07-Open Curve Detection.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "\n",
    "from skimage.io import imread\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from PIL import Image, ImageOps\n",
    "from math import inf, sqrt\n",
    "from skimage import data, color\n",
    "from skimage.transform import rescale, resize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class FastMarching:\n",
    "\n",
    "    def __init__(self, W, start_point, end_point=None):\n",
    "        self.n = W.shape[0]\n",
    "        self.W = W\n",
    "        self.start_point = start_point\n",
    "        self.end_point = end_point\n",
    "        self.neigh = np.array([[1, -1, 0, 0], [0, 0,  1, -1]])\n",
    "        self.D = None\n",
    "        self.S = None\n",
    "\n",
    "    def boundary(self, x):\n",
    "        return np.mod(x, self.n)\n",
    "\n",
    "    def ind2sub1(self, k):\n",
    "        return [int( (k-np.fmod(k,self.n))/self.n ), np.fmod(k,self.n)]\n",
    "\n",
    "    def sub2ind1(self, u):\n",
    "        return int(u[0]*self.n + u[1])\n",
    "\n",
    "    def Neigh(self, k, i):\n",
    "        neigh_coord = self.boundary(self.ind2sub1(k) + self.neigh[:,i])\n",
    "        if self.is_border(neigh_coord):\n",
    "            return None\n",
    "        else:\n",
    "            return self.sub2ind1(neigh_coord)\n",
    "\n",
    "    def is_border(self, pixel_coord):\n",
    "        return bool(np.sum(pixel_coord==0) + np.sum(pixel_coord==self.n))\n",
    "\n",
    "    def extract(self, x, I):\n",
    "        return x[I]\n",
    "\n",
    "    def extract1d(self, x, I):\n",
    "        if I is None:\n",
    "            return inf\n",
    "        else:\n",
    "            return self.extract(x.flatten(), I)\n",
    "\n",
    "    def fast_marching(self, lmbda=5, max_iter=inf, end_point=None):\n",
    "        \n",
    "        x0 = [self.start_point[1], self.start_point[0]]\n",
    "        I = [self.sub2ind1(x0)]\n",
    "\n",
    "        # Initial distance to x0\n",
    "        D = np.ones((self.n, self.n)) + inf\n",
    "        u = self.ind2sub1(I)\n",
    "        D[u[0], u[1]] = 0\n",
    "\n",
    "        # To visit or not\n",
    "        S = np.zeros((self.n, self.n))\n",
    "        S[u[0], u[1]] = 1\n",
    "\n",
    "        count = 0\n",
    "        keypoint_found = False\n",
    "        endpoint_found = False\n",
    "\n",
    "        while I and count < max_iter and not keypoint_found and not endpoint_found:\n",
    "\n",
    "            count += 1\n",
    "            j = np.argsort(self.extract1d(D, I))\n",
    "            if np.ndim(j) == 0:\n",
    "                j = [j]\n",
    "\n",
    "            j = j[0]\n",
    "            i = I[j]\n",
    "            a = I.pop(j)\n",
    "\n",
    "            u = self.ind2sub1(i)\n",
    "            S[u[0], u[1]] = -1\n",
    "\n",
    "            J = []\n",
    "            for k in np.arange(0, 4):\n",
    "                v_ = self.Neigh(i, k)\n",
    "                if v_ is None:\n",
    "                    continue\n",
    "                j = v_\n",
    "                if self.extract1d(S, j) != -1:\n",
    "                    J.append(j)\n",
    "                    if self.extract1d(S, j) == 0:\n",
    "                        # add to the front\n",
    "                        u = self.ind2sub1(j)\n",
    "                        S[u[0], u[1]] = 1\n",
    "                        I.append(j)\n",
    "\n",
    "            DNeigh = lambda D, k: self.extract1d(D, self.Neigh(j, k))\n",
    "\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 = self.ind2sub1(j)\n",
    "                w = self.extract1d(self.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",
    "            # Stopping criterion for keypoint\n",
    "            if lmbda < inf:\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",
    "                self.keypoint = keypoint\n",
    "\n",
    "                if max_euclidian_distance > lmbda:\n",
    "                    keypoint_found = True\n",
    "            \n",
    "            if end_point is not None:\n",
    "                if D[end_point[1], end_point[0]] < inf:\n",
    "                    endpoint_found = True\n",
    "                    \n",
    "        self.D = D\n",
    "        self.S = S\n",
    "        \n",
    "\n",
    "    def visualize_D(self):\n",
    "        if self.D is not None:\n",
    "            plt.figure(figsize=(10, 10))\n",
    "            plt.title('Distance')\n",
    "            plt.scatter(self.start_point[0], self.start_point[1])\n",
    "            plt.imshow(self.D, cmap='jet')\n",
    "            plt.show()\n",
    "\n",
    "    def visualize_S(self):\n",
    "        if self.S is not None:\n",
    "            fig = plt.figure(figsize=(10, 10))\n",
    "            plt.title('Active and Inactive points')\n",
    "            plt.scatter(self.start_point[0], self.start_point[1])\n",
    "            im = plt.imshow(self.S, cmap='jet')\n",
    "            fig.colorbar(im, orientation='horizontal')\n",
    "            plt.show()\n",
    "\n",
    "    def backpropagate(self, end_point, max_iter=300):\n",
    "        self.end_point = end_point\n",
    "        \n",
    "        min_path = [list(self.end_point)]\n",
    "        count = 0\n",
    "\n",
    "        while np.prod(min_path[-1]==self.start_point) != 1 and count < max_iter:\n",
    "\n",
    "            point = min_path[-1]\n",
    "            neighbors_mat = np.array(list(point)).reshape(2, 1) + self.neigh\n",
    "            min_distance = np.inf\n",
    "\n",
    "            for k in range(4):\n",
    "                coord = neighbors_mat[:, k]\n",
    "                distance = self.D[coord[1], coord[0]]\n",
    "                if distance < min_distance:\n",
    "                    min_distance = distance\n",
    "                    next_point = coord\n",
    "\n",
    "            min_path.append(list(next_point))\n",
    "\n",
    "            count += 1\n",
    "\n",
    "        self.min_path = np.array(min_path)\n",
    "\n",
    "    def visualize_min_path(self):\n",
    "\n",
    "        start_point = self.start_point\n",
    "        end_point = self.end_point\n",
    "\n",
    "        plt.figure(figsize=(10, 10))\n",
    "        plt.title('User specified start and end points:')\n",
    "        plt.scatter(start_point[0], start_point[1], color='g', edgecolor='k', s=200, marker='^', alpha=0.6, label='Start point')\n",
    "        plt.scatter(end_point[0], end_point[1], color='r', edgecolor='k', s=200, marker='^', alpha=0.6, label='End point')\n",
    "        plt.scatter(self.min_path[:, 0], self.min_path[:, 1], color='r', edgecolor='k', alpha=0.3)\n",
    "        plt.imshow(self.W, cmap='gray')\n",
    "        plt.legend()\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "# Image loader\n",
    "im = Image.open(\"image/01_sample\")\n",
    "im_array = np.asarray(im.convert('L'))\n",
    "im_array = resize(im_array, (100, 100))*256"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Initialisation of potential function matrix and starting point\n",
    "\n",
    "# Potential\n",
    "W = im_array\n",
    "n = im_array.shape[0]\n",
    "# Matrix\n",
    "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",
    "p = (x_start, y_start)\n",
    "S = [p]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Open Curve Detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Open Curve Detection using the Fast Marching Module\n",
    "# Input W, S\n",
    "StopDetection = False\n",
    "lmbda = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# FMM(S, lmbda)\n",
    "start_point = S[0]\n",
    "fm = FastMarching(W, start_point)\n",
    "fm.fast_marching(lmbda=5)\n",
    "k1 = tuple(fm.keypoint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 21)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6vkiA1PFFiuzKK68EMpfvevXVV4tegzq+SIDU8UUSkkSnj6njiwRIwRcJkIIvEiAFXyRA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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f288fb09630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(W, cmap='gray')\n",
    "plt.imshow(fm.D, cmap='jet')\n",
    "plt.scatter(start_point[0], start_point[1], edgecolor='k', alpha=1, color='g', label='starting point')\n",
    "plt.scatter(k1[0], k1[1], edgecolor='k', alpha=1, color='r', label='end point')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fm.backpropagate(k1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v6upqnM+aNatx/uEPf7hx3tra2jhPkssvv7xxvvfee3f7GQAAQ5kdKgAAgEKC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\nMCSoAAAAhgQVAADAkKACAAAY+idrfhyO0zkZMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f288fa37da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15, 15))\n",
    "plt.imshow(W, cmap='gray')\n",
    "plt.scatter(fm.min_path[:, 0], fm.min_path[:, 1], edgecolor='k', color='y', alpha=0.5, s=30)\n",
    "plt.scatter(start_point[0], start_point[1], edgecolor='k', alpha=1, color='g', label='starting point', s=80)\n",
    "plt.scatter(k1[0], k1[1], edgecolor='k', alpha=1, color='r', label='end point', s=80)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "C = fm.min_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(11, 16), (12, 21)]\n"
     ]
    }
   ],
   "source": [
    "S.append(k1)\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m = {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m[start_point] = k1\n",
    "m[k1] = start_point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12, 21)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(11, 16): (12, 21), (12, 21): (11, 16)}"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Find keypoint k2**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(11, 16), (12, 21)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# FMM(S, lmbda)\n",
    "start_point = S[1]\n",
    "fm = FastMarching(W, start_point)\n",
    "fm.fast_marching(lmbda=5)\n",
    "k2 = tuple(fm.keypoint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(11, 16)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k2 # Symmétrie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f288fb095c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(W, cmap='gray')\n",
    "plt.imshow(fm.D, cmap='jet')\n",
    "plt.scatter(start_point[0], start_point[1], edgecolor='k', alpha=1, color='g', label='starting point')\n",
    "plt.scatter(k2[0], k2[1], edgecolor='k', alpha=1, color='r', label='end point')\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
}