06-Minimal Path with KeyPoint Detection-L Euclidian Distance-Success.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from skimage.io import imread\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from PIL import Image, ImageOps\n",
    "from __future__ import division\n",
    "from math import inf, sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from skimage import data, color\n",
    "from skimage.transform import rescale, resize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "im = Image.open(\"image/01_sample\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQIAAAC6CAIAAADKw9SrAAAMnklEQVR4nO3da0xb5QPH8ael9wtd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\nABBkAECQAQBBBgAEGQAQQv4Dm9+D6ccv6EwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.PngImagePlugin.PngImageFile image mode=RGB size=258x186 at 0x7F1D3BC80A20>"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "im"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(186, 258)\n"
     ]
    }
   ],
   "source": [
    "im_array = np.asarray(im.convert('L'))\n",
    "print(im_array.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tdesfont/.local/lib/python3.5/site-packages/skimage/transform/_warps.py:84: UserWarning: The default mode, 'constant', will be changed to 'reflect' in skimage 0.15.\n",
      "  warn(\"The default mode, 'constant', will be changed to 'reflect' in \"\n"
     ]
    }
   ],
   "source": [
    "im_array = resize(im_array, (100, 100))*256"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZqZkZ0A9YCswFLozXGQbMyE6JIpJp6ezjzyc6iPcusDh+TTkwCrjFzFYCbYFJWaxTRDIo\nrVNvufsdwB27LP4U6JXxikQk6zRzTyRACr5IgBR8kQAp+CIBUvBFAqTgiwRIwRcJkIIvEiAFXyRA\nCr5IgBR8kQAp+CIBUvBFAqTgiwRIwRcJkIIvEiAFXyRACr5IgBR8kQAp+CIBUvBFAqTgiwRIwRcJ\nkIIvEiAFXyRACr5IgBR8kQAp+CIBUvBFAqTgiwRIwRcJkIIvEiAFXyRACr5IgBR8kQAp+CIBUvBF\nAmTunrs3M9sAbAU25uxNG6YdhVMrFFa9hVQrFE69B7l7+7pWymnwAcyswt175vRN66mQaoXCqreQ\naoXCq7cuGuqLBEjBFwlQEsEvT+A966uQaoXCqreQaoXCq3ePcr6PLyLJ01BfJEA5C76Z9Tez5Wa2\n0sxG5+p902Vmnc1srpktNbMlZnZjvLyNmb1iZivi29ZJ11rNzIrM7D0zmxU/7mpm8+Nt/JSZlSRd\nYzUza2Vm083sIzNbZmbH5+u2NbOb438DH5rZVDNrns/btj5yEnwzKwJ+D5wFdAcuNrPuuXjvvbAD\nGOnu3YHewHVxjaOBOe7eDZgTP84XNwLLajweB4x390OBzcDwRKqq3QTgZXc/HDiKqO6827Zm1hH4\nNdDT3XsARcAQ8nvb7j13z/oPcDwwu8bjMcCYXLx3A2qeAZwOLAfK4mVlwPKka4tr6UQUlr7ALMCI\nJpgU17bNE661JbCK+JhSjeV5t22BjsBqoA1QHG/bM/N129b3J1dD/eqNWW1NvCwvmVkX4BhgPtDB\n3Svjp9YBHRIqa1f3A7cDP8SP2wJb3H1H/DiftnFXYAPwWLxr8oiZtSAPt627rwXuAb4AKoGvgIXk\n77atFx3c24WZ7Qs8C9zk7l/XfM6jP/eJfwxiZgOB9e6+MOla0lQMHAtMdPdjiKZt/2hYn0fbtjUw\nmOiP1QFAC6B/okVlQa6CvxboXONxp3hZXjGzpkShn+Luz8WLvzSzsvj5MmB9UvXVcCIwyMw+A6YR\nDfcnAK3MrDheJ5+28RpgjbvPjx9PJ/pDkI/b9jRglbtvcPftwHNE2ztft2295Cr47wDd4iOjJUQH\nS2bm6L3TYmYGTAKWuft9NZ6aCQyL7w8j2vdPlLuPcfdO7t6FaFu+5u6XAnOBC+PV8qJWAHdfB6w2\ns8PiRf2ApeThtiUa4vc2s9L430R1rXm5besthwdNBgAfA58A/5j0wY1a6juJaKj5AbAo/hlAtO88\nB1gBvAq0SbrWXeruA8yK7x8MLABWAs8AzZKur0adRwMV8fZ9AWidr9sWuBP4CPgQeBxols/btj4/\nmrknEiAd3BMJkIIvEiAFXyRACr5IgBR8kQAp+CIBUvBFAqTgiwTo/wAALmtnytHxMQAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d3b742c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(im_array)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minimal Path with KeyPoint Detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "W = im_array\n",
    "n = im_array.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_start = np.where(np.sum(im_array<200, axis=0) != 0)[0][0]\n",
    "y_start = np.where(np.sum(im_array<200, axis=1) != 0)[0][0]\n",
    "start_point = (x_start, y_start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "start_point = (28, 39)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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i5bHxsdUX7Fz1oOWzrecfycJgm9kpAgBIFAEAVKIIAKASRQAAlYPWAByBA09eHpv3XP1h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\neHIZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d3b7f8b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 10))\n",
    "plt.scatter(start_point[0], start_point[1], color='g', \n",
    "            edgecolor='k', alpha=0.6, marker='^', s=500)\n",
    "plt.imshow(im_array, cmap='jet')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "neigh = np.array([[1, -1, 0, 0], [0, 0,  1, -1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### Operation of boundary enforcement\n",
    "boundary = lambda x: np.mod(x,n)\n",
    "# From 1d index to 2d coordinates\n",
    "ind2sub1 = lambda k: [int( (k-np.fmod(k,n))/n ), np.fmod(k,n)]\n",
    "# From 2d coordinates to 1d index\n",
    "sub2ind1 = lambda u: int( u[0]*n + u[1] )\n",
    "# Get Neigh 2d coordinates in constrained space\n",
    "Neigh = lambda k,i: sub2ind1(boundary(ind2sub1(k) + neigh[:,i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def is_border(pixel_coord):\n",
    "    \"\"\"\n",
    "        Input:\n",
    "            pixel_coord: <np.array of length 2>\n",
    "    \"\"\"\n",
    "    global n\n",
    "    return bool(np.sum(pixel_coord==0) + np.sum(pixel_coord==n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Neigh(k, i):\n",
    "    neigh_coord = boundary(ind2sub1(k) + neigh[:,i])\n",
    "    if is_border(neigh_coord):\n",
    "        return None\n",
    "    else:\n",
    "        return sub2ind1(neigh_coord)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lmbda = 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d3b765940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Done.\n"
     ]
    }
   ],
   "source": [
    "x0 = [start_point[1], start_point[0]]\n",
    "# Initial stack\n",
    "I = [sub2ind1(x0)]\n",
    "\n",
    "# Inital distance to x0 (Update through min so inf)\n",
    "D = np.ones((n,n)) + inf\n",
    "u = ind2sub1(I)\n",
    "D[u[0],u[1]] = 0\n",
    "\n",
    "# To visit or not\n",
    "S = np.zeros((n,n))\n",
    "S[u[0],u[1]] = 1\n",
    "\n",
    "extract   = lambda x,I: x[I]\n",
    "\n",
    "def extract1d(x, I):\n",
    "    if I is None:\n",
    "        return inf\n",
    "    else: \n",
    "        return extract(x.flatten(),I)\n",
    "    \n",
    "count = 0\n",
    "keypoint_found = False\n",
    "\n",
    "while I and count<inf and not keypoint_found:\n",
    "    \n",
    "    count += 1\n",
    "    \n",
    "    j = np.argsort( extract1d(D,I)  )\n",
    "    if np.ndim(j)==0:\n",
    "        j = [j]   # make sure that j is a list a not a singleton\n",
    "        \n",
    "    j = j[0]\n",
    "    i = I[j]         \n",
    "    a = I.pop(j)\n",
    "    \n",
    "    u = ind2sub1(i);\n",
    "    S[u[0],u[1]] = -1\n",
    "    \n",
    "    \n",
    "    J = [] \n",
    "    for k in np.arange(0,4):\n",
    "        v_ = Neigh(i,k)\n",
    "        if v_ is None:\n",
    "             continue\n",
    "        j = v_\n",
    "        if extract1d(S,j)!=-1:\n",
    "            # add to the list of point to update\n",
    "            J.append(j)\n",
    "            if extract1d(S,j)==0:\n",
    "                # add to the front\n",
    "                u = ind2sub1(j)\n",
    "                S[u[0],u[1]] = 1\n",
    "                I.append(j)\n",
    "\n",
    "    DNeigh = lambda D,k: extract1d(D,Neigh(j,k))\n",
    "    \n",
    "    # Update distance of the points\n",
    "    for j in J:\n",
    "        \n",
    "        # Update by L1 min\n",
    "        dx = min(DNeigh(D,0), DNeigh(D,1))\n",
    "        dy = min(DNeigh(D,2), DNeigh(D,3))\n",
    "        u = ind2sub1(j)\n",
    "        w = extract1d(W,j);\n",
    "\n",
    "        Delta = 2*w - (dx-dy)**2\n",
    "        if (Delta>=0):\n",
    "            D[u[0],u[1]] = (dx + dy + sqrt(Delta))/ 2\n",
    "        else:\n",
    "            D[u[0],u[1]] = min(dx + w, dy + w)\n",
    "    \n",
    "    # Calcul de la distance euclidienne\n",
    "    x = np.where(S==1)[0]\n",
    "    y = np.where(S==1)[1]\n",
    "    \n",
    "    Front = np.array([y, x]).T\n",
    "    L = np.linalg.norm(Front - np.array(start_point), axis=1)\n",
    "    \n",
    "    keypoint_index = np.argmax(L)\n",
    "    keypoint = Front[keypoint_index]\n",
    "    max_euclidian_distance = L[keypoint_index]\n",
    "    \n",
    "    if max_euclidian_distance > lmbda:\n",
    "        keypoint_found = True\n",
    "\n",
    "plt.imshow(D)\n",
    "plt.show()\n",
    "\n",
    "print('Done.')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ElPgiEVLii0RIiS8SISW+SISU+CIRUuKLREiJLxIhJb5IhNJKfDO73szeNLM3zOxhMys3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\nJpbTrkPK87wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1d3b7655c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(W)\n",
    "plt.scatter(keypoint[0], keypoint[1])\n",
    "plt.imshow(D)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}