challenge-2021.12-dec/challenge-2021.12-dec.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "142559ea",
   "metadata": {},
   "source": [
    "# Challenge: Morphological Operators"
   ]
  },
  {
   "attachments": {
    "erosion-2.png": {
     "image/png": 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"
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   "cell_type": "markdown",
   "id": "a35957fa",
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   "source": [
    "Mathematical morphology is defined as \"the theory for the analysis of spatial structures\". It is considered morphological when focusing on shapes; in the field of mathematics it is considered by set theory, integral geometry and Lattice algebra[1]. \n",
    "\n",
    "## Erosion\n",
    "\n",
    "Erosion is a basic operation of mathematical morphology, which generates a new set from the preprocessed image and the structure element (B).The erosion of a set X by B is denoted as εB(X) and is defined \"of the points x of B that lie on X when their origin is shifted to x\"[1], i.e.:\n",
    "\n",
    "$$\\varepsilon_{\\mathrm{B}}(X)=\\left\\{\\mathrm{x} \\mid \\mathrm{B}_{\\mathrm{x}} \\subseteq X\\right\\}$$\n",
    "\n",
    "It can be rewritten in terms of a set of disjoins and translations, determined by B.\n",
    "\n",
    "\n",
    "$$\\varepsilon_{\\mathrm{B}}(X)=\\bigcap_{\\mathrm{b} \\subset \\mathrm{B}} X_{\\mathrm{b}}$$\n",
    "\n",
    "\n",
    "Example of the erosion operator,\n",
    "\n",
    "![erosion-2.png](attachment:erosion-2.png)\n",
    "\n",
    "\n",
    "###  Erosion Process:\n",
    "\n",
    "The erosion process has to sweep the structuring element over the whole image and the pixel of the origin will be kept, when **the whole structuring element is equal to a subset of the image**.\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "erosion_process.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "id": "14b62d1b",
   "metadata": {},
   "source": [
    "![erosion_process.png](attachment:erosion_process.png)\n",
    "\n",
    "In the process there are two cases, one that does not comply, as it is completely different, it is not considered in the case that it does comply, only the pixel indicating the origin of the structuring element is maintained. \n",
    "\n",
    "## Dilation\n",
    "\n",
    "Dilation is the dual operator of erosion. The dilated set of X generated with B is denoted by δB(X) and is defined as \"the points x marking B of X where its origin coincides with x\"[1].\n",
    "\n",
    "$$\\delta_{\\mathrm{B}}(X)=\\left\\{\\mathrm{x} \\mid \\mathrm{B}_{\\mathrm{x}} \\cap X \\neq \\emptyset\\right\\}$$\n",
    "\n",
    "\n",
    "It can be rewritten in terms of a set of unions and translations, determined by B.\n",
    "\n",
    "$$\\delta_{\\mathrm{B}}(X)=\\bigcup_{\\mathbf{b} \\subset B} X_{\\mathbf{b}}$$\n",
    "\n",
    "\n",
    "Example of the dilation operator,\n"
   ]
  },
  {
   "attachments": {
    "dilation-2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "37e210e0",
   "metadata": {},
   "source": [
    "![dilation-2.png](attachment:dilation-2.png)"
   ]
  },
  {
   "attachments": {
    "dilation_process-2.png": {
     "image/png": 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    }
   },
   "cell_type": "markdown",
   "id": "763def1f",
   "metadata": {},
   "source": [
    "\n",
    "###  Dilation Process:\n",
    "\n",
    "The dilation process has to sweep the structuring element over the whole image and the **structuring element will be added on the image when a pixel of the image has the same value as the origin pixel of the structuring element**.\n",
    "\n",
    "![dilation_process-2.png](attachment:dilation_process-2.png)\n",
    "\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "input_img.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "618470c7",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-success\"><b> Note </b>\n",
    "\n",
    "These same operations **can represent the intersection as the logical AND operation and the union as the logical OR operation**, the idea is to generate these operations between an image and a structuring element that can eliminate noise or highlight certain objects in the image, using the Erosion and Dilation operators.</div>\n",
    "\n",
    "\n",
    "# Challenge\n",
    "\n",
    "## Task 1\n",
    "Perform Amplitude coding or Base coding to pass the example binary image in terms of qubits and perform operations equivalent to erosion and dilation.\n",
    "\n",
    "The input image is\n",
    "\n",
    "![input_img.png](attachment:input_img.png)\n",
    "\n",
    "The structuring element is \n",
    "\n"
   ]
  },
  {
   "attachments": {
    "se.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "0168fc2d",
   "metadata": {},
   "source": [
    "![se.png](attachment:se.png)\n",
    "\n",
    "## Task 2\n",
    "\n",
    "Generate more complex structuring elements and apply to the same input image, these can be:\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "se_table.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "0ca61f8c",
   "metadata": {},
   "source": [
    "![se_table.png](attachment:se_table.png)\n",
    "\n",
    "\n",
    "# Task 3 (Bonus)\n",
    "\n",
    "Generate the erosion and dilation operators on a popular image from image preprocessing, Lena, was already converted into a binary image for this challenge.\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "lenna.png": {
     "image/png": 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"
    }
   },
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   "id": "ceb969ee",
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   "source": [
    "![lenna.png](attachment:lenna.png)\n",
    "\n",
    "\n",
    "\n",
    "# References\n",
    "\n",
    "[1] P. Soille. Morphological Image Analysis: Principles and Applications.  Springer BerlinHeidelberg, 2013.\n",
    "\n",
    "\n",
    "# Resources\n",
    "[1] Suzhen Yuan, Xia Mao, Tian Li, Yuli Xue, Lijiang Chen, and Qingxu Xiong. Quantum morphology operations based on quantum representation model. Quantum Information Processing, 14:1625–1645, 05 2015. [link](https://www.researchgate.net/publication/276481467_Quantum_morphology_operations_based_on_quantum_representation_model)\n",
    "\n",
    "[2] Zhou, Ri-Gui & Chang, Zhi-bo & Fan, Ping & Li, Wei & Huan, Tian-tian. (2014). Quantum Image Morphology Processing Based on Quantum Set Operation. International Journal of Theoretical Physics. 54. 1974-1986. 10.1007/s10773-014-2402-4.  [link](https://www.researchgate.net/publication/277348937_Quantum_Image_Morphology_Processing_Based_on_Quantum_Set_Operation)\n"
   ]
  }
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