{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n",
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       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
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       "        margin-right:auto;\n",
       "    }\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    h3{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "        margin-top:12px;\n",
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       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\";\n",
       "\t\t\tfont-size: 90%;\n",
       "    }\n",
       "    .prompt{\n",
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       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 50pt;\n",
       "\t\tline-height: 100%;\n",
       "        color:#CD2305;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\t\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: #CD2305;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }\n",
       "    \n",
       "    ol ol li {\n",
       "        list-style-type: decimal;\n",
       "    }\n",
       "    /*ol {\n",
       "    counter-reset: num -1;\n",
       "    }\n",
       "    ol li {\n",
       "        list-style-type: none;\n",
       "    }\n",
       "    ol li:before {\n",
       "        counter-increment: num;\n",
       "        content: counter(num) \". \";\n",
       "    }*/\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
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       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n",
       "<script>$.getScript('../ipython_notebook_toc.js');</script><a href=\"./content.ipynb\"><< back to chapter content</a><br><div id=\"toc\"></div><p>Last updated: 05/02/2018 </p><script>code_show=true; \n",
       "    function code_toggle() {\n",
       "     if (code_show){$('div.input').hide();} else {$('div.input').show();}\n",
       "     code_show = !code_show}\n",
       "    $( document ).ready(code_toggle);</script>\n",
       "    <a href=\"javascript:code_toggle()\">show/hide source code</a>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#rem \"%matplotlib notebook\" crashes with networkx\n",
    "%matplotlib inline  \n",
    "import matplotlib.pyplot as plt\n",
    "import sys\n",
    "sys.path.insert(0,'..')\n",
    "from IPython.display import HTML,Image,SVG,YouTubeVideo\n",
    "from helpers import header\n",
    "\n",
    "HTML(header())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model based segmentation\n",
    "\n",
    "As far, we considered the image segmentation as a bottom-up process, where connected pixels are grouped together based on some sort of rule based on gray levels, borders etc.\n",
    "\n",
    "In some cases, one know *a priori* the object we are looking for.\n",
    "\n",
    "An example was already given when looking for lines and circles using the Hough transform.\n",
    "\n",
    "We will see in this chapter other method using this top-down approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Live-wire\n",
    "\n",
    "The live-wire algorithm is an interactive segmentation method that helps the user to delineate object borders in an image. The user select some points located near the object boundary and the algorithm connect them using a best path strategy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dijkstra shortest path algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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2M+W95XFNP3VpiuQFjatLheIhgmqABEIoFiK+OU5sTYxwZv6B0D3jThReGanr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\nM5YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f151d0980b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "G=nx.DiGraph()\n",
    "G.add_weighted_edges_from([('y','s',7),('y','v',6),('x','y',2),('x','u',3),('x','v',9),\n",
    "                          ('s','x',5),('s','u',10),('u','x',2),('u','v',1),('v','y',4)])\n",
    "\n",
    "pos=nx.spring_layout(G) \n",
    "edgewidth=[]\n",
    "for (u,v,d) in G.edges(data=True):\n",
    "    edgewidth.append(d['weight'])\n",
    "    \n",
    "nx.draw_networkx_nodes(G,pos=pos)\n",
    "nx.draw_networkx_labels(G,pos=pos,font_size=20,font_family='sans-serif')\n",
    "nx.draw_networkx_edges(G,pos,alpha=0.3,width=edgewidth, edge_color='m',arrows=True);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['s', 'x', 'u', 'v']\n",
      "['v', 'y', 's']\n"
     ]
    }
   ],
   "source": [
    "print(nx.dijkstra_path(G,source='s',target='v'))\n",
    "print(nx.dijkstra_path(G,source='v',target='s'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (py3)",
   "language": "python",
   "name": "py3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}