{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Morfologické operace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vstup: binární obraz nebo obraz s více úrovněmi jasu\n",
    "\n",
    "Výstup: binární obraz nebo obraz s více úrovněmi jasu\n",
    "\n",
    "Cíl: tvar objektů\n",
    "\n",
    "Vlastnosti: snadné a rychlé předzpracování\n",
    "\n",
    "![input_image](http://www.kky.zcu.cz/uploads/courses/zdo/lesson5/original.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline --no-import-all\n",
    "import skimage\n",
    "import skimage.io\n",
    "import skimage.color\n",
    "import skimage.morphology\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import scipy\n",
    "import scipy.ndimage\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x3f293d0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x3d30ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# thresholding - prahování\n",
    "text_color = skimage.io.imread('http://www.kky.zcu.cz/uploads/courses/zdo/lesson5/original.jpg')\n",
    "text_gray = skimage.color.rgb2gray(text_color)\n",
    "textb = text_gray > 0.5\n",
    "plt.imshow(textb, cmap='gray')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binární dilatace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input \n",
      "[[0 0 0 0 0]\n",
      " [0 0 0 0 0]\n",
      " [0 0 1 0 0]\n",
      " [0 0 0 0 0]\n",
      " [0 0 0 0 0]]\n",
      "kernel \n",
      "[[0 1 0]\n",
      " [1 1 1]\n",
      " [0 1 0]]\n",
      "dilation \n",
      "[[0 0 0 0 0]\n",
      " [0 0 1 0 0]\n",
      " [0 1 1 1 0]\n",
      " [0 0 1 0 0]\n",
      " [0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((5,5), dtype=np.int)\n",
    "a[2, 2] = 1\n",
    "#a[1:6, 2:5] = 1\n",
    "print 'input \\n', a\n",
    "\n",
    "kernel = skimage.morphology.diamond(1).astype(np.uint8)\n",
    "\n",
    "print 'kernel \\n', kernel\n",
    "\n",
    "ad = skimage.morphology.binary_dilation(a, kernel)\n",
    "print 'dilation \\n', ad\n",
    "#dir(skimage.morphology)\n",
    "\n",
    "#skimage.morphology.binary_dilation(a, morphology.diamond(1)).astype(np.uint8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x420acd0>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gYCB69uyJjz76CID9zkeN6upqBAUFYezYsQBoPkxi8bWTzFRVVcW8vb2ZTqdj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\nKBwVckIIUbj/B1eZhJ0XkBzFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3d30a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kernel_big = skimage.morphology.diamond(5).astype(np.uint8)\n",
    "textd = skimage.morphology.binary_dilation(textb, kernel_big)\n",
    "plt.imshow(textd, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binární eroze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input \n",
      "[[0 0 0 0 0 0 0]\n",
      " [0 0 1 1 1 0 0]\n",
      " [0 0 1 1 1 0 0]\n",
      " [0 0 1 1 1 0 0]\n",
      " [0 0 1 1 1 0 0]\n",
      " [0 0 1 1 1 0 0]\n",
      " [0 0 0 0 0 0 0]]\n",
      "erosion \n",
      "[[0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0]\n",
      " [0 0 0 1 0 0 0]\n",
      " [0 0 0 1 0 0 0]\n",
      " [0 0 0 1 0 0 0]\n",
      " [0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "a = np.zeros((7,7), dtype=np.int)\n",
    "a[1:6, 2:5] = 1\n",
    "print 'input \\n', a\n",
    "\n",
    "\n",
    "ad = skimage.morphology.binary_erosion(a, kernel)\n",
    "print 'erosion \\n', ad\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x4730750>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x3f48790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#kernel_big = skimage.morphology.diamond(3).astype(np.uint8)\n",
    "textd = skimage.morphology.binary_erosion(textb, kernel_big)\n",
    "plt.imshow(textd, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binární otevření a uzavření"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kombinace obou předchozích metod\n",
    "\n",
    "* Otevření - eroze + dilatace\n",
    "* Uzavření - dilatace + eroze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x4767210>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x4229150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Otevření\n",
    "#kernel_big = skimage.morphology.diamond(4).astype(np.uint8)\n",
    "textd = skimage.morphology.binary_opening(textb, kernel_big)\n",
    "\n",
    "#plt.subplot(121)\n",
    "#plt.imshow(textb, cmap='gray')\n",
    "#plt.subplot(122)\n",
    "plt.imshow(textd, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x4a42610>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pp/j000+NT9VGvH5bN2KY3Nxc3aE3Ih0zMzMcPHgQQUFBckchMqCv6BPSDnz99ddUxE0Y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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x474b690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Uzavření\n",
    "textd = skimage.morphology.binary_closing(textb, kernel_big)\n",
    "plt.imshow(textd, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kostra (Skeleton)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x4f0c890>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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B+TZZjoaGBnV0dCibzSqdTquvry/3jvZ8GBgYyP351KlTuXeM5zOXMUa7du3SypUr9cYb\nb+Su93rPJstVCHvmJ8yR6fP6nJhMIZwTzJE8yue7TM+ePWsqKytNeXm5eeedd/J56DF++eUXE4/H\nTTweN6tWrcplGR4eNnV1dSYajZpEImFu3bplPUtjY6MpKyszgUDAhMNhc+LEiSlzHDhwwJSXl5vl\ny5ebZDKZt1zHjx83O3bsMLFYzKxevdo8//zzZnBwMO+5Lly4YBzHMfF43KxZs8asWbPGdHV1eb5n\nE+U6e/ZsQeyZ3zBHxmOOzAxzJH/43SUAAMAKPvETAABYQckAAABWUDIAAIAVlAwAAGAFJQMAAFhB\nyQAAAFb8B3Dh2au+FX/cAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4a1c210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = np.zeros((200, 300), dtype=np.int)\n",
    "#a[1:6, 2:5] = 1\n",
    "a[50:100, 50:200] = 1\n",
    "a[30:150, 100:150] = 1\n",
    "\n",
    "skela = skimage.morphology.skeletonize(a)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(9, 4))\n",
    "plt.subplot(121)\n",
    "plt.imshow(a, cmap='gray')\n",
    "plt.subplot(122)\n",
    "plt.imshow(skela, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x5445950>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mb+jQofDy8sLKlSu5jkKITtDdL6RZGzx4MJydnamIG5jTp09j4MCBXMdoNqiQk2ZNJpPh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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x4a27ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "textd = skimage.morphology.skeletonize(textb)\n",
    "plt.imshow(textd, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vyplnění děr (Fill holes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x5477d90>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zckmJAhAWFsYiTmOe34W8ubnZ+/W//vUv7xUtdrsd5eXl8Hg8cLlcqKur4yeJjyFPPfUU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\nkBMR6RwLORGRzrGQExHp3P8B0fKCO7lR8vkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x50b5090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "texth = scipy.ndimage.morphology.binary_fill_holes(textb)\n",
    "plt.imshow(texth, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cvičení"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spočítejte čtverce na obrázku z kamery\n",
    "\n",
    "![ctverce](https://pojabr.zcu.cz/uploads/courses/zdo/lesson5/pocitani_ctvercu.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Příprava na písemku\n",
    "* FT\n",
    "* morfologické operace"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}