bottompoint.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Changed image from the original question because:\n",
    "# https://github.com/leomariga/StackOverflowSolutions/issues/2\n",
    "# import the necessary packages\n",
    "import numpy as np\n",
    "import cv2\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# load the image, clone it for output, and then convert it to grayscale\n",
    "image = cv2.imread('img_circle2.jpg')\n",
    "output = image.copy()\n",
    "gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)\n",
    "#cv2.imshow(\"test\", image)\n",
    "plt.figure(figsize=(20,20))\n",
    "plt.imshow(image)\n",
    "\n",
    "plt.title('my picture')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# detect circles in the image\n",
    "circles = cv2.HoughCircles(gray, cv2.HOUGH_GRADIENT, 1, 100,\n",
    "                           param1=100, param2=35,\n",
    "                           minRadius = 10, maxRadius = 0)\n",
    " \n",
    "# ensure at least some circles were found\n",
    "if circles is not None:\n",
    "    # convert the (x, y) coordinates and radius of the circles to integers\n",
    "    circles = np.round(circles[0, :]).astype(\"int\")\n",
    " \n",
    "    # loop over the (x, y) coordinates and radius of the circles\n",
    "    for (x, y, r) in circles:\n",
    "        # draw the circle in the output image\n",
    "        cv2.circle(output, (x, y), r, (0, 255, 0), 4)\n",
    "        \n",
    "        # Draw low point of the circle \n",
    "        cv2.rectangle(output, (x - 10, y - 10 + r), (x + 10, y + 10 + r), (0, 0, 255), -1)\n",
    " \n",
    "    # show the output image\n",
    "    plt.figure(figsize=(20,20))\n",
    "    plt.imshow(output)\n",
    "    plt.title('my picture')\n",
    "    plt.show()\n",
    "    \n",
    "    cv2.imwrite( \"lowPoint.jpg\", output);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}