03_image_processing/08_Morphological_operations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7765dd92-fd23-4402-a93a-d36fff865e07",
   "metadata": {},
   "source": [
    "# Morphological Image Processing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "130f162d-a1aa-4225-9745-ce7c99b3b551",
   "metadata": {},
   "source": [
    "Morphological operations transform images based on shape; typically we mean binary images in this context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "71721c42-8f09-447a-9c49-6e2685ccb771",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from skimage.io import imread\n",
    "import matplotlib.pyplot as plt\n",
    "from skimage import morphology\n",
    "from skimage import filters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97f1a137-81de-43be-8c3b-3a90b8a5d6e5",
   "metadata": {},
   "source": [
    "## Kernels, footsprints and structural elements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12efc586-1762-4304-8fd1-995630504d02",
   "metadata": {},
   "source": [
    "If we work with scikit-image, many morphological filters have a `footprint` parameter. This footprint is the filter kernel, and in the literature you also find the term `structural element` for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f0097b92-852e-471e-b2d9-bee14fb42b4b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 1, 0, 0, 0],\n",
       "       [0, 1, 1, 1, 1, 1, 0],\n",
       "       [0, 1, 1, 1, 1, 1, 0],\n",
       "       [1, 1, 1, 1, 1, 1, 1],\n",
       "       [0, 1, 1, 1, 1, 1, 0],\n",
       "       [0, 1, 1, 1, 1, 1, 0],\n",
       "       [0, 0, 0, 1, 0, 0, 0]], dtype=uint8)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disk = morphology.disk(3) # creates a disk of 1 with radius = 3\n",
    "disk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6d5445e7-63b3-40c3-9ba4-ea687a64a9fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1528855bbe0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(disk, cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1fc5b90d-c3d8-473a-af8f-68d31b86b6bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1, 1],\n",
       "       [1, 1, 1],\n",
       "       [1, 1, 1]], dtype=uint8)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "square = morphology.square(3) # creates a square with widht and height = 3\n",
    "square"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "372014e4-bae5-4a03-a7ee-fbdb4ae7a9e9",
   "metadata": {},
   "source": [
    "## Binary morphology"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a82d2d22-d8af-4efc-9353-b3feb636e552",
   "metadata": {},
   "source": [
    "For demonstrating morphological filtering of binary images, we use the small nuclei image again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "908dab51-e5bc-409f-950e-02e0dc0fb78b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x152885d9dc0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "image_nuclei = imread('data/mitosis_mod.tif').astype(float)\n",
    "image_binary = image_nuclei > filters.threshold_otsu(image_nuclei)\n",
    "\n",
    "plt.imshow(image_binary, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bde146c-25e3-4999-84c7-a6c4e365f348",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Erosion and Dilation\n",
    "To make white islands in the black ocean smaller, we need to _erode_ its coastlines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "48667a3c-65e1-4875-ac0e-be8233cc51e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x15288661520>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eroded = morphology.binary_erosion(image_binary, disk)\n",
    "\n",
    "plt.imshow(eroded, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03b741b3-a4b5-4c24-b532-b47537775917",
   "metadata": {},
   "source": [
    "If we dilate the image afterwards, we get white islands back that look smoother than in the original binary image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "aad9ad30-8a27-4b72-919e-b11230485595",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1528893ffd0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eroded_dilated = morphology.binary_dilation(eroded, disk)\n",
    "\n",
    "plt.imshow(eroded_dilated, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91379b6e-3620-4465-a95d-5caac9d4fdc5",
   "metadata": {},
   "source": [
    "Calling erosion and dilation subsequently is so common that there is an extra function which does exactly that. As the gab between islands _open_ the operation is called _opening_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "75e2ed53-0024-4c37-b138-9e38a4cb93f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x15288857880>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "opened = morphology.binary_opening(image_binary, disk)\n",
    "\n",
    "plt.imshow(opened, cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d72477be-c22b-4c2d-ac1f-f1c2f8e5a7de",
   "metadata": {},
   "source": [
    "# Exercise 1\n",
    "There is also a _closing_ operation. Apply it to the binary image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ac94c8e3-3758-40cc-b5a3-44b04f9c76ab",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b6b89958-e647-43b9-98e7-479b42ab4e23",
   "metadata": {},
   "source": [
    "# Exercise 2\n",
    "Search the [scikit-image documentation](https://scikit-image.org/) for minimum and maximum filters. Apply the minimum filter to the binary image and the maximum filter to the result afterwards. Compare it to the images shown above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b89eaac-5913-4225-935f-ba2f5bb0431f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.15"
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