jeanpat/C8Skeleton_to_graph-01.ipynb

## C8Skeleton_to_graph-01.ipynb
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#The code is a tentative to produce a graph object from an image of morphological skeleton. \n",
      "Still not work on some cases"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import networkx as nx\n",
      "from PIL import Image, ImageDraw, ImageFont\n",
      "from skimage import morphology\n",
      "import mahotas as mh\n",
      "import string\n",
      "import itertools\n",
      "import graph_tool.all as gt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Making a model image (letter)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def makeLetterImage(character, size):\n",
      "    image = Image.new(\"RGBA\", (720,180), (255,255,255))#600,150\n",
      "    draw = ImageDraw.Draw(image)\n",
      "    font = ImageFont.truetype(\"verdana.ttf\", size)\n",
      "    \n",
      "    draw.text((5, 0), character, (0,0,0), font=font)\n",
      "    img_resized = np.array(image.resize((300,75), Image.ANTIALIAS))\n",
      "    letter = img_resized[0:40,0:30,0]<64\n",
      "    r1 = mh.bbox(letter)[0]\n",
      "    r2 = mh.bbox(letter)[1]\n",
      "    c1 = mh.bbox(letter)[2]\n",
      "    c2 = mh.bbox(letter)[3]\n",
      "    letter = letter[r1-1:r2+1,c1-1:c2+1]\n",
      "    return letter"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Morphology tool: branched/End-points extraction"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def branchedPoints(skel, showSE=False):\n",
      "    X=[]\n",
      "    #cross X\n",
      "    X0 = np.array([[0, 1, 0], \n",
      "                   [1, 1, 1], \n",
      "                   [0, 1, 0]])\n",
      "    X1 = np.array([[1, 0, 1], \n",
      "                   [0, 1, 0], \n",
      "                   [1, 0, 1]])\n",
      "    X.append(X0)\n",
      "    X.append(X1)\n",
      "    #T like\n",
      "    T=[]\n",
      "    #T0 contains X0\n",
      "    T0=np.array([[2, 1, 2], \n",
      "                 [1, 1, 1], \n",
      "                 [2, 2, 2]])\n",
      "            \n",
      "    T1=np.array([[1, 2, 1], \n",
      "                 [2, 1, 2],\n",
      "                 [1, 2, 2]])  # contains X1\n",
      "  \n",
      "    T2=np.array([[2, 1, 2], \n",
      "                 [1, 1, 2],\n",
      "                 [2, 1, 2]])\n",
      "    \n",
      "    T3=np.array([[1, 2, 2],\n",
      "                 [2, 1, 2],\n",
      "                 [1, 2, 1]])\n",
      "    \n",
      "    T4=np.array([[2, 2, 2],\n",
      "                 [1, 1, 1],\n",
      "                 [2, 1, 2]])\n",
      "    \n",
      "    T5=np.array([[2, 2, 1], \n",
      "                 [2, 1, 2],\n",
      "                 [1, 2, 1]])\n",
      "    \n",
      "    T6=np.array([[2, 1, 2],\n",
      "                 [2, 1, 1],\n",
      "                 [2, 1, 2]])\n",
      "    \n",
      "    T7=np.array([[1, 2, 1],\n",
      "                 [2, 1, 2],\n",
      "                 [2, 2, 1]])\n",
      "    T.append(T0)\n",
      "    T.append(T1)\n",
      "    T.append(T2)\n",
      "    T.append(T3)\n",
      "    T.append(T4)\n",
      "    T.append(T5)\n",
      "    T.append(T6)\n",
      "    T.append(T7)\n",
      "    #Y like\n",
      "    Y=[]\n",
      "    Y0=np.array([[1, 0, 1], \n",
      "                 [0, 1, 0], \n",
      "                 [2, 1, 2]])\n",
      "    \n",
      "    Y1=np.array([[0, 1, 0], \n",
      "                 [1, 1, 2], \n",
      "                 [0, 2, 1]])\n",
      "    \n",
      "    Y2=np.array([[1, 0, 2], \n",
      "                 [0, 1, 1], \n",
      "                 [1, 0, 2]])\n",
      "    \n",
      "        \n",
      "    Y3=np.array([[0, 2, 1], \n",
      "                 [1, 1, 2], \n",
      "                 [0, 1, 0]])\n",
      "    \n",
      "    Y4=np.array([[2, 1, 2], \n",
      "                 [0, 1, 0], \n",
      "                 [1, 0, 1]])\n",
      "    Y5 = np.rot90(Y3)\n",
      "    Y6 = np.rot90(Y4)\n",
      "    Y7 = np.rot90(Y5)\n",
      "    Y.append(Y0)\n",
      "    Y.append(Y1)\n",
      "    Y.append(Y2)\n",
      "    Y.append(Y3)\n",
      "    Y.append(Y4)\n",
      "    Y.append(Y5)\n",
      "    Y.append(Y6)\n",
      "    Y.append(Y7)\n",
      "    \n",
      "    bp = np.zeros(skel.shape, dtype=int)\n",
      "    for x in X:\n",
      "        bp = bp + mh.morph.hitmiss(skel,x)\n",
      "    for y in Y:\n",
      "        bp = bp + mh.morph.hitmiss(skel,y)\n",
      "    for t in T:\n",
      "        bp = bp + mh.morph.hitmiss(skel,t)\n",
      "        \n",
      "    if showSE==True:\n",
      "        fig = plt.figure(figsize=(4,5))\n",
      "        tX =['X0','X1']\n",
      "        tY =['Y'+str(i) for i in range(0,8)]\n",
      "        tT =['T'+str(i) for i in range(0,8)]\n",
      "        ti= tX+tY+tT\n",
      "        SE=X+Y+T\n",
      "        print len(SE), len(ti)\n",
      "        n = 1\n",
      "        ti = iter(ti)\n",
      "        for se in SE:\n",
      "            #print next(ti)\n",
      "            #print se\n",
      "            mycmap = mpl.colors.ListedColormap(['black','blue','red'])\n",
      "            ax = fig.add_subplot(4,5,n,frameon=False, xticks=[], yticks=[])\n",
      "            title(str(next(ti)))\n",
      "            imshow(se, interpolation='nearest',vmin=0,vmax=2,cmap=mycmap)\n",
      "            n = n+1\n",
      "        fig.subplots_adjust(hspace=0.1,wspace=0.08)\n",
      "        #ax_cb = fig.add_axes([.9,.25,.1,.3])#\n",
      "        color_vals=[0,1,2]\n",
      "        #cb = mpl.colorbar.ColorbarBase(ax_cb,cmap=mycmap, ticks=color_vals)\n",
      "        #cb.set_ticklabels(['back', 'hit', 'don\\'t care'])\n",
      "        \n",
      "        plt.show()\n",
      "    return bp > 0\n",
      "\n",
      "def endPoints(skel):\n",
      "    endpoint1=np.array([[0, 0, 0],\n",
      "                        [0, 1, 0],\n",
      "                        [2, 1, 2]])\n",
      "    \n",
      "    endpoint2=np.array([[0, 0, 0],\n",
      "                        [0, 1, 2],\n",
      "                        [0, 2, 1]])\n",
      "    \n",
      "    endpoint3=np.array([[0, 0, 2],\n",
      "                        [0, 1, 1],\n",
      "                        [0, 0, 2]])\n",
      "    \n",
      "    endpoint4=np.array([[0, 2, 1],\n",
      "                        [0, 1, 2],\n",
      "                        [0, 0, 0]])\n",
      "    \n",
      "    endpoint5=np.array([[2, 1, 2],\n",
      "                        [0, 1, 0],\n",
      "                        [0, 0, 0]])\n",
      "    \n",
      "    endpoint6=np.array([[1, 2, 0],\n",
      "                        [2, 1, 0],\n",
      "                        [0, 0, 0]])\n",
      "    \n",
      "    endpoint7=np.array([[2, 0, 0],\n",
      "                        [1, 1, 0],\n",
      "                        [2, 0, 0]])\n",
      "    \n",
      "    endpoint8=np.array([[0, 0, 0],\n",
      "                        [2, 1, 0],\n",
      "                        [1, 2, 0]])\n",
      "    \n",
      "    ep1=mh.morph.hitmiss(skel,endpoint1)\n",
      "    ep2=mh.morph.hitmiss(skel,endpoint2)\n",
      "    ep3=mh.morph.hitmiss(skel,endpoint3)\n",
      "    ep4=mh.morph.hitmiss(skel,endpoint4)\n",
      "    ep5=mh.morph.hitmiss(skel,endpoint5)\n",
      "    ep6=mh.morph.hitmiss(skel,endpoint6)\n",
      "    ep7=mh.morph.hitmiss(skel,endpoint7)\n",
      "    ep8=mh.morph.hitmiss(skel,endpoint8)\n",
      "    ep = ep1+ep2+ep3+ep4+ep5+ep6+ep7+ep8\n",
      "    return ep > 0\n",
      "\n",
      "def pruning(skeleton, size):\n",
      "    '''remove iteratively end points \"size\" \n",
      "       times from the skeleton\n",
      "    '''\n",
      "    for i in range(0, size):\n",
      "        endpoints = endPoints(skeleton)\n",
      "        endpoints = np.logical_not(endpoints)\n",
      "        skeleton = np.logical_and(skeleton,endpoints)\n",
      "    return skeleton"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def edges_from_C8skel(c8skeleton):\n",
      "    '''given a skeleton defined on c8 neighborhood (use mahotas),\n",
      "     \\ returns labeled edges\n",
      "    '''\n",
      "    branchedP = branchedPoints(c8skeleton, showSE = False) > 0\n",
      "    endP = endPoints(c8skeleton) > 0\n",
      "    edges = np.logical_not(branchedP)*c8skeleton\n",
      "    label_edges,ne = mh.label(edges)\n",
      "    return label_edges"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def labels_in_labeledImage(labImage):\n",
      "    return np.where(mh.histogram.fullhistogram(np.uint16(labImage))[:]>0)[0][1:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def SkeletonDecomposition(skeletonC8):#images processing: extraction of branchedpoints, end-points, edges\n",
      "    ep = endPoints(skeletonC8)\n",
      "    bp = branchedPoints(skeletonC8, showSE = False)\n",
      "    ## Label branched-points\n",
      "    l_bp,_ = mh.label(bp)\n",
      "    #mh.labeled.relabel(l_bp, inplace=True)\n",
      "    ## Label the edges\n",
      "    l_edges =  edges_from_C8skel(skeletonC8)\n",
      "    ##Make end-points with the same label than their edge\n",
      "    l_ep = ep*l_edges \n",
      "    #mh.labeled.relabel(l_ep, inplace=True)\n",
      "    ##edges between branched-points\n",
      "    endpoints_labels = np.where(mh.histogram.fullhistogram(np.uint16(l_ep))[:]==1)[0]\n",
      "    edges_bp = np.copy(l_edges)\n",
      "    for l in endpoints_labels:\n",
      "        edges_bp[np.where(edges_bp == l)]=0\n",
      "    mh.labeled.relabel(edges_bp, inplace=True)\n",
      "    #edges between end-points and branched points\n",
      "    edges_ep_to_bp = l_edges * np.logical_not(edges_bp > 0)\n",
      "    mh.labeled.relabel(edges_ep_to_bp, inplace=True)\n",
      "    Ep_Bp, _ = mh.labeled.relabel(edges_ep_to_bp)\n",
      "    Bp_Bp, _ = mh.labeled.relabel(edges_bp)\n",
      "    Bp, _ = mh.labeled.relabel(l_bp,inplace=True)\n",
      "    Ep, _ = mh.labeled.relabel(l_ep,inplace=True)\n",
      "    return Ep_Bp, Bp_Bp , Bp, Ep "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def labels_in_the_neighbourhood(label, domainimage, edgesImage):\n",
      "    '''\n",
      "    gives the values of the labels (edgesImages) in the neighbourhood of a domain of label=l in domainimage.\n",
      "    label (int) label value of the domain in domainimage.\n",
      "    domainimage : array of domains (typically branched points of a skeleton of one pixel or more) of label l.\n",
      "    edgesImage : array of labelled edges defining neighbourhood of domains.\n",
      "    '''\n",
      "    se = np.zeros((3,3))\n",
      "    se[:,:]=1\n",
      "    nei = mh.dilate(domainimage==label, Bc=se)\n",
      "    nei = np.logical_not(domainimage==1)*nei\n",
      "    edges_label = mh.histogram.fullhistogram(np.uint16(edgesImage[nei>0])) #np.where()\n",
      "    return np.where(edges_label>0)[0][1:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### This function generate a dict of the form {label domain:[lab of edge1,lab of edge2], lab dom2:[lab edge, lab edge]}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Now try to link thedifferent kind of domain (ep or bp)\n",
      "## we need to know the labels in the neighbourhood of a domain\n",
      "def neighbourhood_of_domain(domainIm, targetIm):\n",
      "    neighbourhood_of_domain_in_targetIm = {}\n",
      "    ##Labels of bp domains\n",
      "    #since labels were relabeled to 1:n, it would be possible to use\n",
      "    #domains_labels = np.arange(1,domainIm.max())\n",
      "    domains_labels = np.where(mh.histogram.fullhistogram(np.uint16(domainIm))[:]>0)[0][1:]#tricky, another way?\n",
      "    for lab in domains_labels:\n",
      "        neighbourhood_of_domain_in_targetIm[lab]=labels_in_the_neighbourhood(lab, domainIm, targetIm)#.tolist()\n",
      "    return neighbourhood_of_domain_in_targetIm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### function to invert the previous dict: {lab edge1:[lab domain1,lab dom2], lab edge2:[lab dom, lab dom]...}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def inverse_dict_non_unique_mappings(domNeighbourhood_dict):\n",
      "    edges_dict = {item: [key for key in domNeighbourhood_dict if item in domNeighbourhood_dict[key]] for value in domNeighbourhood_dict.values() for item in value}\n",
      "    return edges_dict"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Basic tools : convert branched point image  or ep image  to graph vertices"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def add_bp_to_graph(Graph, Bp):\n",
      "    labels_BP = labels_in_labeledImage(Bp)\n",
      "    #print labels_BP\n",
      "    #add_bp_to_graph(Graph, labels_BP)\n",
      "    nodesN = Graph.order()\n",
      "    translate_Bplabel_to_Node_index={}\n",
      "    for lab in labels_BP:\n",
      "        pos = np.where(Bp == lab)\n",
      "        #print pos\n",
      "        translate_Bplabel_to_Node_index[lab] = nodesN+lab\n",
      "        Graph.add_node(nodesN+lab,kind=\"BP\",label=lab, position=pos)\n",
      "    return translate_Bplabel_to_Node_index"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def add_ep_to_graph(Graph, Ep):\n",
      "    '''Adds end-points from labelled Ep image to a graph and\n",
      "    returns a dictionnary mapping Ep labels into Node index (necessary when adding edges into the graph)\n",
      "    '''\n",
      "    translate_Eplabel_to_Node_index={}\n",
      "    labels_EP = labels_in_labeledImage(Ep)\n",
      "    #print labels_EP\n",
      "    nodesN = Graph.order()\n",
      "    for lab in labels_EP:\n",
      "        pos = np.where(Ep == lab)\n",
      "        #print pos\n",
      "        translate_Eplabel_to_Node_index[lab] = nodesN+lab\n",
      "        Graph.add_node(nodesN+lab,kind=\"EP\",label=lab, position=pos)\n",
      "    return translate_Eplabel_to_Node_index\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Make an image of the letter: a"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Let's compare first the skeletons computed with scikit-image or mahotas."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "se8 = np.array([[True,True,True],\n",
      "                [True,True,True],\n",
      "                [True,True,True]])\n",
      "\n",
      "se4 = np.array([[False,True,False],\n",
      "                [True,True,True],\n",
      "                [False,True,False]])    \n",
      "\n",
      "imK = makeLetterImage('k', 70)\n",
      "skel = mh.thin(imK)\n",
      "skel0 = morphology.medial_axis(imK,mask=se8) \n",
      "skel1= morphology.medial_axis(imK,mask=se4)\n",
      "skel2 = morphology.skeletonize(imK)\n",
      "\n",
      "\n",
      "Ep_Bp, Bp_Bp, Bp, Ep = SkeletonDecomposition(skel)\n",
      "BP1 = branchedPoints(skel1)\n",
      "BP2 = branchedPoints(skel2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(15,5)\n",
      "subplot(241,xticks=[],yticks=[])\n",
      "title('mahotas thin')\n",
      "imshow(skel+1*imK, interpolation='nearest')\n",
      "subplot(242,xticks=[],yticks=[])\n",
      "title('skimage medial axis se8')\n",
      "imshow(skel0+1*imK, interpolation='nearest')\n",
      "subplot(243,xticks=[],yticks=[])\n",
      "title('skimage medial axis se4')\n",
      "imshow(skel1+1*imK, interpolation='nearest')\n",
      "subplot(244,xticks=[],yticks=[])\n",
      "title('skimage skeletonize')\n",
      "imshow(skel2+1*imK, interpolation='nearest')\n",
      "subplot(245,xticks=[],yticks=[])\n",
      "title('maho thin()+branched-points')\n",
      "imshow(skel+1*Bp+2*Ep, interpolation='nearest')\n",
      "subplot(246,xticks=[],yticks=[])\n",
      "title('sk medial axis+branched-points')\n",
      "imshow(skel1+1*BP1, interpolation='nearest')\n",
      "subplot(248,xticks=[],yticks=[])\n",
      "title('skeletonize+branched-points')\n",
      "imshow(1*skel2+2.0*BP2, interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "<matplotlib.image.AxesImage at 0x9fd78b0c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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uTnXq1NHDDz/sTM97Wzf3DsWCBQt8Lvvf//5Xbdu2VbVq1ZxpNWrUUNu2bfXh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\nAbqiDgLQ2N/TAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa15968ac>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Decompose the skeleton of the letter a"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(15,20)\n",
      "subplot(151,xticks=[],yticks=[])\n",
      "imshow(skel, interpolation='nearest')\n",
      "subplot(154,xticks=[],yticks=[])\n",
      "imshow(Ep_Bp, interpolation='nearest')\n",
      "title('Lab='+str(labels_in_labeledImage(Ep_Bp)))\n",
      "subplot(155,xticks=[],yticks=[])\n",
      "title('Lab='+str(labels_in_labeledImage(Bp_Bp)))\n",
      "imshow(Bp_Bp, interpolation='nearest')\n",
      "subplot(153,xticks=[],yticks=[])\n",
      "title('Lab='+str(labels_in_labeledImage(Ep)))\n",
      "imshow(Ep, interpolation='nearest')\n",
      "subplot(152,xticks=[],yticks=[])\n",
      "title('Lab='+str(labels_in_labeledImage(Bp)))\n",
      "imshow(Bp, interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<matplotlib.image.AxesImage at 0x9fbeb0ac>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA1MAAAEECAYAAADNrG76AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9fe946ec>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### labels of edges between endpoints and branched-points (Ep_Bp)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(10,20)\n",
      "subplot(151,xticks=[],yticks=[])\n",
      "title('1')\n",
      "imshow(Bp_Bp==1, interpolation='nearest')\n",
      "subplot(152,xticks=[],yticks=[])\n",
      "title('2')\n",
      "imshow(Bp_Bp==2, interpolation='nearest')\n",
      "subplot(153,xticks=[],yticks=[])\n",
      "title('3')\n",
      "imshow(Bp_Bp==3, interpolation='nearest')\n",
      "subplot(154,xticks=[],yticks=[])\n",
      "title('4')\n",
      "imshow(Bp_Bp==4, interpolation='nearest')\n",
      "subplot(155,xticks=[],yticks=[])\n",
      "title('5')\n",
      "imshow(Bp_Bp==5, interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.image.AxesImage at 0x9f8b708c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAjwAAAC3CAYAAAAW54SoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa1589fcc>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Check neighbourhood of bp in Bp_Bp edges"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ND_Bp_in_BPBP = neighbourhood_of_domain(Bp,Bp_Bp)\n",
      "ND_Bp_in_EPBP = neighbourhood_of_domain(Bp,Ep_Bp)\n",
      "ND_Ep_in_EPBP = neighbourhood_of_domain(Ep,Ep_Bp)\n",
      "\n",
      "print ND_Bp_in_BPBP\n",
      "print ND_Bp_in_EPBP\n",
      "print ND_Ep_in_EPBP\n",
      "\n",
      "for bp in ND_Bp_in_EPBP.keys():\n",
      "    for edge in itertools.product([bp],ND_Bp_in_EPBP[bp]):\n",
      "        print 'edge', edge"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{1: array([1]), 2: array([1, 2]), 3: array([2])}\n",
        "{1: array([1, 2]), 2: array([4]), 3: array([3, 5])}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4]), 5: array([5])}\n",
        "edge (1, 1)\n",
        "edge (1, 2)\n",
        "edge (2, 4)\n",
        "edge (3, 3)\n",
        "edge (3, 5)\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print inverse_dict_non_unique_mappings(ND_Bp_in_BPBP)\n",
      "print inverse_dict_non_unique_mappings(ND_Bp_in_EPBP)\n",
      "print inverse_dict_non_unique_mappings(ND_Ep_in_EPBP)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "{1: [1, 2], 2: [2, 3]}\n",
        "{1: [1], 2: [1], 3: [3], 4: [2], 5: [3]}\n",
        "{1: [1], 2: [2], 3: [3], 4: [4], 5: [5]}\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def C8_Skeleton_To_Graph_01(Graph, C8Skeleton):\n",
      "    Ep_Bp, Bp_Bp, Bp, Ep = SkeletonDecomposition(C8Skeleton)\n",
      "    \n",
      "    print \"condition Ep seuls\", Bp.max()==0 and Ep.max()>0\n",
      "    print \"condition Bp \",Bp.max()>0\n",
      "    #print Graph.order()\n",
      "    ## try to add branched points first: check if they exist\n",
      "    if Bp.max()>0:# At least one bp\n",
      "        map_Bp_nodes = add_bp_to_graph(Graph, Bp)#map label of Bp-image into node index\n",
      "        # ex:\n",
      "        # map Bp |-> node {1: 1, 2: 2, 3: 3} the labels in the image are equal to th nodes index in the graph\n",
      "        map_Ep_nodes = add_ep_to_graph(Graph, Ep)\n",
      "        #ex:\n",
      "        # map Ep |-> node {1: 4, 2: 5, 3: 6, 4: 7, 5: 8} : the endpoint of label 1 (image) is the node of index 4 in the graph\n",
      "        \n",
      "        print 'map Bp |-> node',map_Bp_nodes\n",
      "        print 'map Ep |-> node',map_Ep_nodes\n",
      "        \n",
      "        # link End-points and Branched-points\n",
      "        #Search label(s) of edges in image containing edges between ep and bp\n",
      "        ## first get the neighborhood of all branched domains (one or more pixels) in Ep_Bp image\n",
      "                \n",
      "        ND_Bp_in_EPBP = neighbourhood_of_domain(Bp,Ep_Bp)\n",
      "        ND_Ep_in_EPBP = neighbourhood_of_domain(Ep,Ep_Bp)\n",
      "        print ND_Bp_in_EPBP\n",
      "        print 'inv:',inverse_dict_non_unique_mappings(ND_Bp_in_EPBP)\n",
      "        #Neighbourhood Domain 1 (label=1 in Bp image) has two neighbors of label 1 or 2 in image of edges linking Ep to Bp\n",
      "        # {1: array([1, 2]), 2: array([3, 4]), 3: array([5])}\n",
      "        #Inverting the dict yields:\n",
      "        #     {1: [1], 2: [1], 3: [2], 4: [2], 5: [3]}\n",
      "        # edge of label 1 (in Ep_Bp) is close to Branched-point of lab=1 in Bp, edge of lab=2 is close to branched point of lab=1\n",
      "        \n",
      "        print ND_Ep_in_EPBP\n",
      "        print 'inv',inverse_dict_non_unique_mappings(ND_Ep_in_EPBP)\n",
      "        \n",
      "        map_edges_to_bp = inverse_dict_non_unique_mappings(ND_Bp_in_EPBP)\n",
      "        map_edges_to_ep = inverse_dict_non_unique_mappings(ND_Ep_in_EPBP)\n",
      "        #\n",
      "        ### link Bp to Ep\n",
      "        #   get a bp \n",
      "        for bp in ND_Bp_in_EPBP.keys():\n",
      "            #search edges lab in bp neighbourhood in EPBP edges\n",
      "            for ep in  ND_Bp_in_EPBP[bp]:\n",
      "                vertexbp = map_Bp_nodes[bp]# should be here id to bp\n",
      "                vertexep = map_Ep_nodes[ep]\n",
      "                w = np.sum(Ep_Bp==ep) # edge weight\n",
      "                print ep, vertexbp, vertexep\n",
      "                Graph.add_edge(vertexbp,vertexep,weight=w)\n",
      "        #\n",
      "        # try to link branched-points between them\n",
      "        ## get the neighbourhood of branched points in image of edges between bp \n",
      "        ND_Bp_in_BPBP = neighbourhood_of_domain(Bp,Bp_Bp)\n",
      "        map_edges_to_bp_in_Bp = inverse_dict_non_unique_mappings(ND_Bp_in_BPBP)\n",
      "        \n",
      "        #### This loop links branched points between them\n",
      "        print 'LINKING BP to BP'# TODO FIX IT this yield a wrong graph !!\n",
      "        print 'inv EDGES : BP',inverse_dict_non_unique_mappings(ND_Bp_in_BPBP)\n",
      "        print len(map_edges_to_bp_in_Bp.keys())\n",
      "        \n",
      "        for edge in map_edges_to_bp_in_Bp.keys():\n",
      "            Nb_of_BP = map_edges_to_bp_in_Bp[edge]\n",
      "            # Link between two different BP\n",
      "            if Nb_of_BP >= 2:\n",
      "                current_bp1 = map_edges_to_bp_in_Bp[edge][0]\n",
      "                current_bp2 = map_edges_to_bp_in_Bp[edge][1]\n",
      "                vertex1 = map_Bp_nodes[current_bp1]\n",
      "                vertex2 = map_Bp_nodes[current_bp2]\n",
      "                w = np.sum(Bp_Bp==edge)\n",
      "                print edge, map_edges_to_bp_in_Bp[edge], current_bp1, current_bp2, w\n",
      "                Graph.add_edge(vertex1,vertex2,weight=w)\n",
      "            # Self link on one BP\n",
      "            if Nb_of_BP == 1:\n",
      "                current_bp1 = map_edges_to_bp_in_Bp[edge][0]\n",
      "                \n",
      "                vertex1 = map_Bp_nodes[current_bp1]\n",
      "                \n",
      "                w = np.sum(Bp_Bp==edge)\n",
      "                print \"loop:\",edge, map_edges_to_bp_in_Bp[edge], current_bp1, w\n",
      "                Graph.add_edge(vertex1,vertex1,weight=w)\n",
      "        \n",
      "    if Bp.max()==0 and Ep.max()>0:\n",
      "        # add Ep first\n",
      "        Ep_Ep, edge_number = mh.label(np.logical_and(C8Skeleton,np.logical_not(Ep)))\n",
      "        labeled_Ep, Ep_number= mh.label(Ep)\n",
      "        map_Ep_nodes = add_ep_to_graph(Graph, labeled_Ep)\n",
      "        print 'number of Ep:', Ep_number\n",
      "        print 'map Ep |-> node',map_Ep_nodes\n",
      "        #link end-points between them, should be only two EP...\n",
      "        ND_Ep_in_EPEP = neighbourhood_of_domain(labeled_Ep,Ep_Ep)\n",
      "        print \"Neighbor of Ep in EpEp\",ND_Ep_in_EPEP\n",
      "        print 'inv',inverse_dict_non_unique_mappings(ND_Ep_in_EPEP)\n",
      "        map_edges_to_ep_in_Ep = inverse_dict_non_unique_mappings(ND_Ep_in_EPEP)\n",
      "        for edge in map_edges_to_ep_in_Ep.keys():\n",
      "            print \"map edge|-> ep in edge\", map_edges_to_ep_in_Ep[edge]\n",
      "            print \"nb of EP\", Ep_number\n",
      "            # Link between two different EP\n",
      "            if Ep_number == 2:\n",
      "                current_ep1 = map_edges_to_ep_in_Ep[edge][0]\n",
      "                current_ep2 = map_edges_to_ep_in_Ep[edge][1]\n",
      "                vertex1 = map_Ep_nodes[current_ep1]\n",
      "                vertex2 = map_Ep_nodes[current_ep2]\n",
      "                w = np.sum(Ep_Ep==edge)\n",
      "                print \"EpEp\",edge, map_edges_to_ep_in_Ep[edge], current_ep1, current_ep2, w\n",
      "                Graph.add_edge(vertex1,vertex2,weight=w)\n",
      "            "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## try the function skeleton ---> graph"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "image_test= makeLetterImage('a', 75)\n",
      "skeleton_test = mh.thin(image_test)\n",
      "_,_,Bp_test,Ep= SkeletonDecomposition(skeleton_test)\n",
      "Ep_Ep = skeleton_test*np.logical_not(Ep)\n",
      "Ep_Ep,_ = mh.label(Ep,Ep)\n",
      "l_Ep, _ = mh.label(Ep)\n",
      "\n",
      "#Ep_Bp, Bp_Bp, Bp, Ep = SkeletonDecomposition(skel)\n",
      "\n",
      "Graph_test = nx.MultiGraph()\n",
      "C8_Skeleton_To_Graph_01(Graph_test, skeleton_test)\n",
      "print Graph_test.edges(data=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv: {1: [1], 2: [2]}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv {1: [1], 2: [2]}\n",
        "1 1 3\n",
        "2 2 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 32\n",
        "2 [1, 2] 1 2 6\n",
        "[(1, 2, {'weight': 32}), (1, 2, {'weight': 6}), (1, 3, {'weight': 19}), (2, 4, {'weight': 2})]\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(16,8)\n",
      "subplot(131)\n",
      "imshow(skeleton_test+l_Ep+3*Bp_test,interpolation='nearest')\n",
      "subplot(132, xticks=[],yticks=[])\n",
      "nx.write_dot(Graph_test,'multi.dot')\n",
      "!neato -T png multi.dot > multi.png\n",
      "imshow(mh.imread('multi.png'), interpolation='nearest')\n",
      "subplot(133)\n",
      "nx.draw_graphviz(Graph_test, prog='neato')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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A7rvvPq677jri4uKCjHhEZ511FgCtW7dmxIgRlk9JiiAxtedTkqRINXr0aOrV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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9f5f06ac>"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## More checking"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "imTest = makeLetterImage('b', 75)\n",
      "skelTest = mh.thin(imTest)\n",
      "Ep_Bp, Bp_Bp, Bp, Ep = SkeletonDecomposition(skelTest)\n",
      "\n",
      "GraphTest = nx.Graph()\n",
      "C8_Skeleton_To_Graph_01(GraphTest, skelTest)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2, 3: 3}\n",
        "map Ep |-> node {1: 4, 2: 5, 3: 6}\n",
        "{1: array([1, 2]), 2: array([], dtype=int32), 3: array([3])}\n",
        "inv: {1: [1], 2: [1], 3: [3]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [3]}\n",
        "1 1 4\n",
        "2 1 5\n",
        "3 3 6\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [2, 3], 3: [2, 3]}\n",
        "3\n",
        "1 [1, 2] 1 2 6\n",
        "2 [2, 3] 2 3 42\n",
        "3 [2, 3] 2 3 12\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(20,15)\n",
      "subplot(161,xticks=[],yticks=[])\n",
      "imshow(2*imTest+1.0*skelTest, interpolation='nearest')\n",
      "subplot(162,xticks=[],yticks=[])\n",
      "nx.draw(GraphTest)\n",
      "subplot(163,xticks=[],yticks=[])\n",
      "imshow(Ep_Bp, interpolation='nearest')\n",
      "title('Lab='+str(labels_in_labeledImage(Ep_Bp)))\n",
      "subplot(166,xticks=[],yticks=[])\n",
      "title('Lab='+str(labels_in_labeledImage(Bp_Bp)))\n",
      "imshow(Bp_Bp, interpolation='nearest')\n",
      "subplot(165,xticks=[],yticks=[])\n",
      "title('Lab='+str(labels_in_labeledImage(Ep)))\n",
      "imshow(Ep, interpolation='nearest')\n",
      "subplot(164,xticks=[],yticks=[])\n",
      "title('Lab='+str(labels_in_labeledImage(Bp)))\n",
      "imshow(Bp, interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 66,
       "text": [
        "<matplotlib.image.AxesImage at 0x9eed904c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9bub9SWYn+ZMkX0wylOS/7nPNvyfZNGdOzjvvvMk+KgAAwGETaoDivf33fi9/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\nIZjaVfkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9f2f782c>"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# More systematic checking:\n",
      "* Since The function fails sometimes to produce a graph, let's check by varying the number of branched points and the number of en-points.\n",
      "* Bp=0, 1, 2 and Ep=0, 1, 2\n",
      "\n",
      "\n",
      "|Bp*Ep| 0 | 1 | 2 |\n",
      "|--------------------|\n",
      "|    0|   .|.   |   |\n",
      "|    1|   |   |   |\n",
      "|    2|   |   |   |"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Images with BP =0 and Ep=0"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bp0Ep0_a = np.array([[0,0,0,0,0],\n",
      "                   [0,1,1,1,0],\n",
      "                   [0,1,0,1,0],\n",
      "                   [0,1,1,1,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "\n",
      "Bp0Ep0_b = np.array([[0,0,0,0,0],\n",
      "                   [0,0,1,0,0],\n",
      "                   [0,1,0,1,0],\n",
      "                   [0,0,1,0,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep0_c = np.array([[0,0,0,0,0],\n",
      "                   [0,0,1,0,0],\n",
      "                   [0,1,0,1,0],\n",
      "                   [0,0,1,1,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep0_d = np.array([[0,0,0],\n",
      "                     [0,1,0],\n",
      "                   [0,0,0],\n",
      "                   ],dtype=int)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(5,5)\n",
      "subplot(131,xticks=[],yticks=[])\n",
      "imshow(Bp0Ep0_a, interpolation='nearest')\n",
      "subplot(132,xticks=[],yticks=[])\n",
      "imshow(Bp0Ep0_b, interpolation='nearest')\n",
      "subplot(133,xticks=[],yticks=[])\n",
      "imshow(Bp0Ep0_c, interpolation='nearest')\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 28,
       "text": [
        "<matplotlib.image.AxesImage at 0x9f6915ec>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAASUAAABgCAYAAABbhWQcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRHh9A1JECUgRJSBFlIAUUQJSfgM8HemO9saalgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9f6cf4ac>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Images Bp=0 Ep=2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bp0Ep2_a = np.array([[0,0,0,0,0],\n",
      "                   [0,1,1,0,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep2_b = np.array([[0,0,0,0,0],\n",
      "                   [0,1,1,1,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep2_c = np.array([[0,0,0,0,0],\n",
      "                   [0,1,1,1,0],\n",
      "                   [0,0,0,1,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep2_d = np.array([[0,0,0,0,0],\n",
      "                   [0,1,1,0,0],\n",
      "                   [0,0,0,1,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep2_e = np.array([[0,0,0,0,0],\n",
      "                   [0,1,1,0,0],\n",
      "                   [0,0,1,1,0],\n",
      "                   [0,0,0,0,0]],dtype=int)\n",
      "Bp0Ep2_f = np.array([[0,0,0,0,0,0],\n",
      "                   [0,1,1,1,1,0],\n",
      "                   [0,0,0,0,0,0],\n",
      "                   [0,0,0,0,0,0]],dtype=int)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Images Bp=1 Ep=1"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Bp1Ep1_a = np.array([[0,0,0,0,0],\n",
      "                     [0,0,1,0,0],\n",
      "                     [0,1,1,1,0],\n",
      "                     [0,1,0,1,0],\n",
      "                     [0,1,1,1,0],\n",
      "                     [0,0,0,0,0]],dtype=int)\n",
      "\n",
      "Bp1Ep1_b = np.array([[0,0,0,0,0],\n",
      "                     [0,0,0,1,0],\n",
      "                     [0,1,1,1,0],\n",
      "                     [0,1,0,1,0],\n",
      "                     [0,1,1,1,0],\n",
      "                     [0,0,0,0,0]],dtype=int)\n",
      "\n",
      "Bp1Ep1_c = np.array([[0,0,0,0,0],\n",
      "                     [0,0,0,1,0],\n",
      "                     [0,1,1,1,0],\n",
      "                     [0,1,0,1,0],\n",
      "                     [0,1,1,1,0],\n",
      "                     [0,0,0,0,0]],dtype=int)\n",
      "Bp1Ep1_c = np.array([[0,0,0,0,0,0],\n",
      "                     [0,0,0,0,1,0],\n",
      "                     [0,1,1,1,0,0],\n",
      "                     [0,1,0,1,0,0],\n",
      "                     [0,1,1,1,0,0],\n",
      "                     [0,0,0,0,0,0]],dtype=int)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Make an alphabet"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alphabet = list(string.ascii_lowercase)\n",
      "ilphabet = []\n",
      "for l in alphabet:\n",
      "    imLetter = makeLetterImage(l, 75)\n",
      "    skeletter = mh.thin(imLetter)\n",
      "    BP =  branchedPoints(skeletter, showSE=False)\n",
      "    EP = endPoints(skeletter)\n",
      "    ilphabet.append(1*skeletter+2*BP+3*EP)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(20,20)\n",
      "for im,n in zip(ilphabet, range(1,27)):\n",
      "    subplot(6,5,n,xticks=[],yticks=[])\n",
      "    imshow(im,interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x9f9187ec>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "gralphabet=[]\n",
      "imgraph=[]\n",
      "for l in ilphabet:\n",
      "    graph_ = nx.MultiGraph()\n",
      "    gralphabet.append(C8_Skeleton_To_Graph_01(graph_, l))\n",
      "    nx.write_dot(graph_,'multi.dot')\n",
      "    !neato -T png multi.dot > multi.png\n",
      "    imgraph.append(mh.imread('multi.png')) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv: {1: [1], 2: [2]}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv {1: [1], 2: [2]}\n",
        "1 1 3\n",
        "2 2 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 32\n",
        "2 [1, 2] 1 2 6\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2, 3: 3}\n",
        "map Ep |-> node {1: 4, 2: 5, 3: 6}\n",
        "{1: array([1, 2]), 2: array([], dtype=int32), 3: array([3])}\n",
        "inv: {1: [1], 2: [1], 3: [3]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [3]}\n",
        "1 1 4\n",
        "2 1 5\n",
        "3 3 6\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [2, 3], 3: [2, 3]}\n",
        "3\n",
        "1 [1, 2] 1 2 6\n",
        "2 [2, 3] 2 3 42\n",
        "3 [2, 3] 2 3 12\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([1]), 2: array([1, 3]), 3: array([1])}\n",
        "inv {1: [1, 2, 3], 3: [2]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv: {1: [1], 2: [2]}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv {1: [1], 2: [2]}\n",
        "1 1 3\n",
        "2 2 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 42\n",
        "2 [1, 2] 1 2 12\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([2]), 2: array([1])}\n",
        "inv: {1: [2], 2: [1]}\n",
        "{1: array([], dtype=int32), 2: array([2])}\n",
        "inv {2: [2]}\n",
        "2 1 4\n",
        "1 2 3\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 25\n",
        "2 [1, 2] 1 2 11\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4, 4: 5}\n",
        "{1: array([1, 2, 3, 4])}\n",
        "inv: {1: [1], 2: [1], 3: [1], 4: [1]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "4 1 5\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv: {1: [1], 2: [2]}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv {1: [1], 2: [2]}\n",
        "1 1 3\n",
        "2 2 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 40\n",
        "2 [1, 2] 1 2 11\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2, 3: 3}\n",
        "map Ep |-> node {1: 4, 2: 5, 3: 6, 4: 7, 5: 8}\n",
        "{1: array([1, 2]), 2: array([3]), 3: array([4, 5])}\n",
        "inv: {1: [1], 2: [1], 3: [2], 4: [3], 5: [3]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4]), 5: array([5])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4], 5: [5]}\n",
        "1 1 4\n",
        "2 1 5\n",
        "3 2 6\n",
        "4 3 7\n",
        "5 3 8\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [2, 3]}\n",
        "2\n",
        "1 [1, 2] 1 2 6\n",
        "2 [2, 3] 2 3 26\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4, 4: 5}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([], dtype=int32), 2: array([1]), 3: array([2]), 4: array([3])}\n",
        "inv {1: [2], 2: [3], 3: [4]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4, 4: 5}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([], dtype=int32), 2: array([1]), 3: array([2]), 4: array([3])}\n",
        "inv {1: [2], 2: [3], 3: [4]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2, 3: 3}\n",
        "map Ep |-> node {1: 4, 2: 5, 3: 6, 4: 7, 5: 8}\n",
        "{1: array([1, 2]), 2: array([4]), 3: array([3, 5])}\n",
        "inv: {1: [1], 2: [1], 3: [3], 4: [2], 5: [3]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4]), 5: array([5])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4], 5: [5]}\n",
        "1 1 4\n",
        "2 1 5\n",
        "4 2 7\n",
        "3 3 6\n",
        "5 3 8\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [2, 3]}\n",
        "2\n",
        "1 [1, 2] 1 2 13\n",
        "2 [2, 3] 2 3 4\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [3]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2, 3: 3}\n",
        "map Ep |-> node {1: 4, 2: 5, 3: 6, 4: 7, 5: 8}\n",
        "{1: array([1, 3]), 2: array([2, 4]), 3: array([5])}\n",
        "inv: {1: [1], 2: [2], 3: [1], 4: [2], 5: [3]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([5]), 5: array([4])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [5], 5: [4]}\n",
        "1 1 4\n",
        "3 1 6\n",
        "2 2 5\n",
        "4 2 7\n",
        "5 3 8\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 3], 2: [2, 3]}\n",
        "2\n",
        "1 [1, 3] 1 3 12\n",
        "2 [2, 3] 2 3 13\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4, 3: 5, 4: 6}\n",
        "{1: array([1, 2]), 2: array([3, 4])}\n",
        "inv: {1: [1], 2: [1], 3: [2], 4: [2]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4]}\n",
        "1 1 3\n",
        "2 1 4\n",
        "3 2 5\n",
        "4 2 6\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2]}\n",
        "1\n",
        "1 [1, 2] 1 2 26\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  False\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv: {1: [1], 2: [2]}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv {1: [1], 2: [2]}\n",
        "1 1 3\n",
        "2 2 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 41\n",
        "2 [1, 2] 1 2 13\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv: {1: [1], 2: [2]}\n",
        "{1: array([1]), 2: array([2])}\n",
        "inv {1: [1], 2: [2]}\n",
        "1 1 3\n",
        "2 2 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 2]}\n",
        "2\n",
        "1 [1, 2] 1 2 42\n",
        "2 [1, 2] 1 2 12\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4, 4: 5}\n",
        "{1: array([1, 2, 3, 4])}\n",
        "inv: {1: [1], 2: [1], 3: [1], 4: [1]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "4 1 5\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([1]), 2: array([1, 3]), 3: array([1])}\n",
        "inv {1: [1, 2, 3], 3: [2]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4, 3: 5, 4: 6, 5: 7}\n",
        "{1: array([1, 2]), 2: array([3, 4, 5])}\n",
        "inv: {1: [1], 2: [1], 3: [2], 4: [2], 5: [2]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4]), 5: array([5])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4], 5: [5]}\n",
        "1 1 3\n",
        "2 1 4\n",
        "3 2 5\n",
        "4 2 6\n",
        "5 2 7\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2]}\n",
        "1\n",
        "1 [1, 2] 1 2 3\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [3]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [3]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2, 3: 3}\n",
        "map Ep |-> node {1: 4, 2: 5, 3: 6, 4: 7, 5: 8}\n",
        "{1: array([2]), 2: array([1, 4]), 3: array([3, 5])}\n",
        "inv: {1: [2], 2: [1], 3: [3], 4: [2], 5: [3]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4]), 5: array([5])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4], 5: [5]}\n",
        "2 1 5\n",
        "1 2 4\n",
        "4 2 7\n",
        "3 3 6\n",
        "5 3 8\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2], 2: [1, 3]}\n",
        "2\n",
        "1 [1, 2] 1 2 13\n",
        "2 [1, 3] 1 3 14\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4, 3: 5, 4: 6, 5: 7}\n",
        "{1: array([2, 3]), 2: array([1, 4, 5])}\n",
        "inv: {1: [2], 2: [1], 3: [1], 4: [2], 5: [2]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3]), 4: array([4]), 5: array([5])}\n",
        "inv {1: [1], 2: [2], 3: [3], 4: [4], 5: [5]}\n",
        "2 1 4\n",
        "3 1 5\n",
        "1 2 3\n",
        "4 2 6\n",
        "5 2 7\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2]}\n",
        "1\n",
        "1 [1, 2] 1 2 8\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1}\n",
        "map Ep |-> node {1: 2, 2: 3, 3: 4}\n",
        "{1: array([1, 2, 3])}\n",
        "inv: {1: [1], 2: [1], 3: [1]}\n",
        "{1: array([1]), 2: array([2]), 3: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [3]}\n",
        "1 1 2\n",
        "2 1 3\n",
        "3 1 4\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {}\n",
        "0\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "condition Ep seuls False\n",
        "condition Bp  True\n",
        "map Bp |-> node {1: 1, 2: 2}\n",
        "map Ep |-> node {1: 3, 2: 4, 3: 5, 4: 6}\n",
        "{1: array([1, 2]), 2: array([3, 4])}\n",
        "inv: {1: [1], 2: [1], 3: [2], 4: [2]}\n",
        "{1: array([1]), 2: array([2]), 3: array([4]), 4: array([3])}\n",
        "inv {1: [1], 2: [2], 3: [4], 4: [3]}\n",
        "1 1 3\n",
        "2 1 4\n",
        "3 2 5\n",
        "4 2 6\n",
        "LINKING BP to BP\n",
        "inv EDGES : BP {1: [1, 2]}\n",
        "1\n",
        "1 [1, 2] 1 2 18\n"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(20,20)\n",
      "for imG,n in zip(imgraph, range(1,26+1)):\n",
      "    subplot(6,5,n,xticks=[],yticks=[])\n",
      "    imshow(imG, interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KFXz22WcAgAkTJqBChQpSh0skq8TERJQvXx5paWnYt2+f6HCea8SIESgsLISV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\nLl2qxMREHT16VMePH9f58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       "text": [
        "<matplotlib.figure.Figure at 0x9ee0f28c>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Varying size"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "imphabet = []\n",
      "for size in [40,50,60,65,90]:\n",
      "    imLetter = makeLetterImage('a', size)\n",
      "    skeletter = mh.thin(imLetter)\n",
      "    BP =  branchedPoints(skeletter, showSE=False)\n",
      "    EP = endPoints(skeletter)\n",
      "    imphabet.append(imLetter+1.0*skeletter+2.0*BP+3.0*EP)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 67
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "graphs = []\n",
      "for l in imphabet:\n",
      "    graph_size = nx.MultiGraph()\n",
      "    graphs.append(C8_Skeleton_To_Graph_01(graph_size, l))\n",
      "    nx.write_dot(graph_,'multi.dot')\n",
      "    !neato -T png multi.dot > multi.png\n",
      "    imgraph.append(mh.imread('multi.png')) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12,12)\n",
      "for im,n in zip(imphabet, [1,2,3,4,5]):\n",
      "    subplot(1,5,n,xticks=[],yticks=[])\n",
      "    imshow(im,interpolation='nearest')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAqwAAACcCAYAAAC6J/m0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nILT/A0eOuteo7+USAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9ed7202c>"
       ]
      }
     ],
     "prompt_number": 68
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Try another graph library: graph_tool"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import graph_tool.all as gt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mG = gt.Graph(directed = False)\n",
      "edgeP_image = mG.new_edge_property(\"object\")\n",
      "vertexP_image= mG.new_edge_property(\"object\")\n",
      "\n",
      "mG.edge_properties[\"image\"] = edgeP_image\n",
      "\n",
      "v1 = mG.add_vertex()\n",
      "v2 = mG.add_vertex()\n",
      "v3 = mG.add_vertex()\n",
      "mG.add_edge(v1,v1)\n",
      "mG.add_edge(v1,v2)\n",
      "mG.add_edge(v1,v2)\n",
      "mG.add_edge(v2,v3)\n",
      "mG.add_edge(v1,v3)\n",
      "\n",
      "print mG.list_properties()\n",
      "\n",
      "gt.graph_draw(mG, output_size=(260, 260))\n",
      "for e in mG.edges():\n",
      "    print e"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "image          (edge)    (type: python::object)\n",
        "None\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RoD38dst2CNdByR+g/GcwYgOUdGUeR9sFvB14IBdfYz6zHkKWOKItbtJnS6ZH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\n",
       "text": [
        "<IPython.core.display.Image at 0x9ed72b2c>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(0, 0)\n",
        "(0, 1)\n",
        "(0, 1)\n",
        "(0, 2)\n",
        "(1, 2)\n"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}