      "plt.set_cmap('bone')\n",
      "# axis xy\n",
      "plt.xlabel('Pixel position in X')\n",
      "plt.ylabel('Pixel position in Y')\n",
      "plt.title('Image 1 - smoothed with Gaussian kernel of FWHM %s by %s pixels' %\n",
      "          (s_fwhm, s_fwhm))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "<matplotlib.text.Text at 0x4e0f150>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HZQ8M6nrH6U+AQgTv4+ednni8NQhUd4FkqKQLJBsor3/96/HHP/4RixcvxpQp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XSJlu8GEDCDnoFkoLnCqK5XGFsxGKbQAQwoEaFP+k5OwAGdKhny4dguP86UDHUh95KtcWKdxiLQ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\ngvwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x376f0d0>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In our smoothed image, as for the mean-by-square image, we no longer have 16384 independent observations, but some smaller number, because of the averaging across pixels. If we knew how many independent observations there were, we could use a Bonferroni correction as we did for the mean-by-square example. Unfortunately it is not easy to work out how many independent observations there are in a smoothed image. So, we must take a different approach to determine our $Z$ score threshold. One approach used by ``SPM`` and other packages is to use Random Field Theory (RFT)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Using random field theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can think of the application of RFT as proceeding in three steps. First, you determine how many resels there are in your image. Then you use the resel count and some sophisticated maths to work out the expected *Euler characteristic* (EC) of your image, when it is thresholded at various levels. These expected ECs can be used to give the correct threshold for the required control of false positives ($\\alpha$)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What is a resel?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A resel is a \"resolution element\". The number of resels in an image is similar to the number of independent observations in the image. However, they are not the same, as we will see below. A resel is defined as a block of pixels of the same size as the FWHM of the smoothness of the image. In our smoothed image above, the smoothness of the image is 8 pixels by 8 pixels (the smoothing that we applied). A resel is therefore a 8 by 8 pixel block, and the number of resels in our image is (128 / 8) * (128 / 8) = 256. Note that the number of resels depends only on the number of pixels, and the FWHM."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# No of resels\n",
      "resels = np.prod(np.divide(shape, s_fwhm))\n",
      "resels"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "256"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What is the Euler characteristic?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Euler characteristic of an image is a property of the image after it has been thresholded. For our purposes, the EC can be thought of as the number of blobs in an image after it has been thresholded. This is best explained by example. Let us take our smoothed image, and threshold it at $Z > 2.75$. This means we set to zero all the pixels with $Z$ scores less than or equal to 2.75, and set to one all the pixels with $Z$ scores greater than 2.75."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We make a function to show the thresholded image:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def show_threshed(img, th):\n",
      "    thimg = (img > th)\n",
      "    plt.figure()\n",
      "    plt.imshow(thimg)\n",
      "    plt.set_cmap('bone')\n",
      "    # axis xy\n",
      "    plt.xlabel('Pixel position in X')\n",
      "    plt.ylabel('Pixel position in Y')\n",
      "    plt.title('Smoothed image thresholded at Z > %s' % th)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# threshold at 2.75 and display\n",
      "show_threshed(stest_img, 2.75)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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wxkTR7DnzHTt2QCKRNLmfJ5FIMHHixHYtjDHWuTUbPrt3727xIC+HD2OsLfhs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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x47ad090>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Zero in the image displays as black and one as white.  In this picture, there are some blobs, corresponding to areas with $Z$ scores higher than 2.75. The EC of this image is just the number of blobs. If we increase the threshold to $3.25$, we find that some of the blobs disappear (the highest $Z$ values at the blob peaks were less than 3.25)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# threshold at 3.25 and display\n",
      "show_threshed(stest_img, 3.25)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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e3t7eUKlU0NPrMGfb7DnGv4Wd2P/8z//g/v37UCqVSEhIQFhYGAcP6zA61G/irl274O7u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\nxP8C3G8awb7mmAwAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4bbf410>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One blob remains; the EC of the image above is therefore 1. It turns out that if we know the number of resels in our image, it is possible to estimate the most likely value of the EC at any given threshold. The formula for this estimate, for two dimensions, is on page 906 of Worsley 1992, implemented below. The graph shows the expected EC of our smoothed image, of 256 resels, when thresholded at different $Z$ values."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# expected EC at various Z thresholds, for two dimensions\n",
      "plt.figure()\n",
      "Z = np.linspace(0, 5, 1000)\n",
      "\n",
      "def expected_ec_2d(z, resel_count):\n",
      "    # From Worsley 1992\n",
      "    z = np.asarray(z)\n",
      "    return (resel_count * (4 * np.log(2)) * ((2*np.pi)**(-3./2)) * z) * np.exp((z ** 2)*(-0.5))\n",
      "\n",
      "expEC = expected_ec_2d(Z, resels)\n",
      "plt.plot(Z, expEC)\n",
      "plt.xlabel('Z score threshold')\n",
      "plt.ylabel('Expected EC for thresholded image')\n",
      "plt.title('Expected EC for smoothed image with %s resels' % resels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.text.Text at 0x7f7bb4067e90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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pX7+uzc2emKi1GEXxNXcubNoE69bpnUQI21Tocfp+fn7Ur1+fc+fO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\nhBB2RIq+EELYESn6QghhR6ToCyGEHfl/NKchFzO3VvoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4bc2210>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the graph does a reasonable job of predicting the EC in our image; at $Z = 2.75$ threshold it predicted an EC of 2.8, and at a $Z = 3.25 $ it predicted an EC of 0.74"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "expected_ec_2d([2.75, 3.25], resels)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([ 2.82495998,  0.74493991])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "How does the Euler characteristic give a Z threshold?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The useful feature of the expected EC is this: when the $Z$ thresholds become high and the predicted EC drops towards zero, the expected EC is a good approximation of the probability of observing one or more blobs at that threshold. So, in the graph above, when the $Z$ threshold is set to 4, the expected EC is 0.06. This can be rephrased thus: the probability of getting one or more regions where $Z$ is greater than 4, in a 2D image with 256 resels, is 0.06. So, we can use this for thresholding. If $x$ is the $Z$ score threshold that gives an expected EC of 0.05, then, if we threshold our image at $x$, we can expect that any blobs that remain have a probability of less than or equal to 0.05 that they have occurred by chance.  The threshold $x$ depends only on the number of resels in our image."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Is the threshold accurate?  Show me!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can test the treshold with a simulation:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# simulation to test the RFT threshold.\n",
      "# find approx threshold from the vector above. We're trying to find the Z value for which the expected EC is 0.05\n",
      "tmp = (Z > 3) & (expEC<=alpha)\n",
      "alphaTH = Z[tmp][0]\n",
      "print('Using Z threshold of %f' % alphaTH)\n",
      "\n",
      "# Make lots of smoothed images and find how many have one or more blobs above threshold\n",
      "repeats = 1000\n",
      "falsepos = np.zeros((repeats,))\n",
      "maxes = np.zeros((repeats,))\n",
      "edgepix = s_fwhm  # to add edges to image - see below\n",
      "big_size = [s + edgepix * 2 for s in shape]\n",
      "i_slice = slice(edgepix + 1, shape[0] + edgepix + 1)\n",
      "j_slice = slice(edgepix + 1, shape[1] + edgepix + 1)\n",
      "for i in range(repeats):\n",
      "    timg = np.random.standard_normal(size=big_size) # gives extra edges to throw away\n",
      "    stimg = spn.filters.gaussian_filter(timg, sd, mode='wrap')\n",
      "    # throw away edges to avoid artefactually high values\n",
      "    # at image edges generated by the smoothing\n",
      "    stimg = stimg[i_slice, j_slice]\n",
      "    # Reset variance using scale factor from calculation above\n",
      "    stimg *= scf\n",
      "    falsepos[i] = np.any(stimg >= alphaTH)\n",
      "    maxes[i] = stimg.max()\n",
      "print('False positive rate in simulation was %s (%s expected)' %\n",
      "      (sum(falsepos) / float(repeats), alpha))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Using Z threshold of 4.054054\n",
        "False positive rate in simulation was 0.049 (0.05 expected)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "How does the random field correction compare to the Bonferroni correction?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I stated above that the resel count in an image is not exactly the same as the number of independent observations. If it was the same, then instead of using RFT for the expected EC, we could use a Bonferroni correction for the number of resels. However, these two corrections give different answers. Thus, for an alpha of 0.05, the $Z$ threshold according to RFT, for our 256 resel image, is $Z=4.05$. However, the Bonferroni threshold, for 256 independent tests, is 0.05/256 = [$Z$ equivalent] 3.55. So, although the RFT maths gives us a Bonferroni-like correction, it is not the same as a Bonferroni correction. As you can see from the simulation above, the random field correction gives a threshold very close the the observed value for a sequence of smoothed images. A Bonferroni correction with the resel count gives a much lower threshold and would therefore be way off the correct threshold for 0.05 false positive rate."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "To three dimensions"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Exactly the same principles apply to a smoothed random number image in three dimensions. In this case, the EC is the number of 3D blobs - perhaps \"globules\" - of $Z$ scores above a certain threshold. Pixels might better be described as voxels (pixels with volume). The resels are now in 3D, and one resel is a cube of voxels that is of size (FWHM in x) by (FWHM in y) by (FWHM in z). The formula for the expected EC is different in the 3D case, but still depends only on the resels in the image. If we find the threshold giving an expected EC of 0.05, in 3D, we have a threshold above which we can expect that any remaining $Z$ scores are unlikely to have occurred by chance, with a $p<0.05$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "More sophisticated random fielding"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Random fields and search volumes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I oversimplified when I said above that the expected EC depends only on the number of resels in the image. In fact, this is an approximation, which works well when the volume that we are looking at has a reasonable number of resels. This is true for our two dimensional example, where the FWHM was 8 and our image was 128 by 128. However, the precise EC depends not only on the number of resels, but the shape of the volume in which the resels are contained. It is possible to derive a formula for the expected EC, based on the number of resels in the area we are thresholding, and the shape of the area (see Worsley 1996). This formula is more precise than the formula taking account of the number of resels alone. When the area to be thresholded is large, compared to the FWHM, as is the case when we are thresholding the whole brain, the two formulae give very similar results. However, when the volume for thresholding is small, the formulae give different results, and the shape of the area must be taken into account. This is the case when you require a threshold for a small volume, such as a region of interest."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "t and F statistic volumes"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Keith Worsley's 1996 paper gives the random field formulae for $t$ and $F$ statistics.   ``SPM`` and other imaging packages generate $t$ and $F$ statistics maps. They use the random fields formulae for $t$, $F$ to work out the corrected (family-wise) error rate at each $t$, $F$ value."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Estimated instead of assumed smoothness"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`SPM` and other packages also *estimate* how smooth the images are, rather than assuming the smoothness as we have done here. `SPM` in particular looks at the the residuals from the statistical analysis to calculate the smoothness of the image, in terms of FWHM. From these calculations it derives estimates for the FWHM in x, y and z. Other than this, the corrected statistics are calculated just as described above."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "A brain activation example in SPM"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is an `SPM8` results printout for a first level FMRI analysis."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Display some saved SPM results output\n",
      "from IPython.core.display import SVG\n",
      "SVG(filename='spm_t_results.svg')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "prompt_number": 14,
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        "<text id=\"text3078\" transform=\"matrix(1,0,0,-1,306.4168,570.25)\"><tspan id=\"tspan3080\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0\" y=\"0\">}</tspan><tspan id=\"tspan3082\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"-40.8336 -31.9376 -26.6096 -22.1616 -7.9376 0.9584 10.7344 16.9584\" y=\"-179.084\">stim_hrf</tspan></text>\n",
        "</g><g id=\"g3084\" transform=\"scale(10,10)\"><text id=\"text3086\" transform=\"matrix(1,0,0,-1,68.4168,479.75)\"><tspan id=\"tspan3088\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:16;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0 10.672 21.344 34.672 40.896 49.792 58.688 68.464 72.912 78.24 87.136\" y=\"0\">SPMresults:</tspan></text>\n",
        "<text id=\"text3090\" transform=\"matrix(1,0,0,-1,155.5,479.75)\"><tspan id=\"tspan3092\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 2.78 5.56 10.56 16.12 21.12 26.12 31.68 34.46 41.13 47.8 56.13 61.69 67.25 72.81 78.37\" y=\"0\">./sess1/SPM8_ana</tspan><tspan id=\"tspan3094\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"-87.0832 -79.8632 -74.3032 -72.0832 -66.5232 -60.9632 -58.1832 -55.4032 -52.6232 -47.0632 -43.7332 -38.1732 -33.1732 -27.6132 -22.0532 -19.8332 -14.2732 -11.4932 -5.3832 -2.6032 3.2368 6.0168 11.5768 14.3568 19.9168 25.4768 31.0368 36.5968 42.1568 47.7168 53.2768 56.6168 62.1768 68.0168 73.5768 76.3568 81.9168 87.4768 93.0368 95.8168 99.1468 104.7068 110.2668 115.2668 118.0468 121.3768\" y=\"11.6664\">Height threshold T = 3.162616 {p&lt;0.001 (unc.)}</tspan><tspan id=\"tspan3096\" sodipodi:role=\"line\" style=\"fill:#b2b2b2;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"-87.0832 -80.4132 -75.4132 -72.6332 -67.0732 -61.5132 -58.7332 -55.9532 -53.1732 -47.6132 -44.2832 -38.7232 -33.7232 -28.1632 -22.6032 -20.3832 -14.8232 -12.0432 -7.0432 -4.2632 1.5768 4.3568 9.9168 12.6968 17.6968 23.2568 28.2568 33.8168 36.0368\" y=\"23.4164\">Extent threshold k = 0 voxels</tspan></text>\n",
        "</g><path d=\"m 3734.17,4563.33 1270.83,0 0,1831.67 -1270.83,0 0,-1831.67 z\" id=\"path3098\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6395 0,-1831.67 1270.83,0 0,1831.67 -1270.83,0\" id=\"path3100\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3102\"><g clip-path=\"url(#clipPath3106)\" id=\"g3104\"><g id=\"g3110\" transform=\"matrix(1270.83,0,0,1831.67,3734.17,4563.33)\"><image height=\"1\" id=\"image3112\" transform=\"matrix(1,0,0,-1,0,1)\" width=\"1\" xlink:href=\"data:image/png;base64,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\"/></g></g></g><g id=\"g3114\"><g clip-path=\"url(#clipPath3118)\" id=\"g3116\"><g id=\"g3122\" transform=\"scale(10,10)\"><text id=\"text3124\" transform=\"matrix(1,0,0,-1,406.167,432.334)\"><tspan id=\"tspan3126\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 7.22 12.78 17.78 20 25.56 31.12 33.9 42.23 47.79 50.57 53.9 56.12\" y=\"0\">Design matrix</tspan></text>\n",
        "</g><path d=\"M 3734.17,6395 5005,6395\" id=\"path3128\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3130\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3132\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6395 0,-1831.66\" id=\"path3134\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3136\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3138\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,4563.34 0,18.33\" id=\"path3140\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,6395 0,-17.5\" id=\"path3142\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3144\" transform=\"scale(10,10)\"><text id=\"text3146\" transform=\"matrix(1,0,0,-1,391.833,444.25)\"><tspan id=\"tspan3148\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 4369.17,4563.34 0,18.33\" id=\"path3150\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4369.17,6395 0,-17.5\" id=\"path3152\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3154\" transform=\"scale(10,10)\"><text id=\"text3156\" transform=\"matrix(1,0,0,-1,434.167,444.25)\"><tspan id=\"tspan3158\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">2</tspan></text>\n",
        "</g><path d=\"m 4792.5,4563.34 0,18.33\" id=\"path3160\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4792.5,6395 0,-17.5\" id=\"path3162\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3164\" transform=\"scale(10,10)\"><text id=\"text3166\" transform=\"matrix(1,0,0,-1,476.5,444.25)\"><tspan id=\"tspan3168\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">3</tspan></text>\n",
        "</g><path d=\"m 3734.17,6111.67 17.5,0\" id=\"path3170\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6111.67 -18.33,0\" id=\"path3172\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3174\" transform=\"scale(10,10)\"><text id=\"text3176\" transform=\"matrix(1,0,0,-1,359.417,607.5)\"><tspan id=\"tspan3178\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">20</tspan></text>\n",
        "</g><path d=\"m 3734.17,5820.84 17.5,0\" id=\"path3180\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5820.84 -18.33,0\" id=\"path3182\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3184\" transform=\"scale(10,10)\"><text id=\"text3186\" transform=\"matrix(1,0,0,-1,359.417,578.417)\"><tspan id=\"tspan3188\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">40</tspan></text>\n",
        "</g><path d=\"m 3734.17,5530.84 17.5,0\" id=\"path3190\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5530.84 -18.33,0\" id=\"path3192\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3194\" transform=\"scale(10,10)\"><text id=\"text3196\" transform=\"matrix(1,0,0,-1,359.417,549.417)\"><tspan id=\"tspan3198\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">60</tspan></text>\n",
        "</g><path d=\"m 3734.17,5240 17.5,0\" id=\"path3200\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,5240 -18.33,0\" id=\"path3202\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3204\" transform=\"scale(10,10)\"><text id=\"text3206\" transform=\"matrix(1,0,0,-1,359.417,520.334)\"><tspan id=\"tspan3208\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">80</tspan></text>\n",
        "</g><path d=\"m 3734.17,4949.17 17.5,0\" id=\"path3210\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,4949.17 -18.33,0\" id=\"path3212\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3214\" transform=\"scale(10,10)\"><text id=\"text3216\" transform=\"matrix(1,0,0,-1,353.833,491.25)\"><tspan id=\"tspan3218\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">100</tspan></text>\n",
        "</g><path d=\"m 3734.17,4658.34 17.5,0\" id=\"path3220\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,4658.34 -18.33,0\" id=\"path3222\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3224\" transform=\"scale(10,10)\"><text id=\"text3226\" transform=\"matrix(1,0,0,-1,353.833,462.167)\"><tspan id=\"tspan3228\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">120</tspan></text>\n",
        "</g><path d=\"M 3734.17,6395 5005,6395\" id=\"path3230\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,4563.34 1270.83,0\" id=\"path3232\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6395 0,-1831.66\" id=\"path3234\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 5005,6395 0,-1831.66\" id=\"path3236\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3238\" transform=\"scale(10,10)\"><text id=\"text3240\" transform=\"matrix(1,0,0,-1,413.333,702.334)\"><tspan id=\"tspan3242\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 10.56 16.12 18.9 22.23 27.79 32.79 35.57 38.9 43.9\" y=\"0\">contrast(s)</tspan></text>\n",
        "</g><path d=\"m 3734.17,6450 1270.83,0 0,494.168 -1270.83,0 0,-494.168 z\" id=\"path3244\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6450 0,494.17 1270.83,0 0,-494.17 -1270.83,0\" id=\"path3246\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"M 3734.17,6450 5005,6450\" id=\"path3248\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6450 0,494.17\" id=\"path3250\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3945.83,6450 0,-12.5\" id=\"path3252\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4369.17,6450 0,-12.5\" id=\"path3254\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4792.5,6450 0,-12.5\" id=\"path3256\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6491.67 -13.34,0\" id=\"path3258\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 3734.17,6903.34 -13.34,0\" id=\"path3260\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3262\"><g clip-path=\"url(#clipPath3266)\" id=\"g3264\"><path d=\"m 3734.17,6491.67 423.332,0 0,411.664 -423.332,0 0,-411.664 z\" id=\"path3270\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 3734.17,6491.67 0,411.66 423.33,0 0,-411.66 -423.33,0\" id=\"path3272\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4157.5,6491.67 423.332,0 0,0 -423.332,0 z\" id=\"path3274\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 4157.5,6491.67 423.33,0 -423.33,0\" id=\"path3276\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 4580.83,6491.67 424.168,0 0,0 -424.168,0 z\" id=\"path3278\" style=\"fill:#808080;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 4580.83,6491.67 424.17,0 -424.17,0\" id=\"path3280\" style=\"fill:none;stroke:#000000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3282\"><g clip-path=\"url(#clipPath3286)\" id=\"g3284\"><g id=\"g3290\" transform=\"scale(10,10)\"><text id=\"text3292\" transform=\"matrix(0,1,1,0,362.417,666.917)\"><tspan id=\"tspan3294\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 557.5,1267.5 4574.17,0 0,2930 -4574.17,0 0,-2930 z\" id=\"path3296\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:evenodd;stroke:none\"/><path d=\"m 557.5,1267.5 0,2930 4574.17,0 0,-2930 -4574.17,0\" id=\"path3298\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 4574.17,0\" id=\"path3300\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 0,2930\" id=\"path3302\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><path d=\"m 557.5,1267.5 0,45.83\" id=\"path3304\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3306\" transform=\"scale(10,10)\"><text id=\"text3308\" transform=\"matrix(1,0,0,-1,53,114.667)\"><tspan id=\"tspan3310\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">0</tspan></text>\n",
        "</g><path d=\"m 1014.17,1267.5 0,45.83\" id=\"path3312\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3314\" transform=\"scale(10,10)\"><text id=\"text3316\" transform=\"matrix(1,0,0,-1,94.5,114.667)\"><tspan id=\"tspan3318\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.1</tspan></text>\n",
        "</g><path d=\"m 1471.67,1267.5 0,45.83\" id=\"path3320\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3322\" transform=\"scale(10,10)\"><text id=\"text3324\" transform=\"matrix(1,0,0,-1,140.25,114.667)\"><tspan id=\"tspan3326\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.2</tspan></text>\n",
        "</g><path d=\"m 1929.17,1267.5 0,45.83\" id=\"path3328\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3330\" transform=\"scale(10,10)\"><text id=\"text3332\" transform=\"matrix(1,0,0,-1,186,114.667)\"><tspan id=\"tspan3334\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.3</tspan></text>\n",
        "</g><path d=\"m 2386.67,1267.5 0,45.83\" id=\"path3336\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3338\" transform=\"scale(10,10)\"><text id=\"text3340\" transform=\"matrix(1,0,0,-1,231.75,114.667)\"><tspan id=\"tspan3342\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.4</tspan></text>\n",
        "</g><path d=\"m 2844.17,1267.5 0,45.83\" id=\"path3344\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3346\" transform=\"scale(10,10)\"><text id=\"text3348\" transform=\"matrix(1,0,0,-1,277.5,114.667)\"><tspan id=\"tspan3350\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.5</tspan></text>\n",
        "</g><path d=\"m 3301.67,1267.5 0,45.83\" id=\"path3352\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3354\" transform=\"scale(10,10)\"><text id=\"text3356\" transform=\"matrix(1,0,0,-1,323.25,114.667)\"><tspan id=\"tspan3358\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.6</tspan></text>\n",
        "</g><path d=\"m 3759.17,1267.5 0,45.83\" id=\"path3360\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3362\" transform=\"scale(10,10)\"><text id=\"text3364\" transform=\"matrix(1,0,0,-1,369,114.667)\"><tspan id=\"tspan3366\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.7</tspan></text>\n",
        "</g><path d=\"m 4216.67,1267.5 0,45.83\" id=\"path3368\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3370\" transform=\"scale(10,10)\"><text id=\"text3372\" transform=\"matrix(1,0,0,-1,414.75,114.667)\"><tspan id=\"tspan3374\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.8</tspan></text>\n",
        "</g><path d=\"m 4674.17,1267.5 0,45.83\" id=\"path3376\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3378\" transform=\"scale(10,10)\"><text id=\"text3380\" transform=\"matrix(1,0,0,-1,460.5,114.667)\"><tspan id=\"tspan3382\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 8.34\" y=\"0\">0.9</tspan></text>\n",
        "</g><path d=\"m 5131.67,1267.5 0,45.83\" id=\"path3384\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3386\" transform=\"scale(10,10)\"><text id=\"text3388\" transform=\"matrix(1,0,0,-1,510.417,114.667)\"><tspan id=\"tspan3390\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">1</tspan></text>\n",
        "</g><path d=\"m 557.5,1267.5 45,0\" id=\"path3392\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3394\" transform=\"scale(10,10)\"><text id=\"text3396\" transform=\"matrix(1,0,0,-1,47.3332,123.083)\"><tspan id=\"tspan3398\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">0</tspan></text>\n",
        "</g><path d=\"m 557.5,1754.17 45,0\" id=\"path3400\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3402\" transform=\"scale(10,10)\"><text id=\"text3404\" transform=\"matrix(1,0,0,-1,41.75,171.75)\"><tspan id=\"tspan3406\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56\" y=\"0\">50</tspan></text>\n",
        "</g><path d=\"m 557.5,2240.83 45,0\" id=\"path3408\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3410\" transform=\"scale(10,10)\"><text id=\"text3412\" transform=\"matrix(1,0,0,-1,36.1668,220.417)\"><tspan id=\"tspan3414\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">100</tspan></text>\n",
        "</g><path d=\"m 557.5,2727.5 45,0\" id=\"path3416\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3418\" transform=\"scale(10,10)\"><text id=\"text3420\" transform=\"matrix(1,0,0,-1,36.1668,269.083)\"><tspan id=\"tspan3422\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">150</tspan></text>\n",
        "</g><path d=\"m 557.5,3214.17 45,0\" id=\"path3424\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3426\" transform=\"scale(10,10)\"><text id=\"text3428\" transform=\"matrix(1,0,0,-1,36.1668,317.75)\"><tspan id=\"tspan3430\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">200</tspan></text>\n",
        "</g><path d=\"m 557.5,3700.83 45,0\" id=\"path3432\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3434\" transform=\"scale(10,10)\"><text id=\"text3436\" transform=\"matrix(1,0,0,-1,36.1668,366.417)\"><tspan id=\"tspan3438\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">250</tspan></text>\n",
        "</g><path d=\"m 557.5,4186.67 45,0\" id=\"path3440\" style=\"fill:none;stroke:#ffffff;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/><g id=\"g3442\" transform=\"scale(10,10)\"><text id=\"text3444\" transform=\"matrix(1,0,0,-1,36.1668,415)\"><tspan id=\"tspan3446\" sodipodi:role=\"line\" style=\"fill:#ffffff;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12\" y=\"0\">300</tspan></text>\n",
        "</g><g id=\"g3448\" transform=\"scale(10,10)\"><text id=\"text3450\" transform=\"matrix(1,0,0,-1,55.75,409.917)\"><tspan id=\"tspan3452\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:bold;font-size:12;writing-mode:lr;-inkscape-font-specification:Helvetica-Bold\" x=\"0 8.004 12 18.672 22.668 26.004 32.676 36.672 40.008 46.68 53.352 57.348\" y=\"0\">Statistics: </tspan></text>\n",
        "<text id=\"text3454\" transform=\"matrix(1,0,0,-1,119.25,409.917)\"><tspan id=\"tspan3456\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-weight:bold;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica-BoldOblique\" x=\"0 6.11 11.95 17.51 23.07 25.85 31.96 37.52 43.08 45.86 51.42 57.53 60.31 66.42 71.98 75.31 80.87 86.98 89.76 93.09 99.2 103.09 105.87 111.43 116.99 122.55 126.44 132 138.11 140.89 146.45 152.56 155.34 161.45 170.34\" y=\"0\">p\u2212values adjusted for search volume</tspan></text>\n",
        "</g></g></g><g id=\"g3458\"><g clip-path=\"url(#clipPath3462)\" id=\"g3460\"><path d=\"m 557.5,4050.83 4574.17,0\" id=\"path3466\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:30;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3468\"><g clip-path=\"url(#clipPath3472)\" id=\"g3470\"><g id=\"g3476\" transform=\"scale(10,10)\"><text id=\"text3478\" transform=\"matrix(1,0,0,-1,60.25,394.167)\"><tspan id=\"tspan3480\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 10.56 13.34 19.18 21.4 26.96 31.96 37.52\" y=\"0\">set\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3482\"><g clip-path=\"url(#clipPath3486)\" id=\"g3484\"><path d=\"m 557.5,3916.67 502.5,0\" id=\"path3490\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3492\"><g clip-path=\"url(#clipPath3496)\" id=\"g3494\"><g id=\"g3500\" transform=\"scale(10,10)\"><text id=\"text3502\" transform=\"matrix(1,0,0,-1,92.3332,383.167)\"><tspan id=\"tspan3504\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0 4.5 -27.5 -22.496\" y=\"0\">c p </tspan></text>\n",
        "<text id=\"text3506\" transform=\"matrix(1,0,0,-1,156.3332,394.167)\"><tspan id=\"tspan3508\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5 7.22 12.78 17.78 20.56 26.12 29.45 35.29 37.51 43.07 48.07 53.63\" y=\"0\">cluster\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3510\"><g clip-path=\"url(#clipPath3514)\" id=\"g3512\"><path d=\"m 1197.5,3916.67 1372.5,0\" id=\"path3518\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3520\"><g clip-path=\"url(#clipPath3524)\" id=\"g3522\"><g id=\"g3528\" transform=\"scale(10,10)\"><text id=\"text3530\" transform=\"matrix(1,0,0,-1,124.333,383.167)\"><tspan id=\"tspan3532\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3534\" transform=\"matrix(1,0,0,-1,129.333,378.667)\"><tspan id=\"tspan3536\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 10.885 15.554 19.642 23.142 27.034 29.365\" y=\"0\">FWE\u2212corr</tspan></text>\n",
        "<text id=\"text3538\" transform=\"matrix(1,0,0,-1,165.4998,383.167)\"><tspan id=\"tspan3540\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">q</tspan></text>\n",
        "<text id=\"text3542\" transform=\"matrix(1,0,0,-1,170.4998,378.667)\"><tspan id=\"tspan3544\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 9.331 14.385 18.473 21.973 25.865 28.196\" y=\"0\">FDR\u2212corr</tspan></text>\n",
        "<text id=\"text3546\" transform=\"matrix(1,0,0,-1,234.083,383.167)\"><tspan id=\"tspan3548\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3550\" transform=\"matrix(1,0,0,-1,239.083,378.667)\"><tspan id=\"tspan3552\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 3.892 7.784 11.284 15.176 17.507\" y=\"0\">uncorr</tspan></text>\n",
        "<text id=\"text3554\" transform=\"matrix(1,0,0,-1,211.2498,383.167)\"><tspan id=\"tspan3556\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">k</tspan></text>\n",
        "<text id=\"text3558\" transform=\"matrix(1,0,0,-1,215.7498,378.667)\"><tspan id=\"tspan3560\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">E</tspan></text>\n",
        "<text id=\"text3562\" transform=\"matrix(1,0,0,-1,348.4168,394.167)\"><tspan id=\"tspan3564\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:10;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.56 11.12 16.68 21.68 27.52 29.74 35.3 40.3 45.86\" y=\"0\">peak\u2212level</tspan></text>\n",
        "</g></g></g><g id=\"g3566\"><g clip-path=\"url(#clipPath3570)\" id=\"g3568\"><path d=\"m 2752.5,3916.67 1830,0\" id=\"path3574\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:5;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3576\"><g clip-path=\"url(#clipPath3580)\" id=\"g3578\"><g id=\"g3584\" transform=\"scale(10,10)\"><text id=\"text3586\" transform=\"matrix(1,0,0,-1,279.833,383.167)\"><tspan id=\"tspan3588\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3590\" transform=\"matrix(1,0,0,-1,284.833,378.667)\"><tspan id=\"tspan3592\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 10.885 15.554 19.642 23.142 27.034 29.365\" y=\"0\">FWE\u2212corr</tspan></text>\n",
        "<text id=\"text3594\" transform=\"matrix(1,0,0,-1,320.9998,383.167)\"><tspan id=\"tspan3596\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">q</tspan></text>\n",
        "<text id=\"text3598\" transform=\"matrix(1,0,0,-1,325.9998,378.667)\"><tspan id=\"tspan3600\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 4.277 9.331 14.385 18.473 21.973 25.865 28.196\" y=\"0\">FDR\u2212corr</tspan></text>\n",
        "<text id=\"text3602\" transform=\"matrix(1,0,0,-1,430.7498,383.167)\"><tspan id=\"tspan3604\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">p</tspan></text>\n",
        "<text id=\"text3606\" transform=\"matrix(1,0,0,-1,435.7498,378.667)\"><tspan id=\"tspan3608\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 3.892 7.784 11.284 15.176 17.507\" y=\"0\">uncorr</tspan></text>\n",
        "<text id=\"text3610\" transform=\"matrix(1,0,0,-1,362.1666,383.167)\"><tspan id=\"tspan3612\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">T</tspan></text>\n",
        "<text id=\"text3614\" transform=\"matrix(1,0,0,-1,398.7498,383.167)\"><tspan id=\"tspan3616\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">(</tspan></text>\n",
        "<text id=\"text3618\" transform=\"matrix(1,0,0,-1,401.6666,383.167)\"><tspan id=\"tspan3620\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0\" y=\"0\">Z</tspan></text>\n",
        "<text id=\"text3622\" transform=\"matrix(1,0,0,-1,407.08301,378.667)\"><tspan id=\"tspan3624\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Symbol;font-variant:normal;font-weight:normal;font-size:7;writing-mode:lr;-inkscape-font-specification:Symbol\" x=\"0\" y=\"0\">\u2261</tspan></text>\n",
        "<text id=\"text3626\" transform=\"matrix(1,0,0,-1,410.9166,383.167)\"><tspan id=\"tspan3628\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0\" y=\"0\">)</tspan><tspan id=\"tspan3630\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"65.5832 73.0802 80.5772 83.0792 90.5762 98.0732 100.5752 108.0722\" y=\"-6.0832\">mm mm mm</tspan></text>\n",
        "</g></g></g><g id=\"g3632\"><g clip-path=\"url(#clipPath3636)\" id=\"g3634\"><path d=\"m 557.5,3770.83 4574.17,0\" id=\"path3640\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:10;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3642\"><g clip-path=\"url(#clipPath3646)\" id=\"g3644\"><g id=\"g3650\" transform=\"scale(10,10)\"><text id=\"text3652\" transform=\"matrix(1,0,0,-1,181.333,130.667)\"><tspan id=\"tspan3654\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-style:oblique;font-variant:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica-Oblique\" x=\"0 2.502 7.506 12.51 14.508 19.512 22.014 26.514 31.518 36.522 43.02 47.52 50.022 55.026 57.528 59.526 64.53 69.03 74.034 76.032 78.534 86.031 91.035 95.535 97.533 105.03 110.034 112.536 120.033 125.037 128.034 133.038 135.54 138.042 143.046 148.05 153.054 155.556 160.56 163.062 168.066 175.563 183.06 185.562 190.566 195.57 200.574 203.571\" y=\"0\">table shows 3 local maxima more than 8.0mm apart</tspan></text>\n",
        "</g></g></g><g id=\"g3656\"><g clip-path=\"url(#clipPath3660)\" id=\"g3658\"><path d=\"m 557.5,1267.5 4574.17,0\" id=\"path3664\" style=\"fill:none;stroke:#ff0000;stroke-opacity:1;stroke-width:10;stroke-linecap:butt;stroke-linejoin:round;stroke-miterlimit:10;stroke-dasharray:none\"/></g></g><g id=\"g3666\"><g clip-path=\"url(#clipPath3670)\" id=\"g3668\"><g id=\"g3674\" transform=\"scale(10,10)\"><text id=\"text3676\" transform=\"matrix(1,0,0,-1,55.75,117.083)\"><tspan id=\"tspan3678\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.498 11.502 13.5 18.504 23.508 26.01 28.512 31.014 36.018 39.015 44.019 48.519 53.523 58.527 60.525 65.529 68.031 70.533 76.032 78.534 83.79 86.292 91.296 93.798 98.802 103.806 106.308 108.81 113.814 116.316 121.572 124.074 129.078 131.58 136.584 141.588 146.592 149.094 152.091 157.095 159.597 164.601 169.605 174.609\" y=\"0\">Height threshold: T = 3.16, p = 0.001 (0.999)</tspan><tspan id=\"tspan3680\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 13.005 18.009 23.013 25.515 28.017 30.519 35.523 38.52 43.524 48.024 53.028 58.032 60.03 65.034 67.536 70.038 74.538 77.04 82.296 84.798 89.802 92.304 96.804 101.808 106.308 111.312 113.31 117.81 120.312 122.814 127.818 130.32 135.576 138.078 143.082 145.584 150.588 155.592 160.596 163.098 166.095 171.099 173.601 178.605 183.609 188.613\" y=\"9.75\">Extent threshold: k = 0 voxels, p = 1.000 (0.999)</tspan><tspan id=\"tspan3682\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 15.507 20.511 25.011 27.513 32.517 37.521 40.023 44.523 49.527 54.027 59.031 61.029 65.529 68.031 73.035 78.039 81.036 83.538 88.038 90.036 95.04 99.54 102.042 107.046 110.043 112.545 115.047 120.303 124.803 130.059 132.561 137.817 140.319 145.323 147.825 152.829 157.833\" y=\"19.5\">Expected voxels per cluster, &lt;k&gt; = 7.463</tspan><tspan id=\"tspan3684\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 6.003 10.503 15.507 20.511 25.011 27.513 32.517 37.521 40.023 45.027 50.031 57.528 62.532 67.536 70.533 73.035 78.039 80.541 83.043 87.543 89.541 94.545 99.045 101.547 106.551 109.548 114.048 116.55 119.052 124.308 128.808 134.064 136.566 141.822 144.324 149.328 151.83 156.834\" y=\"29.25\">Expected number of clusters, &lt;c&gt; = 6.75</tspan><tspan id=\"tspan3686\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"0 5.499 13.995 19.998 25.002 27.504 30.006 35.01 37.512 42.516 47.52 52.524 55.026 57.528 63.027 69.525 76.023 81.027 83.529 86.031 91.035 93.537 98.541 103.545 108.549 111.051 113.553 119.052 127.548 133.551 138.051 140.553 143.055 148.059 153.063 155.565 158.067 163.566 170.064 176.562 181.062 183.564 186.066 191.07\" y=\"38.91641\">FWEp: 4.810, FDRp: 4.894, FWEc: 69, FDRc: 69</tspan><tspan id=\"tspan3688\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 235.165 240.169 245.173 248.17 253.174 258.178 262.678 265.18 270.184 272.686 275.188 277.69 280.687 285.691 290.695 295.699 300.703 308.2 310.702 315.958 318.46 320.962 325.966 328.468 333.472 335.974 338.476 343.48 348.484 353.488 355.99 360.994\" y=\"1e-05\">Degrees of freedom = [1.0, 115.0]</tspan><tspan id=\"tspan3690\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.166 242.662 249.16 256.657 259.159 264.415 266.917 271.921 276.925 279.427 284.431 286.933 291.937 296.941 299.443 304.447 306.949 311.953 316.957 319.459 324.463 326.965 334.462 341.959 344.461 351.958 359.455 361.957 369.454 376.951 379.453 381.955 386.959 389.461 394.465 396.967 401.971 404.473 409.477 411.979 416.983 419.485 424.489 426.991 429.997 434.497 439.501 444.001 449.005 451.003 455.503\" y=\"9.75001\">FWHM = 12.2 12.1 12.4 mm mm mm; 4.1 4.0 4.1 {voxels}</tspan><tspan id=\"tspan3692\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.67 239.674 241.672 246.676 254.173 259.177 261.679 264.181 269.185 274.189 279.193 284.197 289.201 294.205 299.209 301.711 306.967 309.469 314.473 319.477 324.481 329.485 334.489 336.991 341.491 346.495 350.995 355.999 357.997 362.497 364.999 370.255 372.757 377.761 382.765 387.769 390.271 395.275 397.777 400.774 405.778 410.278 415.282 417.28\" y=\"19.50001\">Volume: 1202364 = 44532 voxels = 592.9 resels</tspan><tspan id=\"tspan3694\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Helvetica;font-variant:normal;font-weight:normal;font-size:9;writing-mode:lr;-inkscape-font-specification:Helvetica\" x=\"228.667 234.67 239.674 244.174 249.178 251.176 253.678 258.178 260.176 264.676 269.68 272.182 274.684 279.688 282.19 287.194 289.696 294.7 297.202 302.206 304.708 309.712 312.214 317.218 319.72 327.217 334.714 337.216 344.713 352.21 354.712 362.209 369.706 372.208 374.71 377.707 380.704 385.708 390.208 395.212 397.21 399.712 404.968 407.47 412.474 417.478 419.98 424.984 429.988 432.49 436.99 441.994 446.494 451.498 453.496 457.996\" y=\"29.25001\">Voxel size: 3.0 3.0 3.0 mm mm mm; (resel = 67.06 voxels)</tspan></text>\n",
        "<text id=\"text3696\" transform=\"matrix(1,0,0,-1,60.25,364.91699)\"><tspan id=\"tspan3698\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:bold;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier-Bold\" x=\"0 4.8 9.6 14.4 19.2 32.0832 36.8832 64.0832 68.8832 73.6832 78.4832 83.2832 105.25 110.05 114.85 119.65 124.45 146.4168 151.2168 156.0168 173.8332 178.6332 183.4332 188.2332 193.0332 219.5832 224.3832 229.1832 233.9832 238.7832 260.75 265.55 270.35 275.15 279.95 292.75 302.35 307.15 311.95 316.75 333.9168 338.7168 343.5168 348.3168 353.1168 375.0832 379.8832 384.6832 389.4832 394.2832 416.25 421.05 425.85 430.65 435.45 440.25 445.05 449.85 454.65 459.45 464.25\" y=\"0\">0.000370.0000.0009030.0000.0000.000 7.14 6.480.000 36 \u221278 \u221218</tspan></text>\n",
        "<text id=\"text3700\" transform=\"matrix(1,0,0,-1,279.833,355.25019)\"><tspan id=\"tspan3702\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 220.6668 225.4668 230.2668 235.0668 239.8668 244.6668\" y=\"0\">0.0000.000 6.39 5.900.000 33 \u221287 \u221221</tspan><tspan id=\"tspan3704\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 220.6668 225.4668 230.2668 235.0668 239.8668 244.6668\" y=\"9.75\">0.0000.000 6.20 5.740.000 21 \u221296 \u221218</tspan></text>\n",
        "<text id=\"text3706\" transform=\"matrix(1,0,0,-1,124.333,335.75019)\"><tspan id=\"tspan3708\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:bold;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier-Bold\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 82.3336 87.1336 109.75 114.55 119.35 124.15 128.95 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 215.8668 228.6668 238.2668 243.0668 247.8668 252.6668 269.8336 274.6336 279.4336 284.2336 289.0336 311 315.8 320.6 325.4 330.2 352.1668 356.9668 361.7668 366.5668 380.9668 385.7668 395.3668 400.1668\" y=\"0\">0.1100.106460.0170.0060.010 5.40 5.090.000\u221218 0 72</tspan></text>\n",
        "<text id=\"text3710\" transform=\"matrix(1,0,0,-1,279.833,326.00019)\"><tspan id=\"tspan3712\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 225.4668 230.2668 239.8668 244.6668\" y=\"0\">0.2880.180 4.25 4.090.000\u221224 3 66</tspan><tspan id=\"tspan3714\" sodipodi:role=\"line\" style=\"fill:#000000;fill-opacity:1;fill-rule:nonzero;stroke:none;font-family:Courier;font-variant:normal;font-weight:normal;font-size:8;writing-mode:lr;-inkscape-font-specification:Courier\" x=\"0 4.8 9.6 14.4 19.2 41.1668 45.9668 50.7668 55.5668 60.3668 73.1668 82.7668 87.5668 92.3668 97.1668 114.3336 119.1336 123.9336 128.7336 133.5336 155.5 160.3 165.1 169.9 174.7 196.6668 201.4668 206.2668 211.0668 220.6668 225.4668 230.2668 239.8668 244.6668\" y=\"9.75\">0.8610.509 3.66 3.550.000 \u22126 \u22126 69</tspan></text>\n",
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        "<IPython.core.display.SVG at 0x49152d0>"
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     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You will see the FWHM values at the bottom of the page - here they are 4.1 voxels in x, 4.0 voxels in y, and 4.1 voxels in z. These values are rounded; I can get the exact values from MATLAB by looking at ``xSPM.FWHM``.  These are:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FWHM = [4.0528, 4.0172, 4.1192]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A resel is therefore a block of volume approx:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "resel_volume = np.prod(FWHM)\n",
      "resel_volume"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "67.064316892672011"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "That's the value you see at the bottom the SPM printout after ``resel =``.  The resel count of 592.9 in the printout comes from a calculation based on this estimated FWHM smoothness and the shape of the brain. In other words it applies the search volume correction I mentioned above.  If it did not apply this correction then the resel count would simply be the number of voxels divided by the resel volume:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "44532 / resel_volume"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "664.0192886966679"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The table gives statistics for each detected cluster in the analysis, ordered by significance level.  Each line in bold in the table is the peak voxel for a particular cluster.  Lines in standard type are sub-clusters within the same cluster.\n",
      "\n",
      "Look at the peak voxel for the third-most significant cluster.  This is the third bold line in the table, and the seventh line overall. On the left-hand side of the table, you see the values for the \"peak-level\" statistics.  The extreme left gives the voxel location in millimeters.  Our voxel of interest is at location x=-42, y=18, z=3.\n",
      "\n",
      "The value in the \"T\" column for this voxel is 4.89.  This is the raw $t$ statistic. The column $P_{FWE-corr}$ gives the random field corrected $p$ value. In this case the value is 0.037. 0.037 is the expected EC, in a 3D image of 592.9 resels when thresholded at $t = 4.89$. This is equivalent to saying that the probability of getting one or more blobs of $t$ value 4.89 or greater, is 0.037.\n",
      "\n",
      "There are other corrected $p$ values here, based on cluster size, and based on the false discovery rate, but I didn't cover those corrections here.\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Worsley, K.J., Marrett, S., Neelin, P., and Evans, A.C. (1992). [A three-dimensional statistical analysis for CBF activation studies in human brain](http://www.math.mcgill.ca/~keith/jcbf/jcbf.abstract.html) Journal of Cerebral Blood Flow and Metabolism, 12:900-918.\n",
      "\n",
      "Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C., Friston, K.J., and Evans, A.C. (1996). [A unified statistical approach for determining significant signals in images of cerebral activation](http://www.math.mcgill.ca/~keith/unified/unified.abstract.html) Human Brain Mapping, 4:58-73."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}