A ipython notebook showing how to convert the skeleton of a binary image into a networkw graph

FromSkeletonToGraph.ipynb

{
 "metadata": {
  "name": "from skeleton to graph"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import networkx as nx\nfrom PIL import Image, ImageDraw, ImageFont",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "\nfrom skimage import morphology as mo\nfrom skimage import measure as mea\nimport mahotas as mh",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": "Some functions need to work: extraction from a skeleton of branched points, of end-points, pruning is also needed"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def branchedPoints(skel, showSE=True):\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    Y2=np.array([[1, 0, 2], \n                 [0, 1, 1], \n                 [1, 0, 2]])\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\ndef 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\ndef 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": "heading",
     "level": 3,
     "metadata": {},
     "source": "Model images will be used, images of letters can do the job, so we need to produce images of letters using PIL"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def makeLetterImage(character, size):\n    image = Image.new(\"RGBA\", (600,150), (255,255,255))\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": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "imA = makeLetterImage(\"A\", 70)\nimB = makeLetterImage(\"B\", 70)\nimH = makeLetterImage(\"H\", 70)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "\nsubplot(131)\nimshow(imA, interpolation='nearest')\nsubplot(132)\nimshow(imB, interpolation='nearest')\nsubplot(133)\nimshow(imH, interpolation='nearest')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": "<matplotlib.image.AxesImage at 0x3338490>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": "<matplotlib.figure.Figure at 0x3285510>"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": "Let's generate the C4 skeleton (medial axis) of a binary image with scikits-image"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "medaxA = mo.medial_axis(imA)\nma_bpA = branchedPoints(medaxA, showSE = False)\nma_epA = endPoints(medaxA)\nma_edgesA = edges_from_C8skel(mo.skeletonize(imA))#np.logical_not(ma_bpA)*medaxA",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(12,12)\nsubplot(141, xticks=[],yticks=[])\ntitle('Medial Axis (C4)')\nimshow(medaxA, interpolation='nearest')\nsubplot(142, xticks=[],yticks=[])\ntitle('Branched Points')\nimshow(ma_bpA, interpolation='nearest')\nsubplot(143, xticks=[],yticks=[])\ntitle('End Points')\nimshow(ma_epA, interpolation='nearest')\nsubplot(144, xticks=[],yticks=[])\ntitle('Labeling of medial axis-BP')\nimshow(ma_edgesA, interpolation='nearest')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": "<matplotlib.image.AxesImage at 0x56ffb10>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AAIArEWQBAADgSgRZAAAAuBJBFgAAAK5EkAUAAIArVejht+BboOHHGLIMAABI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\nAADgSgRZAAAAuNL/A3q8o0vd5+P8AAAAAElFTkSuQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x4cc2e90>"
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## The aim is to extract the skeleton edges defined as the skeleton deprived of the branched points \n### Let's label the edges obtained from medial axis computed with scikit-image:\n### 1.with mahotas using a neighborhood defined on 4 pixels. \n### 2.with skimage using a neighborhood defined on 8 pixels."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "edgesA_lab_mh4, _ = mh.label(ma_edgesA)\nedgesA_lab_sk8 = mo.label(ma_edgesA, neighbors=8)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## C4 or C8 labelling of C4 skeleton fails to isolate edges:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(7,7)\nsubplot(121, xticks=[],yticks=[])\nimshow(edgesA_lab_mh4, interpolation='nearest')\nsubplot(122, xticks=[],yticks=[])\nimshow(edgesA_lab_sk8, interpolation='nearest')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": "<matplotlib.image.AxesImage at 0x5810bd0>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAADeCAYAAAAacfYeAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nqNcpuUlGAAAAAElFTkSuQmCC\n",
       "text": "<matplotlib.figure.Figure at 0x58459d0>"
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Let's generate a skelton of the letter \"A\" by morphological thinning implemented in mahotas. Contrary to scikit-image, the skeleton is computed with a neighborhood of 8 pixels.\n###The resulting skeleton is compared to the skeletonization algo implemented in scikit-image."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "skelC8 = mh.thin(imA)\nskel_sk = mo.skeletonize(imA)\nth_bpA = branchedPoints(skelC8, showSE = False) > 0\nth_epA = endPoints(skelC8) > 0\nth_edgesA = np.logical_not(th_bpA)*skelC8\n ",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "figsize(16,12)\nsubplot(151, xticks=[],yticks=[])\ntitle('mahotas: skeleton by thining')\nimshow(skelC8, interpolation='nearest')\nsubplot(152, xticks=[],yticks=[])\ntitle('Branched Points')\nimshow(th_bpA, interpolation='nearest')\nsubplot(153, xticks=[],yticks=[])\ntitle('End-Points')\nimshow(th_epA, interpolation='nearest')\nsubplot(154, xticks=[],yticks=[])\ntitle('Binary Edges : thin-BP')\nimshow(th_edgesA, interpolation='nearest')\nsubplot(155, xticks=[],yticks=[])\ntitle('skimage skeletonization')\nimshow(skel_sk, interpolation='nearest')",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 24,
       "text": "<matplotlib.image.AxesImage at 0x682d650>"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAA5UAAADSCAYAAADaHeSaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nfuvPycn