dpieces.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# mmdpieces\n",
    "Classify two dimensional pieces."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Description\n",
    "\n",
    "The input image is a binary image typically found in industrial automation applications. It has three types of objects: rings, nails and T-pins. Our procedure for identification of these classes of objects is based on thickening, thinning and reconstruction.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:22.835503Z",
     "start_time": "2019-01-06T03:42:22.346928Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ia870 Python Morphology Toolbox version 0.8 25th Aug 2014 - in progress - migrating to Python 3\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from PIL import Image\n",
    "import ia870 as ia\n",
    "import matplotlib.pyplot as plt\n",
    "print(ia.__version__)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reading\n",
    "\n",
    "The gray scale image to be processed is read. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:23.203124Z",
     "start_time": "2019-01-06T03:42:22.838815Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVgAAAE/CAYAAAADnduiAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAGpVJREFUeJzt3TuOLrtxwHG24UyBEyeKvAFrCY68Am/AgHfhTPACvAKn2oAWYShVpEwLMJwIUGx8Ds7tezkcPoqPIovk/wcc4JwzM/11s7urq4uPeT6fjwMAjPc3q3cAAE5FgAUAJQRYAFBCgAUAJQRYAFBCgAUAJQRYAFBCgAUAJQRYAFBCgMWRnuf59+d5/vw8z1+f5/nT8zz/snqfcB8CLE71Z+fcPznn/s459x/Oud89z/PrtbuE2zysRYAbPM/zR+fcbz+fz+9X7wvuQQaLIz3P86/P8/zxeZ6/PM/zF+fcPzrn/n71fuEuf7t6B4DRnuf5B+fcfznn/tk594fP5/N/P2Wwz9o9w23IYHGiXznnPs65/3XOued5/s39yGCBqQiwOM7n8/mTc+4/nXN/cM79j3PuN865/166U7gSnVwAoIQMFgCUEGABQAkBFgCUEGABQAkBFgCUmJho8DwPQxkAbOPz+YgmrZDBAoASAiwAKCHAAoASAiwAKCHAAoASAiwAKCHAAoASAiyGY4U24AcTEw1wBj+w+n9/Hn6RAO5EBgsASshg0a1UEni/TiaL25DBYpjnebJB9PP5UJ8NvO3htw1tdA4yWAzxPM+XTDUXJG7OaGPtEqtdU8M+Axkshvh8Pj9nsO/fJT9zi57s/aZ2Og0BFgCUmPitsqwHe54wi5VcZ6e+Co+6x05tnx1J14OlBgsVseD6/l8q4JxYdywF11RJJfy5U9rjNgRYqAsDaynQvl/bOaikji0VSEsPl93b41bUYAFACRkspqmtye5cMshl6ZLjCoe67Xb8+IEAiyVKNcfQbq/IqRpq6xC23Y4fPxBgsVRtXfa1S7AZlYnucrz4ihosACghwGIpf/0CfzZYieV1DcKpr28W27O/Vo8VeZQIYEa4noGvNHbW0it0WBYYUT+1dHyQI8DClNRIg50WkCHbxIsSAQAoIYOFWWE2W8pi3++L/fxMsf3sybAtZOVow2Iv2MYuC8iMuKeYaGAbi73gOLtmtC1SGbBzex3H7ajBAoASAmzBO37RQikFv/CX+asZOztDuC+jM06uxX1Qg83wa36WhgHhO2nJwKd1LmPXjSauyfmkNVgCbIJ0PU/Y0dIJ5pzOOZX+Asjwe1JrwZZwXc5FJ5cSMlm7Yp1g799zNDqQcqtnlR4EuZW4UlhtyyZqsACghBJBguS1Dva11EM1O6Vi+yLtoJMeB9emPmqwA+Tahov4qzAAhHXF2NdX7ePK2myPVFCOHY+1fZ9N+94lwHa6NUtIBUcNK4Ps+3cJi+dachwW91vbrHMqDbDUYAFACRlsxs5ZbO71fIXSUKSZan5NTWj1vvtyx2FpP2dova5b24kSQScLYw9nvq6vYCHo7rKATMnNk2Jqxhmnvt7wmQTYXrWZjaTzJtcZtJPcfqeyZus3vKXZYJArdfJJHqK155EaLAAsRgabYaFttKTqj7FMXPI9vp1nFZ1SMjiV5C0jV3qKnV9KBItYaJtWuWmjscWcrY1ZtaAm2N7aRiOMvM+k5yE1HVmKADvAirYp1Tadi48QSHWESWvDiKvNaGnnMs37qnVWHDVYANgMq2lVaOlhzr2KSKaUpn4m3F7s/1L/hlxtbzTWqLnGY9+r9ZZHgK1Qqk3mXs39YJoLgLlAmfo/zBErvzhHoJ2t1IfQu72RqMFm1LYNwe8u1LbnSiUpPeehdfYbNVgAWIwSQScymHvFykUaWe0tmbJkjOv7td4371lv7gTYDjdc9Cgr1c1b7TLFeJRYh21JGHCttRUlggxrJwv3eLM5rsE6n8+nmAHH6q5a7UwGm2GhAxBAXqyskBplENK+x8lgAUAJATaD17O80usY2tCmctKpsbGf0y4POEeAzeJCT/Pb5pZ2mvFAsdpZs4uaxV5mrMdMDTajZlHpG9wSSH2tA9Fb7boA+2q1s+pmrRZHBgsASshgG92eZZycac3OWlOfDbmwtCJdu1f7/JLBVrh5larcsJdT2sGvy60IrIx9bfe2mx9oUyvNzXyIkcFWuDW7KC0AvrPUr8N5/75if05o11VSD/9Vv6GDDBYAlJDBFqQWvz49m02NHUx9bSeljHxFeYCsdRzJAvWzEGArrH59HKX0SxBjTqm75h4cK51wXVm0uj1ZcPsCo87x6ou1l8UgRva6JxbcBoDFKBEcSuN3zVvMAEusjRJ4hVONa/dFu9QRKx1ZabudEGARFeso2O2mSnVMWjqOlsWlpV/vDdq5f1PakCHAHqg0iyX2q8FbtmWRdAbPSq2/YqZ2FIck4PacX4JsGTVYAFBCBnuoVIYU1tZSGcgumeuuq531litapnzuck5PQoCt5N8Y2r9NtEeu/pgKuv737WiHtSJGXCep4xxx7krXc6oua7GtLWAcrFBtO6264FK95r2dKdZuoBHHuYJGQIodd+99XUogejvUdsc4WABYjAw2Y0QWsMLI4TqWxj7ukFmnzJhmnPqM2lX+35/J7ScZLBlsl1znyapFQSRGPzAtPICdO+eG1tzv99rMLdkXq9/mfgZ9yGADqRs5NyMo9u/w52eK7deoLPb99wxW2rOXhcBV6siU7tfJawPXkGawBFiPZFpl7jXMQhYgOZ+S/VoV3E7JVH1WOt/CkSTv39+vndYRqokSAQAsxjjYQOo1KtXRE8sK/K/NfqpLShe1WeK7Dc3OrlRGZaWDrZeF48iNa6VEoIMA+5PYDS0JkCPqWqP5xyEpGaxajyC23dNKBFbKA75cUoCxjgmwI27M0TOzVt5cqUzQgh0WZOllqb1D4RuJlKRTF19RgwUAJUdksKlXzdq60uia38psrPc1sDRqomefYp9zKovHJ7lfSm8+FmrKO9h6mFbLDJXSdkYOW5F8trZUbbmGRmAN96X1M1I185XlmdVD9SRyww+lrB7bDNJhWttmsLnB9K0PjZMyWH8fYsGm1FY10yZTJNvumQAR+3//6ys7zCyce4nee2WX41yFGiwAKNk2g62tF9XOXho1iuBlZfyjdHxp775bKD2FZmRcFo87pvWtz0IJZidb12B9kotFEkw0WbwgR03xnTH0atR50jwPuwWeUpsSUOOOr8GGamYwWVhww4p3f3r2q/RA0zru0swkesDzcklJ6n66vc1qUYMFACXHZLDOtS0yHP58z2uo5OdPzgJSGatW9hrLwFbNYNsxK66pxT/P97VkUXZMDdYnGePXGoxrhzdJtrWrVElG47hahlzFBs+HRuyrlc7MXlbGEe9AWoM9MsA6J5s3HV5ApY6yWBDJ/fvUAJvKFmd97qs2yGqMi90xc73doBFCrAcLACsdVYP11ZYAUsOVwgwllbmGnyspU/ROx52ZNeV6mVdkr1Kx8+PP+urd95l1Xuzn2BKBc/LX9VgQLA3Erp24kNuH3LYslBlWlQRS+/GS7kPqOhg1kYTywD5GXbvXjYONkc6/fxu9ZcZT6fNjc+RbttO7jVqrM9bS/tQonXfcZeZ5PzrAhlo6oEa8Qr6fHftcSfaay4RHXyy5zsCVwcjSq/gpowZuNfOc0ckFAEquyWBLnV7arw0tGVjs1VZj3y1Picy12epM0koboQ4lAiU1JQINo2qppcBbunhKQctK4MiVK2L11Fn7tLqzD/VWPYyvCrClIVSzbpjWz3gfDJLpuLXbtBYocp1sqzF6YD8rOoqdowYLAGquymBfq55mrXJjcXuPwVr2mjqe1CiMFq3nn8z1K2n7WWivVff6lQE2lBqvauHCCPWOrd2lJBBKTRJoaYPesc2oa3fr95SmqwNsaYyqNTdlrM59H/mRW5yntC1/e62Za2o/bjHi/ljdfrM/mxosACi5OoP1rRgb2yI1G8zCmgW1ataHiO1/LsNNrSPRc04ttuEsI9/uZteyV76BHL3YSy3p66oVqZrk6EVNNJQWvmm9CUefQ412tPjgTql5cKfW77BwX40O6iz20mjXhUFKs72s6w2s4XZGGrXqVu7/LF9bMbH7JFyzQhJoZ9xXK+8HarAAoIQM1hO+3ljPBHfYx5KwtGEpk0u98tZuo+b7LB1/TM35imWyu1+vtQiwCbt0eu0odsNZbdfWc94aSCxfY63nqzQc0vo10INOroTS2FhLF0NYB8stkmKJ1WDSe8OXOnV2GvExulYcG92hebxanyHt5KIGCwBKCLAJ/pRSSxlFjGQ2k2QVrtmst+vI9nqvI/+aSh2/tfPke6+j0eNitY7Zz5ZXtCs12IJUgd7q6+1rtwVtrOg9r6lX6tSQpV06flK105q2Sq2hsWOJQIoarNAOtVjnZAHV2j5b0juxIDXLrrStHermLbXj1fVmarAAcChKBAW7vMrl9nO38sYqI8e7hkOTevandZ9Gio0JTg23klp9TDMQYAtKNbTVNZ5X7vN3n5Y5U+8U3Za2jg1din1P7rO1H5rhZ/QkGzOHaa1GgBWS3ABWLpTYYi+Ws+/VRtzoIwJO72drP0h7ZzquCqwr70sCbKMRvaqzWHrVRJxkYZTebY6QK32UOoJnBlYrJTE6uQBACRlspdK8aisYBysT1hVHZTqt2ZrG+dLI4CR135W1Vo1z2oIA2yFW9LdWuJ/RAbKrGZ1/rWNg/f0pbSPVw6/9kE3tU7jfK649K4kFEw06lXp3YVcsMI3YZo40+NUsChN7m5p97VmbKKGd6DDRAAAWo0QwyE6jCvDV6F72XOaZGlIV24Z0v97vs3CtWeuXWH0PEmA77dLphV+kapWjtt1zHexWM7eYVFgalnhEicDPCmYHuPczUzfVin1C2ozB+K0/t1twde6X/fb/vfqat9R+RwRYALBoy1EE0n22NjzE0pN1R7meamnmpzXuNfcZJTtfFxbXuZhRImAUgZv/el46sRYeZrvKrQERlohK60X4ZR0Nks8IX61Xv1aPQB/Ed9sFWP+i9S/SmtWktIQ3jIWn+a1SwXbW4Pewppr6zPB7dsY1/912ARYAdrHNMK3Y0JqapdNm1Yok0yJ5ysulzlvNW8nKYTux/V0960rDCcegYYsAG+uYCJcjc65uTGpv2UA6v5xFV8aqeaiGVg6DOr18ZGUNDiv78dpiFEHq6R82Ys/NV0t6AnP7ZOUikMotJjLjWGLtV3vOR689cDuLmfiM65FRBACwmPkMNlVvLY0a0Mpia5+M1lYZalXTlprHV7PClISFc2ExC5Sytu+z3k6kGewWAfan7/n5360DyiU3Z+mVc8SJ2+0VtWdevZbSOW2t0c52ygPYCgJsbCcEAdb7XvF2a2uGuRpf7WefYsT1MSOjLQVb/3ulFGcBffuc26+zUSb2B5wZYH/6/qrtp7YxYurl6XI3vpWygXPfz9eozHb0fpeCq9bnjmL97ctaBksnFwAoMZvBSjszckpZzKqnsPUswDnZkChJxuj//AwaJYORdffSPli7JmrayMJbHyWC2E5Ulgi8nxN/BjWuOj2jNqy+9rYG3N79lpQFVrdNjMXOzZTZ9/dxJYKncjGMz+fz5Y/FC3gHkhEYfhC2ksnEpPYpvEZqr7WcmskPFpKdV8++rDiWkedspG0CLADsZou1CJyLP1Fr6lpWs6odSNouV6O1lJnlRkLMuEZiQ7J2uTbDmnvpzWbmcVm6xnxbBFjpnPPYhSu1y0U+Q2t9sHZihxX+fo+qjUof/rtcd6UHg5Vzbq0tzXdyOddfbN/lIg6t7Ajp/WyLnVwlsZERLfu8a6eWTzrSJfy+VeedTi4AuMx2JYLYv0vfvxtJOUTrM2OsZ1ujhFnYjdlrrIThXHqfa+uyGiwPwdwiwDonO5GpepC1RpeaVa+rfVjt2p5SI45v1w7Xno7JVZ2b/jVqrW23CbA54ThC6xexVCxzH6Vn5lWs7lZ6oO1+LnJqR7hYboveoEgG+xU1WABQsmUGmxoi8rKeJUhpZAK12yyNcyz9/UaxLG72eNtWI17vw23sXqrrsWWAdS4/NnbnE6n1sJDeMBr1s53PR4mkU+v9/9j3WzNi/1bU7K1eY1uMg72JRm9+Tb01VV+VbCfc5umZS+yhXppgsEsy0DOeNXWdaB3rivZkHCwALEYGa9DI0RCpTKQmo4qVLSR26TmvVTPWNVXy2SW7b3ndn10iWHF9STNYAqwxo0sEpQAr3W5p3vkur74j9Axxi/28lbbSjgUzxnBbKxEQYI2JBa1RM4r8r/VeiKXOuNOy1ldtp5Z0e6vaasegGrKcwVKDBQAl2w7TQl5ultWoqaC5sZ4nZq/OlZfOrD3u2CzEWWa8vWpnlxbewHMIsIaNGKj9/ozGRX5qEM1JDVsb1aE343W3tpPy/ZnaabA3Xh8hAuxiNRfsqXXN3eSy1p6HoL/9GR1CpX2JvaFIRpPcUIuXIsAu0PNac/sFa4nGwiapERojtpuTy8pT20kNNxtdjiqxfD/QyQUAShimNdHo9QAsP7lvoPkqPzKLzb3Kj5rU4u/zrKFZrxX3AeNgjZFMIJCOsYz9LM4S60wbGWStXDct61tYmNQiDbDUYBcq3UCxhVdC1GTjZmdUo+Xqn7XHI7mOVqjdj3BUTWw71s45NVgAUEKJQFmuxiXNSGqH1+CHnimsFq1+LdYwO/6MajdKBMaMqKlpDAvSZDEgWHp9rOVfPzsfxyvV56BZypj90CXAKopdLC03Rm4Vq12sCLapG3X1AiujnHIcr1SNNXb9W6snp1CDBQAlBFhl/kIevU/b3TKVWTN5cqxnOC3Cdt31GGuWdAzvIf//3m3F1t2QfIZm+9HJpWj0GFbJ3G8rLI7fPa3T63VKqSC28tuI+JSbUNFay2aigRE1IwBiJ1sy+cD6jbU6sJVuWOvtl5I6rl2Px7n8b86ITTQYGYQr95MFtwFgJTJYZanVh0awNmslZC1zLM1ostqOEicdS0nuFb9l1ppmiYBhWpOk5lG3bss5+2M6rQ2lsbY/I4VBxvq10SPXiRU75ljZbda1QAY7Sc8YvlxNage5B8uKLDbX/ru0ac5N2ewq1GABYDEy2ImkJQJJL+puLGaOqfOxY/uGRgxFQhrDtAyTFuJPu/mtLVqz07jiHruVlHZAgN2AdLGLE26M3o4FzTY4NdCeOE7WiqsDbOoV1PqrtsV9GmnE4PDR7WOxdKGFIDsOnVwAsNg1GWyt1Jzlk17bV1kxtTHH2oQIbVzD/SgRLDZqUYmT5F5RWyZhaJQL/O2e1MEYIsj2IcB+3f7U2RsjSVYC2iF4S4am5d4YUj+j4dROrxA12XbUYAFgsaMyWEmmF/t6+PPBvkW3sasVGW/pjeL9nlK2HtI+hpvqsc6dd2yariwR5Mb9pVbdyX1PbJulmmrpldZCe+dodB6F25YEeMkDULtEcEunl3PUZGtJA+xRq2nlBuiPWHUnlmHl9iF1sea+Z/cAnVI7AmPljb5jrb7Xe34sBFoL+zAKNVgAUHJUicAiyewl6VhbSS1Z8hm5r480cqrmylf1W0YVOLe+JrvL0Lgra7AnSnUGvX8PSSdIaAeNUTfK6htudUfbKqvafZc2JsDiZ7ksd8ZY0taRC6mOyPfvs9zY6eXcumx2hzcGxsECwGJHjSJAnGQExUhhBvL+O5fVSsYZr5qxdtpY6Bq5kTkadp1xmUKJACpGX1dWXg93eH3VsuoBt7rjLYYSAbZXM0Z4lud5fv7j88eQnsjP3mceZ+ptaBcEWABQQokA6nquMSuvhL5bRxX4ZtRktWreI/b5yqmysCU39lYanCxOm7y50+s147glC/60mFlLJoPFFKl1F1LrMqzqUGlxYxZbmnU4+rO0dEyAYaLBTKtnHO1Ecs3t1n63ji6Y3cMvjVfStwztAEsnFwAooQbbSVJXxFenZXW5OuFOpY4WM8o6pTKEZDjfqskLZLAd3gvqpJknqOePDz05mEpo3APvPRYmM7H/D8frjljJrWvfLQSFXWuwIxY0wVlurcX6tDq+RnUmjugvoQYLAItRg20Uvn5YeBPAerlarP/1k1nNXGPb0j4fBNhK4Sye1DhO3OvmTi8NI/o4Vg2jJMC6r9modPzczbN4kBcOwOca6ZNKanZADRYAlFw5imDEMa8e/oE9MKpgnNb7TWO0D4u9RIwKrP62uFGQQ6dXv5b7tlTam+WqABvqWRWJ2hqk6PQar/be89t/ZptTgwUAJddksLkRAn5dptT7S931F6wgJsOogvVWlWSuCLCltStjkwUYhpVHcK2Tax/KBHnhgjK925jpigDrXLwOVmp0jdXUd5ZrA4KETOrBTaeXjtWd0tRgAUDJNRmsc+09j7H/Y3m676MwUPa2E6MK6sXaRvKra1a26VUB1jdqsYhbxGquvNa2y3V60a5xsWsuNsXd/3r499mumMkVNnrrBZxrK+s3Q2mRmlIG4GMW2ziS+4/2TVuVnbIeLAAsdkUG61x/9rlzFqd1ji0f8252fju6ERmspxRgWl7TLDyYJEbup//7x7jpx3lfc2nT81zRyRWrvaY6Fvyf2XkcbGoiQM9AbTpf9OzyNoQ6VwRY5+onDcRmd8VYvBlyU3wlDxvMxcPrXFeUCABghWsC7JsljMoUrGcaqXppbgHo1DH55RLrx70j2vZc15QInEvPwjrxFbn0e4xK42DDhW+gh8B6rqsC7CtWdyzVIlNT9Kwr7ad0VMAOxwpYc02JAABmuzKDde57xlrK9HZe/3REtr1Lxg5Ycm2AdS7/2i+Zo7+Lnfcd2NnVATYUW4Fn9+A0Ykrv6BEYwC2owQKAEgLsgXLjXluGXPmZK9krIEeJ4EClMb6tHXaUCIA6BNgD1a4vIP1eAitQhxIBACghwB6OuimwDgH2UG9gHTFBgiANtCHAHi5cCaum3ipZhQtAGgEWAJQwiuACqaUKX7mVxVLLHQIoI8BeJvW7xnLlAIIr0IYAe6HYmguprwNoRw0WAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQ8rPMJADrIYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFACQEWAJQQYAFAyf8DrNnl6n8TRbsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_pil = Image.open('data/pieces_bw.tif').convert('L')\n",
    "a = np.array (a_pil)\n",
    "a = a.astype(np.bool)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('a')\n",
    "axes.imshow(a, cmap='gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contour noise reduction\n",
    "\n",
    "A thickening that preserves the number of connected objects is applied to reduce contour noise. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:23.473520Z",
     "start_time": "2019-01-06T03:42:23.206252Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".0.\n",
      "000\n",
      "...\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seA = ia.iaimg2se(ia.iabinary([[0,1,0],[1,0,1],[0,0,0]]))\n",
    "seB = ia.iaimg2se(ia.iabinary([[0,0,0],[0,1,0],[0,0,0]]))\n",
    "iAB = ia.iase2hmt(seA,seB)\n",
    "print(ia.iaintershow(iAB))\n",
    "\n",
    "b = ia.iathick(a, iAB);\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('b')\n",
    "axes.imshow(b, cmap='gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Skeleton\n",
    "\n",
    "The homotopic skeleton by thinning is created.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:23.720270Z",
     "start_time": "2019-01-06T03:42:23.477170Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = ia.iathin(b);\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('c')\n",
    "axes.imshow(c, cmap='gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Skeleton pruning\n",
    "\n",
    "The open lines of the skeleton are pruned by the end point thinning. The remaining skeleton components will be loops, identifying the rings. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:24.254843Z",
     "start_time": "2019-01-06T03:42:23.725763Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "d = ia.iathin(c,ia.iaendpoints());\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('c, d')\n",
    "axes.imshow(ia.iagshow(c, d).transpose(1, 2, 0))\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Detect rings\n",
    "\n",
    "Extraction of the rings by reconstruction of the thicked image from the filtered skeleton. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:24.565797Z",
     "start_time": "2019-01-06T03:42:24.260373Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e = ia.iainfrec(d,b)\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('c, d')\n",
    "axes.imshow(e, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rings in the input image\n",
    "\n",
    "Restriction of the objects detected to the input-image. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:24.765863Z",
     "start_time": "2019-01-06T03:42:24.569565Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = ia.iaintersec(a,e)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('f')\n",
    "axes.imshow(f, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Skeleton of the remaining objects\n",
    "\n",
    "It eliminates the skeleton of the rings. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:24.979909Z",
     "start_time": "2019-01-06T03:42:24.771124Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = ia.iasubm(c,e)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('g')\n",
    "axes.imshow(g, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# End points filtering\n",
    "\n",
    "It removes sucessively 4 end-points to let T junctions just on T-pins. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:25.208749Z",
     "start_time": "2019-01-06T03:42:24.983161Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = ia.iathin(g, ia.iaendpoints(), 4)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('h')\n",
    "axes.imshow(h, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# T-pins markers\n",
    "\n",
    "It detects triple points, applying the union of matchings with the template rotated 90 degrees. These points will identify (mark) the T-pins. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:25.444018Z",
     "start_time": "2019-01-06T03:42:25.215077Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "seA1 = ia.iaimg2se(ia.iabinary([[0,1,0],[0,1,0],[1,0,1]]))\n",
    "seB1 = ia.iaimg2se(ia.iabinary([[0,0,0],[1,0,1],[0,1,0]]))\n",
    "seA2 = ia.iaimg2se(ia.iabinary([[0,1,0],[1,1,1],[0,0,0]]))\n",
    "seB2 = ia.iaimg2se(ia.iabinary([[1,0,1],[0,0,0],[0,1,0]]))\n",
    "i1 = ia.iasupcanon(h, ia.iase2hmt(seA1,seB1))\n",
    "i2 = ia.iasupcanon(h, ia.iase2hmt(seA2,seB2))\n",
    "i = ia.iaunion(i1,i2)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('h, i')\n",
    "axes.imshow(ia.iagshow(h, ia.iadil(i, ia.iasedisk(2))).transpose(1, 2, 0))\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Detect T-pins\n",
    "\n",
    "Detection of the T-pins by reconstruction of the ticked image from the T-pin markers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:25.690515Z",
     "start_time": "2019-01-06T03:42:25.449123Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "j = ia.iainfrec(i,b,ia.iasebox())\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('j')\n",
    "axes.imshow(j, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## T-pins in the input image\n",
    "\n",
    "Restriction of the objects detect to the input image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:25.874800Z",
     "start_time": "2019-01-06T03:42:25.694535Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = ia.iaintersec(a,j)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('k')\n",
    "axes.imshow(k, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Detect nails\n",
    "\n",
    "The nails are imediatly detected by the subtration of the images of the rings and T-pints from the input image. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:26.064368Z",
     "start_time": "2019-01-06T03:42:25.880682Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l = ia.iasubm(ia.iasubm(a,f),k)\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('l')\n",
    "axes.imshow(l, cmap = 'gray')\n",
    "axes.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Color composition\n",
    "\n",
    "The result of the classification is presented in a pseudo color image. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-06T03:42:26.291318Z",
     "start_time": "2019-01-06T03:42:26.068235Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.5, 228.5, 206.5, -0.5)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = ia.iagray(f,'uint8',1);\n",
    "n = ia.iagray(k,'uint8',2);\n",
    "o = ia.iagray(l,'uint8',3);\n",
    "p = ia.iaunion(m,n,o);\n",
    "\n",
    "(fig, axes) = plt.subplots(nrows=1, ncols=1,figsize=(10, 5))\n",
    "axes.set_title('h, i')\n",
    "axes.imshow(ia.iaglblshow(p).transpose(1, 2, 0))\n",
    "axes.axis('off')"
   ]
  }
 ],
 "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": "3.6.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}