counting impacts on a target

Traces.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Counting traces left by a heavy ions beam:\n",
    "When studying effect of ionizing radiation (heavy ions with high LET) on cells, the fluence ($particules/cm^2$) of the particles beam must be known.\n",
    "\n",
    "Detectors in the GANIL (Caen, France) particles accelerator can estimate the fluence. However when irradiating cells, radiobiologists may need to localize the impacts of the ions and to count the number of impact per cell.\n",
    "\n",
    "A script for the aphelion application was written: it was capable of recording and saving images from a camera, segmenting and counting traces:\n",
    "![](Traces.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Replaying with traces images\n",
    "Let's try to perform image segmentation and possibly classify impacts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import mahotas as mh\n",
    "import numpy as np\n",
    "import cv2\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from skimage import segmentation as sg\n",
    "from skimage import morphology as mo\n",
    "from skimage import filters as fi\n",
    "from skimage import measure as me"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import sklearn as sk\n",
    "from sklearn import cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "kernel100 = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(50,50))\n",
    "kernel18 = cv2.getStructuringElement(cv2.MORPH_ELLIPSE,(15,15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load an image of traces:\n",
    "Image is obtained by absorbance imaging microscopy (white background with black blobs). For convenience, image is inverted (black background, white particles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "trace = 255-cv2.imread('/home/jeanpat/QFISH/Traces isabelle/A19 1,5x10p5 X25/c01.tif')[:510,:748,0]\n",
    "#s = mh.regmin(trace)\n",
    "#seg = cv2.morphologyEx(trace, cv2.MORPH_TOPHAT, kernel100)\n",
    "top = cv2.morphologyEx(trace, cv2.MORPH_TOPHAT, kernel18)\n",
    "#blu = fi.gaussian(top, sigma=0.5)\n",
    "#locmax = mo.local_maxima(blu, selem=mo.disk(1))\n",
    "#remax = mh.regmax(top, Bc = mh.disk(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f7cb4ad21d0>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MLZlimmSTqn39zJkzWF9f73rDHhd2M2jCTFs9RxGyIF0CcUkZR0E/iSv13AqS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c60492630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,5))\n",
    "plt.subplot(121)\n",
    "plt.title('Traces: impacts of heavy ions')\n",
    "plt.imshow(trace, cmap=plt.cm.gray_r)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.title('Two horizontal densitometric plots')\n",
    "plt.plot(trace[200,:])\n",
    "plt.plot(trace[450,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perform image segmentation :\n",
    "\n",
    "   * by local thresholding\n",
    "   * followed by morphological openning cleanup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "seg = cv2.adaptiveThreshold(\n",
    "    trace.astype(np.uint8), 255, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 71, -1)\n",
    "\n",
    "cross = cv2.getStructuringElement(cv2.MORPH_CROSS,(3,3))\n",
    "\n",
    "seg = cv2.morphologyEx(seg, cv2.MORPH_OPEN, cross) > 0\n",
    "k = int((255/top.max()))\n",
    "overl = mh.overlay(k*top, red=mh.bwperim(seg))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "347  particles detected\n"
     ]
    }
   ],
   "source": [
    "lab,n = mh.label(seg)\n",
    "print(n, ' particles detected')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7c4c7b7828>"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c4c0dff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(35,30))\n",
    "plt.subplot(121)\n",
    "plt.title(' zoom on segmented particles')\n",
    "plt.imshow(overl[50:150,250:450,:])\n",
    "plt.subplot(122)\n",
    "plt.title(str(n)+' particles detected')\n",
    "plt.imshow(lab, cmap = plt.cm.jet)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visual inspection shows that segmented traces may correspond to noise, single impacts, 2tuples impacts and a bigger group of impacts.\n",
    "\n",
    "## Let's classify the traces according to their size:\n",
    "\n",
    "First, let's visualize the traces size with a histogramm. Visual analysis of the histogramm allows to guess the intervals of size corresponding to the different classes of impacts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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00qMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c5f886f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sizes = mh.labeled.labeled_size(lab)[1:]\n",
    "plt.hist(sizes,bins = 30)\n",
    "class0, n0 = mh.labeled.filter_labeled(lab, max_size=19)\n",
    "class1, n1 = mh.labeled.filter_labeled(lab, min_size=20,max_size=65)\n",
    "class2, n2 = mh.labeled.filter_labeled(lab, min_size=66,max_size=110)\n",
    "class3, n3 = mh.labeled.filter_labeled(lab, min_size=111)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7c5f9b7208>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZvegbLB3Mq6syTw9RISAakSkAAIC60ZgCAACIQJoPADokpPPz+J79PuXnU3uu4675Hv0A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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c5f998080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "overlay1 = mh.overlay(k*top, \n",
    "                      red = mh.bwperim(class1 > 0),\n",
    "                      green = np.logical_or(class0 > 0, mh.bwperim(class2 > 0)),\n",
    "                      blue = np.logical_or(class0 > 0, mh.bwperim(class3 > 0)),\n",
    "                      )\n",
    "plt.imshow(overlay1[50:150,250:450,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measure traces shape descriptors to classify the traces:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "particles = me.regionprops(lab,intensity_image=top)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "mes =[]\n",
    "for prop in particles:\n",
    "    mes.append((prop.label,prop.area, prop.convex_area, prop.eccentricity, prop.solidity, prop.equivalent_diameter))\n",
    "dta = np.array(mes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised traces classification using kmeans clustering:\n",
    "It is assumed that there are 3 classes of segmented particles (blobs):\n",
    "\n",
    "   * noise\n",
    "   * blob made of a single impact\n",
    "   * unresolved blobs generated by two impacts\n",
    "   \n",
    "Kmean clustering is the simpliest unsupervised classifier. Five features are used to classify the blobs according to their shape:\n",
    "\n",
    "   * area\n",
    "   * convex hull area\n",
    "   * eccentricity\n",
    "   * solidity\n",
    "   * equivalent diameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(347, 6)\n"
     ]
    }
   ],
   "source": [
    "classif = cluster.k_means(dta[:,1:],3)\n",
    "print(dta.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(347,)\n"
     ]
    }
   ],
   "source": [
    "centroids = classif[0]\n",
    "labels = classif[1]\n",
    "print(labels.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result of the classifier can be merged with the features and the blobs labels in a single array (first a numpy array, then in a pandas dataframe ...), merging the columns of a 2D numpy array and a 1D numpy array is not that easy, so:\n",
    "\n",
    "https://stackoverflow.com/questions/41989950/numpy-array-concatenate-valueerror-all-the-input-arrays-must-have-same-number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(347, 6) (347,)\n"
     ]
    }
   ],
   "source": [
    "print(dta.shape,labels.shape)\n",
    "extented_data = np.concatenate((dta, labels[:, None]), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Converting the numpy array into a pandas dataframe is helpful :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "feat = ['lab','area','cvx_area','ecce','solid','eq_dia','class']\n",
    "df = pd.DataFrame(data = extented_data,columns= feat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lab</th>\n",
       "      <th>area</th>\n",
       "      <th>cvx_area</th>\n",
       "      <th>ecce</th>\n",
       "      <th>solid</th>\n",
       "      <th>eq_dia</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>37.0</td>\n",
       "      <td>0.807094</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.863663</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>0.895258</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.652426</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0.163984</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.058239</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>92.0</td>\n",
       "      <td>0.829978</td>\n",
       "      <td>0.956522</td>\n",
       "      <td>10.585135</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>88.0</td>\n",
       "      <td>0.869359</td>\n",
       "      <td>0.920455</td>\n",
       "      <td>10.155413</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.918559</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.191538</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>36.0</td>\n",
       "      <td>0.782494</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.770275</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.456716</td>\n",
       "      <td>0.980000</td>\n",
       "      <td>7.898654</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>0.629289</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.222008</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>11.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.408514</td>\n",
       "      <td>0.962963</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>12.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0.347548</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.368284</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>13.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>49.0</td>\n",
       "      <td>0.365893</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.898654</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>14.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>63.0</td>\n",
       "      <td>0.655367</td>\n",
       "      <td>0.873016</td>\n",
       "      <td>8.368284</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>15.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0.163984</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.058239</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>16.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.284194</td>\n",
       "      <td>0.950000</td>\n",
       "      <td>8.519076</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>0.184328</td>\n",
       "      <td>0.962264</td>\n",
       "      <td>8.058239</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>18.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.261204</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.291860</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>19.0</td>\n",
       "      <td>94.0</td>\n",
       "      <td>107.0</td>\n",
       "      <td>0.870617</td>\n",
       "      <td>0.878505</td>\n",
       "      <td>10.940042</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>20.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>21.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>0.349955</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.214724</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>22.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.402048</td>\n",
       "      <td>0.983333</td>\n",
       "      <td>8.667245</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>23.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>0.321357</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.214724</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>24.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.255673</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.978846</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>25.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>48.0</td>\n",
       "      <td>0.378604</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>7.817640</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>26.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.577350</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.191538</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>27.0</td>\n",
       "      <td>78.0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0.704957</td>\n",
       "      <td>0.975000</td>\n",
       "      <td>9.965575</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>28.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.816497</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.191538</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>29.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>30.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>317</th>\n",
       "      <td>318.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>318</th>\n",
       "      <td>319.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.368694</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.291860</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>319</th>\n",
       "      <td>320.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>0.243824</td>\n",
       "      <td>0.982759</td>\n",
       "      <td>8.519076</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>320</th>\n",
       "      <td>321.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>321</th>\n",
       "      <td>322.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0.329693</td>\n",
       "      <td>0.981818</td>\n",
       "      <td>8.291860</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>323.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>323</th>\n",
       "      <td>324.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>324</th>\n",
       "      <td>325.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>0.154303</td>\n",
       "      <td>0.965517</td>\n",
       "      <td>8.444016</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>325</th>\n",
       "      <td>326.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>326</th>\n",
       "      <td>327.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0.398675</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.368284</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>327</th>\n",
       "      <td>328.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.368694</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.291860</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>328</th>\n",
       "      <td>329.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.519076</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>329</th>\n",
       "      <td>330.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>17.0</td>\n",
       "      <td>0.707107</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.652426</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>331.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>0.355975</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.593480</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>331</th>\n",
       "      <td>332.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.439361</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.740387</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>332</th>\n",
       "      <td>333.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>52.0</td>\n",
       "      <td>0.282261</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.136858</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>333</th>\n",
       "      <td>334.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>0.422459</td>\n",
       "      <td>0.982759</td>\n",
       "      <td>8.519076</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>334</th>\n",
       "      <td>335.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.368694</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.291860</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>335</th>\n",
       "      <td>336.0</td>\n",
       "      <td>61.0</td>\n",
       "      <td>62.0</td>\n",
       "      <td>0.354845</td>\n",
       "      <td>0.983871</td>\n",
       "      <td>8.812923</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>336</th>\n",
       "      <td>337.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>337</th>\n",
       "      <td>338.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>0.370296</td>\n",
       "      <td>0.982759</td>\n",
       "      <td>8.519076</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>338</th>\n",
       "      <td>339.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>339</th>\n",
       "      <td>340.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>56.0</td>\n",
       "      <td>0.101419</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.444016</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>340</th>\n",
       "      <td>341.0</td>\n",
       "      <td>99.0</td>\n",
       "      <td>108.0</td>\n",
       "      <td>0.850930</td>\n",
       "      <td>0.916667</td>\n",
       "      <td>11.227231</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>341</th>\n",
       "      <td>342.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>0.577350</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>4.513517</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>342</th>\n",
       "      <td>343.0</td>\n",
       "      <td>58.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.167132</td>\n",
       "      <td>0.966667</td>\n",
       "      <td>8.593480</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>343</th>\n",
       "      <td>344.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.523133</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>344</th>\n",
       "      <td>345.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0.368694</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.291860</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>345</th>\n",
       "      <td>346.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>60.0</td>\n",
       "      <td>0.439361</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.740387</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>346</th>\n",
       "      <td>347.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0.163984</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>8.058239</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>347 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       lab  area  cvx_area      ecce     solid     eq_dia  class\n",
       "0      1.0  37.0      37.0  0.807094  1.000000   6.863663    0.0\n",
       "1      2.0  17.0      17.0  0.895258  1.000000   4.652426    1.0\n",
       "2      3.0  51.0      51.0  0.163984  1.000000   8.058239    0.0\n",
       "3      4.0  88.0      92.0  0.829978  0.956522  10.585135    2.0\n",
       "4      5.0  81.0      88.0  0.869359  0.920455  10.155413    2.0\n",
       "5      6.0   8.0       8.0  0.918559  1.000000   3.191538    1.0\n",
       "6      7.0  36.0      36.0  0.782494  1.000000   6.770275    0.0\n",
       "7      8.0  49.0      50.0  0.456716  0.980000   7.898654    0.0\n",
       "8      9.0  52.0      52.0  0.000000  1.000000   8.136858    0.0\n",
       "9     10.0  14.0      14.0  0.629289  1.000000   4.222008    1.0\n",
       "10    11.0  52.0      54.0  0.408514  0.962963   8.136858    0.0\n",
       "11    12.0  55.0      55.0  0.347548  1.000000   8.368284    0.0\n",
       "12    13.0  49.0      49.0  0.365893  1.000000   7.898654    0.0\n",
       "13    14.0  55.0      63.0  0.655367  0.873016   8.368284    0.0\n",
       "14    15.0  51.0      51.0  0.163984  1.000000   8.058239    0.0\n",
       "15    16.0  57.0      60.0  0.284194  0.950000   8.519076    0.0\n",
       "16    17.0  51.0      53.0  0.184328  0.962264   8.058239    0.0\n",
       "17    18.0  54.0      54.0  0.261204  1.000000   8.291860    0.0\n",
       "18    19.0  94.0     107.0  0.870617  0.878505  10.940042    2.0\n",
       "19    20.0  52.0      52.0  0.000000  1.000000   8.136858    0.0\n",
       "20    21.0  53.0      53.0  0.349955  1.000000   8.214724    0.0\n",
       "21    22.0  59.0      60.0  0.402048  0.983333   8.667245    0.0\n",
       "22    23.0  53.0      53.0  0.321357  1.000000   8.214724    0.0\n",
       "23    24.0  50.0      50.0  0.255673  1.000000   7.978846    0.0\n",
       "24    25.0  48.0      48.0  0.378604  1.000000   7.817640    0.0\n",
       "25    26.0   8.0       8.0  0.577350  1.000000   3.191538    1.0\n",
       "26    27.0  78.0      80.0  0.704957  0.975000   9.965575    2.0\n",
       "27    28.0   8.0       8.0  0.816497  1.000000   3.191538    1.0\n",
       "28    29.0  52.0      52.0  0.000000  1.000000   8.136858    0.0\n",
       "29    30.0  52.0      52.0  0.000000  1.000000   8.136858    0.0\n",
       "..     ...   ...       ...       ...       ...        ...    ...\n",
       "317  318.0  52.0      52.0  0.000000  1.000000   8.136858    0.0\n",
       "318  319.0  54.0      54.0  0.368694  1.000000   8.291860    0.0\n",
       "319  320.0  57.0      58.0  0.243824  0.982759   8.519076    0.0\n",
       "320  321.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "321  322.0  54.0      55.0  0.329693  0.981818   8.291860    0.0\n",
       "322  323.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "323  324.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "324  325.0  56.0      58.0  0.154303  0.965517   8.444016    0.0\n",
       "325  326.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "326  327.0  55.0      55.0  0.398675  1.000000   8.368284    0.0\n",
       "327  328.0  54.0      54.0  0.368694  1.000000   8.291860    0.0\n",
       "328  329.0  57.0      57.0  0.000000  1.000000   8.519076    0.0\n",
       "329  330.0  17.0      17.0  0.707107  1.000000   4.652426    1.0\n",
       "330  331.0  58.0      58.0  0.355975  1.000000   8.593480    0.0\n",
       "331  332.0  60.0      60.0  0.439361  1.000000   8.740387    0.0\n",
       "332  333.0  52.0      52.0  0.282261  1.000000   8.136858    0.0\n",
       "333  334.0  57.0      58.0  0.422459  0.982759   8.519076    0.0\n",
       "334  335.0  54.0      54.0  0.368694  1.000000   8.291860    0.0\n",
       "335  336.0  61.0      62.0  0.354845  0.983871   8.812923    0.0\n",
       "336  337.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "337  338.0  57.0      58.0  0.370296  0.982759   8.519076    0.0\n",
       "338  339.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "339  340.0  56.0      56.0  0.101419  1.000000   8.444016    0.0\n",
       "340  341.0  99.0     108.0  0.850930  0.916667  11.227231    2.0\n",
       "341  342.0  16.0      16.0  0.577350  1.000000   4.513517    1.0\n",
       "342  343.0  58.0      60.0  0.167132  0.966667   8.593480    0.0\n",
       "343  344.0   5.0       5.0  0.000000  1.000000   2.523133    1.0\n",
       "344  345.0  54.0      54.0  0.368694  1.000000   8.291860    0.0\n",
       "345  346.0  60.0      60.0  0.439361  1.000000   8.740387    0.0\n",
       "346  347.0  51.0      51.0  0.163984  1.000000   8.058239    0.0\n",
       "\n",
       "[347 rows x 7 columns]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now let's isolate the blob labels according their classification (0, 1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 23)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sub_df0 = df.loc[df['class'] == 0]\n",
    "sub_df1 = df.loc[df['class'] == 1]\n",
    "sub_df2 = df.loc[df['class'] == 2]\n",
    "\n",
    "lab0 = np.array([sub_df0['lab']])\n",
    "lab1 = np.array([sub_df1['lab']])\n",
    "lab2 = np.array([sub_df2['lab']])\n",
    "\n",
    "lab2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the labels corresponding to the different class of traces can be used to select the traces themselves in the image, there's a numpy trick for that:\n",
    "\n",
    "https://stackoverflow.com/questions/44853829/how-to-mask-elements-of-2d-numpy-array-from-an-array-of-values?noredirect=1#comment76688501_44853829\n",
    "\n",
    "https://stackoverflow.com/questions/44031145/assign-1-and-0-values-to-numpy-array-depending-on-whether-values-are-in-list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "selected_0 = np.in1d(lab, lab0).reshape(lab.shape).astype(int)\n",
    "selected_1 = np.in1d(lab, lab1).reshape(lab.shape).astype(int)\n",
    "selected_2 = np.in1d(lab, lab2).reshape(lab.shape).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(510, 748)"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selected_2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7c4c85f438>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3eQyMK/xVLQj24ZhF9D6pHuUJAMDMPinyBABEbWpxyN3/TtKPhxafI+nS8PhSSa8tLf+U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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c4c171128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,15))\n",
    "\n",
    "plt.subplot(131)\n",
    "plt.title('class 0 blobs')\n",
    "plt.imshow(selected_0)\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.title('class 1 blobs')\n",
    "plt.imshow(selected_1)\n",
    "\n",
    "plt.subplot(133)\n",
    "plt.title('class 2 blobs')\n",
    "plt.imshow(selected_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7c4c150e80>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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4X+hLUUpvDPWxSm++z0t6sZk93cxM0sskHUv6qKS9bJt7JX2wnSICAAAMV5Vn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\n4qLDEwgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c4c6fe908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,10))\n",
    "overlay1 = mh.overlay(k*top, \n",
    "                      red = selected_0,\n",
    "                      green = selected_1,\n",
    "                      blue = selected_2,\n",
    "                      )\n",
    "plt.imshow(overlay1[50:150,250:450,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classification issues:\n",
    "\n",
    "The Kmeans clustering provides classes but it doesn't map the classes (0, 1, 2) to the number of impacts of the traces. For that, a supervised classifier should be used.\n",
    "\n",
    "Here the class 0 (red) traces maps to traces of 1 impact, the class 1 (green) maps to noise detection and the class 2 maps to traces with 2 impacts or more. The identification can be done after visualisation of the classified traces.\n",
    "\n",
    "### When the traces are classified, the number of impacts can be counted:\n",
    "\n",
    "$N_{impacts} = \\displaystyle\\sum_{i=1}^{k} i \\times n_i$ with $n_i$ the number of traces with $i$ impacts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of impacts: 305\n"
     ]
    }
   ],
   "source": [
    "N1 = len(sub_df0.index)\n",
    "N2 = len(sub_df2.index)\n",
    "\n",
    "Impacts = N1 + 2*N2\n",
    "print('Number of impacts:', Impacts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fluence can be calculated after spatial calibration using a slide with microscopic motifs engraved."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}