notebooks/examples.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "#import sys # Uncomment this and the next line if imageruler is cloned rather than installed.\n",
    "#sys.path.append(\"../imageruler\")\n",
    "import imageruler\n",
    "from matplotlib import pyplot as plt\n",
    "# In the next line, remove \"imageruler.\" if imageruler is cloned rather than installed.\n",
    "from imageruler.regular_shapes import disc, rounded_square, stripe # Import functions that generate regular shapes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examples based on regular 2d shapes are as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale of the solid region:  50\n",
      "Estimated minimum length scale of the solid region:  50.9443359375\n"
     ]
    }
   ],
   "source": [
    "resolution = 1  # number of pixels per unit length\n",
    "phys_size = (200, 200)  # physical size of the entire image\n",
    "declared_mls = 50  # declared minimum length scale\n",
    "\n",
    "image = rounded_square(resolution, phys_size, declared_mls, angle=20)  # generate a rounded square\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image)\n",
    "plt.show()\n",
    "\n",
    "solid_mls = imageruler.minimum_length_solid(image)  # estimate the minimum length scale of the solid region\n",
    "print(\"Declared minimum length scale of the solid region: \", declared_mls)\n",
    "print(\"Estimated minimum length scale of the solid region: \", solid_mls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale of the solid region:  50\n",
      "Estimated minimum length scale of the solid region:  49.0009765625\n"
     ]
    }
   ],
   "source": [
    "diameter = 50\n",
    "image = disc(resolution, phys_size, diameter)  # generate a disc\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image)\n",
    "plt.show()\n",
    "\n",
    "solid_mls = imageruler.minimum_length_solid(image)  # estimate the minimum length scale of the solid region\n",
    "print(\"Declared minimum length scale of the solid region: \", diameter)\n",
    "print(\"Estimated minimum length scale of the solid region: \", solid_mls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale:  35.0 (solid),  50 (void)\n",
      "Estimated minimum length scale:  35.0087890625 (solid),  49.0009765625 (void),  35.0087890625 (minimum)\n"
     ]
    }
   ],
   "source": [
    "outer_diameter, inner_diameter = 120, 50\n",
    "declared_solid_mls, declared_void_mls = (outer_diameter - inner_diameter) / 2, inner_diameter\n",
    "\n",
    "solid_disc = disc(resolution, phys_size, diameter=outer_diameter)\n",
    "void_disc = disc(resolution, phys_size, diameter=inner_diameter)\n",
    "image = solid_disc ^ void_disc  # ring\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image)\n",
    "plt.show()\n",
    "\n",
    "solid_mls = imageruler.minimum_length_solid(image)\n",
    "void_mls = imageruler.minimum_length_void(image)\n",
    "mls = imageruler.minimum_length(image)\n",
    "\n",
    "print(\"Declared minimum length scale: \", declared_solid_mls, \"(solid), \", declared_void_mls, \"(void)\")\n",
    "print(\"Estimated minimum length scale: \", solid_mls, \"(solid), \", void_mls, \"(void), \", mls, \"(minimum)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale:  30 (solid),  40 (void)\n",
      "Estimated minimum length scale:  30.41845703125 (solid),  40.54931640625 (void),  30.41845703125 (minimum)\n"
     ]
    }
   ],
   "source": [
    "resolution = 1  # number of pixels per unit length\n",
    "phys_size = (400, 400)  # physical size of the entire image\n",
    "\n",
    "outer_diameter, middle_diameter, inner_diameter = 300, 200, 100\n",
    "declared_solid_mls, declared_void_mls = (\n",
    "    outer_diameter - inner_diameter) / 2, inner_diameter\n",
    "\n",
    "outer_solid_disc = disc(resolution, phys_size, diameter=outer_diameter, center= (0, 0))\n",
    "void_disc = disc(resolution, phys_size, diameter=middle_diameter, center= (-20, 0))\n",
    "inner_solid_disc = disc(resolution, phys_size, diameter=inner_diameter, center= (-10, 0))\n",
    "image = outer_solid_disc^void_disc^inner_solid_disc\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image)\n",
    "plt.show()\n",
    "\n",
    "solid_mls = imageruler.minimum_length_solid(image)\n",
    "void_mls = imageruler.minimum_length_void(image)\n",
    "mls = imageruler.minimum_length(image)\n",
    "print(\"Declared minimum length scale: \", 30, \"(solid), \", 40, \"(void)\")\n",
    "print(\"Estimated minimum length scale: \", solid_mls, \"(solid), \", void_mls, \"(void), \", mls, \"(minimum)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The images that illustrate the areas of violation at various probe diameters are shown as follows. The three rows from top to bottom show violations at solid, void, and either region."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x864 with 15 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "diameters = [31,41,61,71,101]\n",
    "nd = len(diameters)\n",
    "plt.figure(figsize=(20,12))\n",
    "\n",
    "for idx in range(nd):\n",
    "\n",
    "    plt.subplot(3,nd,idx+1)\n",
    "    ax = plt.gca()\n",
    "    ax.set_axis_off()\n",
    "    image_violation_solid = imageruler.length_violation_solid(image,diameter=diameters[idx])\n",
    "    plt.imshow(image_violation_solid)\n",
    "    plt.title(\"probe diameter = \"+str(diameters[idx]))\n",
    "\n",
    "    plt.subplot(3,nd,nd+idx+1)\n",
    "    ax = plt.gca()\n",
    "    ax.set_axis_off()\n",
    "    image_violation_void = imageruler.length_violation_void(image,diameter=diameters[idx])\n",
    "    plt.imshow(image_violation_void)\n",
    "\n",
    "    plt.subplot(3,nd,2*nd+idx+1)\n",
    "    ax = plt.gca()\n",
    "    ax.set_axis_off()\n",
    "    image_violation = imageruler.length_violation(image,diameter=diameters[idx])\n",
    "    plt.imshow(image_violation);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALgAAAD8CAYAAADE+m69AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAI8klEQVR4nO3df6hfdR3H8edra2UuRcKgUkFBsUQkaVhREKXEFEkKgvyjBIURVBj0h4lQRASB4F8JISRFrCTSkaTiFhgSZKVisrUZq4iGUkk/NANr7d0f96tc3dz31vnsnsu75wMu7Ht37jlv7p47O/ec8f2kqpC62jT3ANKJZOBqzcDVmoGrNQNXawau1iYHnuSkJD9L8osk+5J8ccRg0giZeh88SYCtVfX3JFuAHwPXV9VDIwaUpnjV1B3Uyt+Qvy9ebll8+PRIG8LkwAGSbAYeAc4Fbq2qnx5jmx3ADoDNbH77yZw64tAbVjZt4pwLn+FV6/hjzmGO8Nu9p1JHjqzbMefyLH95uqresGy7yZcoL9lZchqwC/h0Ve19pe1OzevrHbl02HE3ok1bt/KtA7s5ffPWdTvm0/9+jo+95QMcee65dTvmXH5Y33ukqrYt227o6aWq/gr8CNg+cr/S/2rEXZQ3LM7cJHktcBlwYOp+pRFGXIO/Cfjm4jp8E/DdqvrBgP1Kk424i/I4cPGAWaThfJKp1gxcrRm4WjNwtWbgas3A1ZqBqzUDV2sGrtYMXK0ZuFozcLVm4GrNwNWagas1A1drBq7WDFytGbhaM3C1ZuBqzcDVmoGrNQNXawau1gxcrRm4Whvx7rJnJXkgyf7FGj3XjxhMGmHEu8seBj5bVY8mOQV4JMmeqvrlgH1Lk0w+g1fVU1X16OLXzwL7gTOm7lcaYeg1eJKzWXkr5aPW6JHmMGQRKoAkrwPuBD5TVc8c4/dfXITqJE4edVjpuIacwRfrY94J7Kyqu461TVXdVlXbqmrbFl4z4rDSUiPuogT4OrC/qm6ZPpI0zogz+LuBjwHvT/LY4uOKAfuVJhuxRs+PgQyYRRrOJ5lqzcDVmoGrNQNXawau1gxcrRm4WjNwtWbgas3A1ZqBqzUDV2sGrtYMXK0ZuFozcLVm4GrNwNWagas1A1drBq7WDFytGbhaM3C1ZuBqzcDVmoGrNQNXa6PeH/z2JH9MsnfE/qRRRp3BvwFsH7QvaZghgVfVg8CfR+xLGmnYGj3LuEaP5rBuP2S6Ro/m4F0UtWbgam3UbcLvAD8Bzk9yKMl1I/YrTTXkh8yqunrEfqTRvERRawau1gxcrRm4WjNwtWbgas3A1ZqBqzUDV2sGrtYMXK0ZuFozcLVm4GrNwNWagas1A1drBq7WDFytGbhaM3C1ZuBqzcDVmoGrNQNXawau1gxcrY16883tSZ5IcjDJ50bsUxphcuBJNgO3ApcDFwBXJ7lg6n6lEUacwS8BDlbVb6rqn8AdwFUD9itNNiLwM4Dfr3p9aPG5l0iyI8nDSR7+F88POKy03IjAc4zP1VGfcI0ezWBE4IeAs1a9PhN4csB+pclGBP5z4Lwk5yR5NfBR4O4B+5Umm7yESVUdTvIp4H5gM3B7Ve2bPJk0wKg1eu4F7h2xL2kkn2SqNQNXawau1gxcrRm4WjNwtWbgas3A1ZqBqzUDV2sGrtYMXK0ZuFozcLVm4GrNwNWagas1A1drBq7WDFytGbhaM3C1ZuBqzcDVmoGrNQNXawau1iYFnuQjSfYlOZJk26ihpFGmnsH3Ah8GHhwwizTcpHeXrar9AMmxFnmQ5jfk7ZPXIskOYAfASZy8XofV/7mlgSf5IfDGY/zWTVX1/bUeqKpuA24DODWvP2oNH+lEWBp4VV22HoNIJ4K3CdXa1NuEH0pyCHgXcE+S+8eMJY0x9S7KLmDXoFmk4bxEUWsGrtYMXK0ZuFozcLVm4GrNwNWagas1A1drBq7WDFytGbhaM3C1ZuBqzcDVmoGrNQNXawau1gxcrRm4WjNwtWbgas3A1ZqBqzUDV2sGrtYMXK1NffPNm5McSPJ4kl1JThs0lzTE1DP4HuDCqroI+BVw4/SRpHEmBV5Vu6vq8OLlQ8CZ00eSxhl5DX4tcN/A/UmTDVmjJ8lNwGFg53H24yJUWneT1+hJcg1wJXBpVb3i4lIuQqU5TFrhIcl24AbgvVX1jzEjSeNMvQb/KnAKsCfJY0m+NmAmaZipa/ScO2oQ6UTwSaZaM3C1ZuBqzcDVmoGrNQNXawau1gxcrRm4WjNwtWbgas3A1ZqBqzUDV2sGrtYMXK0ZuFozcLVm4GrNwNWagas1A1drBq7WDFytGbhaM3C1ZuBqzcDV2tRFqL60WIDqsSS7k7x51GDSCFPP4DdX1UVV9TbgB8Dnp48kjTN1EapnVr3cCrhygzaUHGfVkbXtIPky8HHgb8D7qupPr7Ddi2v0ABcCeycdeKzTgafnHmKVjTYPbLyZzq+qU5ZttDTwtSxCtdjuRuCkqvrC0oMmD1fVtmXbrRfnWW6jzbTWeSYvQrXKt4F7gKWBS+tl6l2U81a9/CBwYNo40liT1ugBvpLkfOAI8DvgE2v8utsmHnc051luo820pnkm/5ApbWQ+yVRrBq7WZgs8yc1JDiwe9e9Kctpcsyzm+UiSfUmOJJntdliS7UmeSHIwyefmmmPVPLcn+WOS2Z9bJDkryQNJ9i/+rK5f9jVznsH3ABdW1UXAr4AbZ5wFVh48fRh4cK4BkmwGbgUuBy4Ark5ywVzzLHwD2D7zDC84DHy2qt4KvBP45LLvz2yBV9Xuqjq8ePkQcOZcsyzm2V9VT8w5A3AJcLCqflNV/wTuAK6ac6CqehD485wzvKCqnqqqRxe/fhbYD5xxvK/ZKNfg1wL3zT3EBnAG8PtVrw+x5A/w/1WSs4GLgZ8eb7up98GXDbH0MX+Sm1j5p2fniZxlrfPMLMf4nPdxXybJ64A7gc+87D/8HeWEBr7sMX+Sa4ArgUtrHW7I/xf/7WAuh4CzVr0+E3hyplk2pCRbWIl7Z1XdtWz7Oe+ibAduAD5YVf+Ya44N5ufAeUnOSfJq4KPA3TPPtGEkCfB1YH9V3bKmL6qqWT6Ag6xcbz62+PjaXLMs5vkQK2fQ54E/APfPNMcVrNxV+jUrl06zfU8W83wHeAr41+L7c92Ms7yHlUu2x1d1c8XxvsZH9Wpto9xFkU4IA1drBq7WDFytGbhaM3C1ZuBq7T/Ykur0tAhieQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale of the solid region:  0.8\n",
      "Estimated minimum length scale of the solid region:  0.8090039062499998\n"
     ]
    }
   ],
   "source": [
    "resolution = 50\n",
    "width, height = 6, 4  # size of the binary image\n",
    "phys_size = (width, height)\n",
    "\n",
    "stripe_width = 0.8\n",
    "image = stripe(resolution, phys_size, stripe_width)\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image,extent=[-phys_size[1]/2,phys_size[1]/2,-phys_size[0]/2,phys_size[0]/2])\n",
    "plt.show()\n",
    "\n",
    "solid_mls = imageruler.minimum_length_solid(image, phys_size)\n",
    "\n",
    "print(\"Declared minimum length scale of the solid region: \", stripe_width)\n",
    "print(\"Estimated minimum length scale of the solid region: \", solid_mls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale of the solid region:  0.8\n",
      "Estimated minimum length scale of the solid region:  0.811298828125\n"
     ]
    }
   ],
   "source": [
    "image = stripe(resolution, phys_size, stripe_width, center = (0, -2)) | stripe(\n",
    "    resolution, phys_size, stripe_width, center = (0, 2))\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image,extent=[-phys_size[1]/2,phys_size[1]/2,-phys_size[0]/2,phys_size[0]/2])\n",
    "plt.show()\n",
    "\n",
    "# Assume this image is periodic along the horizontal direction, which corresponds to the axis 1.\n",
    "solid_mls = imageruler.minimum_length(image, phys_size, periodic_axes=1)\n",
    "\n",
    "print(\"Declared minimum length scale of the solid region: \", stripe_width)\n",
    "print(\"Estimated minimum length scale of the solid region: \", solid_mls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Declared minimum length scale of the solid region:  1\n",
      "Estimated minimum length scale of the solid region:  0.9877929687499998\n"
     ]
    }
   ],
   "source": [
    "stripe_width,intercept,angle = 1,1/np.sqrt(2),0.25*np.pi\n",
    "image = stripe(resolution, phys_size, stripe_width, center=(intercept,0), angle=135)\n",
    "\n",
    "plt.figure()\n",
    "plt.imshow(image,extent=[-phys_size[1]/2,phys_size[1]/2,-phys_size[0]/2,phys_size[0]/2])\n",
    "plt.show()\n",
    "\n",
    "solid_mls = imageruler.minimum_length_solid(image, phys_size)\n",
    "\n",
    "print(\"Declared minimum length scale of the solid region: \", stripe_width)\n",
    "print(\"Estimated minimum length scale of the solid region: \", solid_mls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Padding schemes can affect estimated minimum length scales. The default padding schemes are padding solid/void materials when estimating minimum length scales of solid/void regions and padding solid/void materials for morphological opening/closing in the dual approach that involves both openning and closing. In the preceding example, if we use void padding or edge-mode padding, the boundary stuctures will influence the estimated minimum length scale, and consequently, the results will be away from the width of the strip. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated minimum length scale of the solid region:  0.08607421875 (void padding),  0.7079492187499998 (edge-mode padding)\n"
     ]
    }
   ],
   "source": [
    "solid_mls_void = imageruler.minimum_length_solid(image, phys_size, pad_mode='void')\n",
    "solid_mls_edge = imageruler.minimum_length_solid(image, phys_size, pad_mode='edge')\n",
    "print(\"Estimated minimum length scale of the solid region: \", solid_mls_void, \"(void padding), \", solid_mls_edge, \"(edge-mode padding)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some tests based on 1d images are as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated minimum length scales:  0.39999999999999997 (solid),  0.3 (void)\n",
      "Estimated minimum length scales with some end regions disregarded:  0.9999999999999999 (solid),  2.0999999999999996 (void)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "phys_size = 10.1\n",
    "image = np.sin(np.linspace(0,100,101)/5) > 0.5\n",
    "plt.plot(np.linspace(-phys_size/2,phys_size/2,len(image)),image);\n",
    "\n",
    "solid_mls, void_mls = imageruler.minimum_length_solid_void(image, phys_size)\n",
    "print(\"Estimated minimum length scales: \", solid_mls, \"(solid), \", void_mls, \"(void)\")\n",
    "\n",
    "# disregard the short void and solid regions at both ends\n",
    "solid_mls, void_mls = imageruler.minimum_length_solid_void(image, phys_size, margin_size=(void_mls,solid_mls))\n",
    "print(\"Estimated minimum length scales with some end regions disregarded: \", solid_mls, \"(solid), \", void_mls, \"(void)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This package can also be used via the command line, which allows you to invoke the function \"minimum_length_solid_void()\" being invoked. The syntax is \"imageruler file\", where \"file\" is a string of the path of the text file that contains the array of the input image. All other arguments of the function take default options."
   ]
  }
 ],
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