Hough_Transform_Circle.ipynb

{
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  "metadata": {
    "colab": {
      "name": "8B.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0E6KAKMipRmj",
        "colab_type": "text"
      },
      "source": [
        "### **Rebecca** **Dsouza** | **Roll No 56** | **Batch D** | **Group 2**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TXEuxTTgpZLl",
        "colab_type": "text"
      },
      "source": [
        "# **Circle Detection in OCR by Hough Transform**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O_fHaT7gwGc-",
        "colab_type": "text"
      },
      "source": [
        "### **Introduction**\n",
        "\n",
        "The Hough transform in its simplest form is a method to detect straight lines but it can also be used to detect circles or ellipses. The algorithm assumes that the edge is detected and it is robust against noise or missing points.\n",
        "\n",
        "\n",
        "<img src=\"https://lh3.googleusercontent.com/5I6IWUSrVAqKibGltRW8sLuP_OOO5JmJlQ2nXxR3cVRPtnQKUZGXkYs12JEvzXIAmlziP1_ptgbwsOuoDbPCW8DvRPbesAq3pOmocWiN3s-88YeQkygjfgptg8u7HVVbAKfvg3SjM0kuzC64uh6VsdbLP1DAbEJQyfVNR6Lw8jqcLQLct79O177Xe_-QC74gPyZM2TqU4IqhUZF_GfKK0B42CtWuR-hrQczhM-EUyEGHxOINnVWs0wUp-lyfGJTim2ZKBhhIQGbGsfIH1sjp9sAwbkUcc8oTMzaVbAwGBCWZXX3tWXWzSKmZPpfGJpeYLGKN8qeyYgzl4zsFz1ZdoC9EIJHNrEMKm29YvCmK0xpN-V6ZdqfwPg_My7ijVmyDhZo5FCVXTFzrgk3RZn9E3YpkjrgvF0ImlPwWef8SGl_HNOttvzjUyRRqsKkhpw5I2dJms8ObczrwTYwFTKZ-96bFvYnWlyEp-6VaYY7sWe6CNZiHTUsWDmPepo-o3MKVH5p0cPgZsgE1-kPbMaS5Y4eLzK6xuPZmC4dYF1-agH-tIPCeNQu11A2ebYxkLumBECzA7j0OnosOHJJ9MJoLKdD7kXSFBn6_LSmBfZ7U_D78fqAgvnclbgdhfxf9iQbS-yxWy-WDJWBeOUZiP7Mx4pgOL6oSlWImZOtSvSsckWbOu_G1SKHGL4Xe=w320-h240-no\"/>\n",
        "\n",
        "### **Mathematics**\n",
        "A circle can be described completely with three pieces of information: the center (a, b) and the radius. (The center consists of two parts, hence a total of three)\n",
        "\n",
        "```\n",
        "x = a + Rcosθ\n",
        "y = b + Rsinθ\n",
        "\n",
        "```\n",
        "\n",
        "When the θ varies from 0 to 360, a complete circle of radius R is generated.\n",
        "\n",
        "So with the Circle Hough Transform, we expect to find triplets of (x, y, R) that are highly probably circles in the image. That is, we want to find three parameters. Thus, the parameter space is 3D.\n",
        "\n",
        "If different values of R are tried, every point in the xy space will be equivalent to a circle in the ab space (R isn't a parameter, we already know it). This is because on rearranging the equations, we get:\n",
        "\n",
        "```\n",
        "a = x1 - Rcosθ\n",
        "b = y1 - Rsinθ\n",
        "```\n",
        "\n",
        "for a particular point (x1, y1). And θ sweeps from 0 to 360 degrees.\n",
        "\n",
        "\n",
        "### **Algorithmic Steps** \n",
        "\n",
        "\n",
        "*   Load an image\n",
        "*   Detect edges and generate a binary image\n",
        "*   For every 'edge' pixel, generate a circle in the ab space\n",
        "*   For every point on the circle in the ab space, cast 'votes' in the accumulator cells\n",
        "*   The cells with greater number of votes are the centers"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XGY43YxowHMs",
        "colab_type": "text"
      },
      "source": [
        "# **Uploading Image from Desktop**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lmlazpr4izxQ",
        "colab_type": "code",
        "outputId": "88a61ab1-ec7b-4315-87e3-101d9ba2bf71",
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": 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",
              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 76
        }
      },
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-27a4d991-a25d-4666-8e8c-69d45b82b556\" name=\"files[]\" multiple disabled />\n",
              "     <output id=\"result-27a4d991-a25d-4666-8e8c-69d45b82b556\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Saving ip.png to ip.png\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NCi8PrAdwOdw",
        "colab_type": "text"
      },
      "source": [
        "# **Importing Numpy, Scikit Image and Open-CV**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8-lZVP77hDsP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "from skimage import color\n",
        "from skimage.transform import hough_circle, hough_circle_peaks\n",
        "from skimage.feature import canny\n",
        "from skimage.draw import circle_perimeter\n",
        "\n",
        "from cv2 import imread\n",
        "from google.colab.patches import cv2_imshow"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O25v8miDwPRk",
        "colab_type": "text"
      },
      "source": [
        "# **Reading Image in Binary Form**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KdpOZnbVvyJQ",
        "colab_type": "code",
        "outputId": "4b835280-25bc-4227-b08f-a18e562d5d95",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        }
      },
      "source": [
        "image = imread('ip.png', 0)\n",
        "cv2_imshow(image)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgEAAACUCAAAAAAvuaVkAAAML0lEQVR4nO2d313juhLHf/d+zvvq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\nBEEQBEEQBEEQBEEQBEEQBEH45PwfdOC6WE5RLQ0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<PIL.Image.Image image mode=L size=513x148 at 0x7F98248FD6D8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EwjhUYfPwP5l",
        "colab_type": "text"
      },
      "source": [
        "# **Applying Canny Edge Detection to Binary Image**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OB85vZ2svaPQ",
        "colab_type": "code",
        "outputId": "03c684b2-0282-4de3-9bdc-46c865e904c3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        }
      },
      "source": [
        "edges = canny(image, sigma=3, low_threshold=10, high_threshold=50)\n",
        "cv2_imshow(np.where(edges.astype(int)==1, 255, edges.astype(int)))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgEAAACUCAAAAAAvuaVkAAAGXklEQVR4nO2dy5bjKgwAzT3z/7/M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\nAAAAAAAAAAAAAIBv5H9zVQ9U5JwvFgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<PIL.Image.Image image mode=L size=513x148 at 0x7F9804F8EA58>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AK-LdXmLwQgJ",
        "colab_type": "text"
      },
      "source": [
        "# **Computing Hough Circles on Edge Detected Image**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1yxTgqMWvcbI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "hough_radii = np.arange(20, 35, 2)\n",
        "hough_res = hough_circle(edges, hough_radii)\n",
        "accums, cx, cy, radii = hough_circle_peaks(hough_res, hough_radii,total_num_peaks=5)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0P-JtMhUw4AT",
        "colab_type": "text"
      },
      "source": [
        "# **Plotting Hough Circles on Image**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SKTouVGcw2Kh",
        "colab_type": "code",
        "outputId": "56a746d0-74f2-47a2-c5a2-c549e780fa31",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 165
        }
      },
      "source": [
        "image = color.gray2rgb(image)\n",
        "for center_y, center_x, radius in zip(cy, cx, radii):\n",
        "    circy, circx = circle_perimeter(center_y, center_x, radius, shape=image.shape)\n",
        "    image[circy, circx] = (57, 255, 20)\n",
        "\n",
        "cv2_imshow(image)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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}