mask2poly.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polygon fitting from binary mask\n",
    "\n",
    "First we create a mask with binary blobs and then add a black border of one pixel to this mask."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage.io import imread\n",
    "from skimage import data\n",
    "import numpy as np\n",
    "from skimage import io\n",
    "\n",
    "binary_mask = data.binary_blobs(length=98, blob_size_fraction=0.1)\n",
    "binary_mask = np.pad(binary_mask, pad_width=1)\n",
    "\n",
    "io.imshow(binary_mask)\n",
    "io.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can determine all contours of the blobs in this binary mask. The level argument specifies the value along which to find contours in the mask. It should be half the minimum and maximum value. Since we have a binary mask, we choose 0.5.\n",
    "\n",
    "\"This means that to find reasonable contours, it is best to find contours midway between the expected “light” and “dark” values. In particular, given a binarized array, do not choose to find contours at the low or high value of the array. This will often yield degenerate contours, especially around structures that are a single array element wide. Instead choose a middle value, as above.\" (https://scikit-image.org/docs/stable/api/skimage.measure.html#skimage.measure.find_contours)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of contours: 14\n"
     ]
    }
   ],
   "source": [
    "contours_list = measure.find_contours(binary_mask, level=0.5)\n",
    "print(\"Number of contours:\", len(contours_list))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we want to find a polygon for each contour that fits as close as possible by using the approximate_polygon function from skimage. With the tolerance argument we can control the accuracy of the fit. Higher values cause a lower accuracy of fitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Contour 00 has  32 points.\n",
      "Contour 01 has   9 points.\n",
      "Contour 02 has  12 points.\n",
      "Contour 03 has  12 points.\n",
      "Contour 04 has  14 points.\n",
      "Contour 05 has   9 points.\n",
      "Contour 06 has  50 points.\n",
      "Contour 07 has  11 points.\n",
      "Contour 08 has  11 points.\n",
      "Contour 09 has   9 points.\n",
      "Contour 10 has  53 points.\n",
      "Contour 11 has   3 points.\n",
      "Contour 12 has   6 points.\n",
      "Contour 13 has   6 points.\n"
     ]
    }
   ],
   "source": [
    "polygons = []\n",
    "for i, contour in enumerate(contours_list):\n",
    "    polygon_points = measure.approximate_polygon(contour, tolerance=1)\n",
    "    polygons.append(polygon_points)\n",
    "    print(\"Contour {:02d} has {: >3} points.\".format(i, len(polygon_points)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the polygons, we can use them to create binary masks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAARgAAAEYCAYAAACHjumMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAMEElEQVR4nO3dUajed33H8fdniaVru9JkIyEm7dpCqBNBK2G01otidThXTG+KFQqZTHKzzSobLvXOi4EXIvZiDEJUAg4l1EJCLqwhKniz0NQg2sYspR1p7LHpyLBjV5Z+d/H8Gw/uJM+Tc873OfmfvF8QnvP8z3Oe/++Xnrz7+/2f5ySpKiSpwx+s9QAkrV8GRlIbAyOpjYGR1MbASGpjYCS1WVFgknw8yZkkLyXZt1qDkrQ+ZLnvg0myAfgP4GPAeeA54NNV9eLqDU/SmG1cwdf+OfBSVb0MkOS7wG7gsoFJ4rv6pHWoqrLU8ZVskbYDry66f344JknAylYwSxXr/61QkuwF9q7gPJJGaiWBOQ/cvuj+DuC1339QVe0H9oNbJOl6s5It0nPAziR3JbkBeAw4sjrDkrQeLHsFU1VvJfk74FlgA/DNqnph1UYmafSW/TL1sk7mFklalzpeRZKkKzIwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGpjYCS1MTCS2hgYSW0MjKQ2BkZSGwMjqY2BkdTGwEhqY2AktTEwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGozNTBJbk/yoySnk7yQ5Inh+OYkx5KcHW439Q9X0pikqq78gGQbsK2qfprkj4DngUeAvwYuVtVXkuwDNlXVP015riufTNIoVVWWOj51BVNVC1X10+Hj/wFOA9uB3cDB4WEHmURHki65qmswSe4E7gVOAFuragEmEQK2rPbgJI3bxlkfmOQW4HvA56vqzWTJFdFSX7cX2Lu84Ukas6nXYACSvAs4CjxbVV8bjp0BHqyqheE6zY+r6p4pz+M1GGkdWvY1mEyWKt8ATr8Tl8ERYM/w8R7g8EoHKWl9meVVpA8DPwF+Drw9HP4Sk+swh4A7gHPAo1V1ccpzuYKR1qHLrWBm2iKtFgMjrU/L3iJJ0nIZGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGpjYCS1MTCS2hgYSW0MjKQ2BkZSGwMjqY2BkdTGwEhqY2AktTEwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYb13oAq6Gqrvj5JHMaiaTFXMFIamNgJLUZ9RZp2tZolse5fZL6uIKR1MbASGozc2CSbEhyKsnR4f7mJMeSnB1uN/UNU9IYXc0K5gng9KL7+4DjVbUTOD7cl6RLZgpMkh3AXwEHFh3eDRwcPj4IPLK6Q1taVV36dS0+n6TfmXUF83Xgi8Dbi45traoFgOF2y1JfmGRvkpNJTq5opJJGZ2pgkjwMXKiq55dzgqraX1W7qmrXcr5e0njN8j6YB4BPJvkEcCNwa5JvA68n2VZVC0m2ARc6ByppfKauYKrqyaraUVV3Ao8BP6yqx4EjwJ7hYXuAw22jlDRKK3kn71eAQ0n+BjgHPLo6Q1o7v3+h13f5SiuTeb56kmTFJ5vzeOd2LmnMqmrJPyyj+1mkxX/ou2Oz+PmNjXT1/FEBSW0MjKQ2o9sirZWltmNum6QrcwUjqc2oVzBLrSD8mSLp2uEKRlIbAyOpzai3SEtx2yRdO1zBSGpzXQQmSctLyv5FVdKVXReBkbQ2DIykNgZGUhsDI6nNunuZ+kpW+6968GeRpCtzBSOpzXW1glkNrlqk2bmCkdTGwEhqc91uka72Z5bcGklXzxWMpDbX7QpmKa5SpNXlCkZSGwMjqY2BkdTGwEhqY2AktTEwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlKbmQKT5LYkTyf5ZZLTSe5PsjnJsSRnh9tN3YOVNC6zrmCeAr5fVe8B3g+cBvYBx6tqJ3B8uC9Jl2TaP6Ga5FbgZ8DdtejBSc4AD1bVQpJtwI+r6p4pz7Xyf69V0jWnqpb8C61nWcHcDbwBfCvJqSQHktwMbK2qheHJF4AtS31xkr1JTiY5ucyxSxqpWVYwu4B/Bx6oqhNJngLeBP6+qm5b9Lj/rqorXodxBSOtTytZwZwHzlfVieH+08AHgdeHrRHD7YXVGKik9WNqYKrq18CrSd65vvIQ8CJwBNgzHNsDHG4ZoaTRmrpFAkjyAeAAcAPwMvAZJnE6BNwBnAMeraqLU57HLZK0Dl1uizRTYFaLgZHWp5Vcg5GkZTEwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGpjYCS1MTCS2hgYSW0MjKQ2BkZSGwMjqY2BkdTGwEhqY2AktTEwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGozU2CSfCHJC0l+keQ7SW5MsjnJsSRnh9tN3YOVNC5TA5NkO/A5YFdVvQ/YADwG7AOOV9VO4PhwX5IumXWLtBH4wyQbgZuA14DdwMHh8weBR1Z/eJLGbGpgqupXwFeBc8AC8Juq+gGwtaoWhscsAFs6ByppfGbZIm1islq5C3g3cHOSx2c9QZK9SU4mObn8YUoao1m2SB8FXqmqN6rqt8AzwIeA15NsAxhuLyz1xVW1v6p2VdWu1Rq0pHGYJTDngPuS3JQkwEPAaeAIsGd4zB7gcM8QJY1Vqmr6g5IvA58C3gJOAZ8FbgEOAXcwidCjVXVxyvNMP5mk0amqLHV8psCsFgMjrU+XC4zv5JXUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGpjYCS1MTCS2hgYSW0MjKQ2BkZSGwMjqY2BkdTGwEhqY2AktTEwktoYGEltDIykNgZGUhsDI6mNgZHUxsBIamNgJLUxMJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGpjYCS1MTCS2hgYSW0MjKQ2BkZSGwMjqY2BkdTGwEhqY2Aktdk45/P9F/C/w+2Y/QnjnwOsj3k4h7X3p5f7RKpqngMhycmq2jXXk66y9TAHWB/zcA7XNrdIktoYGElt1iIw+9fgnKttPcwB1sc8nMM1bO7XYCRdP9wiSWoz18Ak+XiSM0leSrJvnuderiS3J/lRktNJXkjyxHB8c5JjSc4Ot5vWeqzTJNmQ5FSSo8P9Uc0hyW1Jnk7yy+G/x/1jmwNAki8M30u/SPKdJDeOcR6zmFtgkmwA/gX4S+C9wKeTvHde51+Bt4B/qKo/A+4D/nYY9z7geFXtBI4P9691TwCnF90f2xyeAr5fVe8B3s9kLqOaQ5LtwOeAXVX1PmAD8Bgjm8fMqmouv4D7gWcX3X8SeHJe51/FeRwGPgacAbYNx7YBZ9Z6bFPGvYPJN+5HgKPDsdHMAbgVeIXhuuGi46OZwzDG7cCrwGYmb3Q9CvzF2OYx6695bpHe+Y19x/nh2GgkuRO4FzgBbK2qBYDhdsvajWwmXwe+CLy96NiY5nA38AbwrWGbdyDJzYxrDlTVr4CvAueABeA3VfUDRjaPWc0zMFni2GhewkpyC/A94PNV9eZaj+dqJHkYuFBVz6/1WFZgI/BB4F+r6l4mP3Iyum3EcG1lN3AX8G7g5iSPr+2o+swzMOeB2xfd3wG8NsfzL1uSdzGJy79V1TPD4deTbBs+vw24sFbjm8EDwCeT/CfwXeAjSb7NuOZwHjhfVSeG+08zCc6Y5gDwUeCVqnqjqn4LPAN8iPHNYybzDMxzwM4kdyW5gcmFrSNzPP+yJAnwDeB0VX1t0aeOAHuGj/cwuTZzTaqqJ6tqR1XdyeT3/YdV9TjjmsOvgVeT3DMcegh4kRHNYXAOuC/JTcP31kNMLlaPbR4zmesb7ZJ8gsm1gA3AN6vqn+d28mVK8mHgJ8DP+d31iy8xuQ5zCLiDyTfNo1V1cU0GeRWSPAj8Y1U9nOSPGdEcknwAOADcALwMfIbJ/yRHMweAJF8GPsXkFcpTwGeBWxjZPGbhO3kltfGdvJLaGBhJbQyMpDYGRlIbAyOpjYGR1MbASGpjYCS1+T/9c/9FyEBUIgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage.draw import polygon2mask\n",
    "\n",
    "comb_img = np.zeros(binary_mask.shape, dtype=int)\n",
    "for polygon in polygons:\n",
    "    img_poly = polygon2mask(binary_mask.shape, polygon)\n",
    "    comb_img += img_poly \n",
    "    io.imshow(img_poly)\n",
    "    io.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "io.imshow(comb_img)\n",
    "io.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The last point is to evaluate how good the fitting actually is.\n",
    "The squared error of binary origin mask and the newly created mask clearly shows where the differences are."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "io.imshow((comb_img-binary_mask)**2)\n",
    "io.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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}