03-Grid-Detection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.pieriandata.com\"><img src=\"../DATA/Logo.jpg\"></a>\n",
    "*Copyright by Pierian Data Inc.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grid Detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "flat_chess = cv2.imread('../DATA/flat_chessboard.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f177dc7ac8>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dwO7M/ELbrlGve3FELCzbE98R2g08BFxVph1d98Tv4yrgwSwXGIZu2Bc1aF19fprW+dffDns9fa7tHmA/8DNa/zJcT+u8cRvwTLlfVOYG8E/l9/ADYMWw199lzb9L6zB4J63vxOwo/41Hve4PAt8rde8C/q6Mnws8Suu7QP8KzCvjp5THe8v+c4ddw8TNTzRKqgz79EHSDGMoSKoYCpIqhoKkiqEgqWIoSKoYCpIqhoKkyv8DiLVFExdkFKQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(flat_chess,cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "found, corners = cv2.findChessboardCorners(flat_chess,(7,7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OpenCV was able to find the corners\n"
     ]
    }
   ],
   "source": [
    "if found:\n",
    "    print('OpenCV was able to find the corners')\n",
    "else:\n",
    "    print(\"OpenCV did not find corners. Double check your patternSize.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(49, 1, 2)"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corners.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        ...,\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209]],\n",
       "\n",
       "       [[158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        ...,\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209]],\n",
       "\n",
       "       [[158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        ...,\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        ...,\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255]],\n",
       "\n",
       "       [[ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        ...,\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255]],\n",
       "\n",
       "       [[ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        [ 71, 139, 209],\n",
       "        ...,\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255],\n",
       "        [158, 206, 255]]], dtype=uint8)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flat_chess_copy = flat_chess.copy()\n",
    "cv2.drawChessboardCorners(flat_chess_copy, (7, 7), corners, found)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f177e1fba8>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(flat_chess_copy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------\n",
    "# Circle Based Grids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "dots = cv2.imread('../DATA/dot_grid.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f101505828>"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(dots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "found, corners = cv2.findCirclesGrid(dots, (10,10), cv2.CALIB_CB_SYMMETRIC_GRID)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        ...,\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255]],\n",
       "\n",
       "       [[255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        ...,\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255]],\n",
       "\n",
       "       [[255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        ...,\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255]],\n",
       "\n",
       "       ...,\n",
       "\n",
       "       [[255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        ...,\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255]],\n",
       "\n",
       "       [[255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        ...,\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255]],\n",
       "\n",
       "       [[255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        ...,\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255],\n",
       "        [255, 255, 255]]], dtype=uint8)"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dbg_image_circles = dots.copy()\n",
    "cv2.drawChessboardCorners(dbg_image_circles, (10, 10), corners, found)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1f10189fbe0>"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(dbg_image_circles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keep this in mind for later lectures on camera calibration! We've only scratched the surface here :)"
   ]
  }
 ],
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