Grid-Detection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Grid Detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "flat_chess = cv2.imread('../DATA/flat_chessboard.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1d5b6ca4888>"
      ]
     },
     "execution_count": 3,
     "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,cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "found, corners = cv2.findChessboardCorners(flat_chess,(7,7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(49, 1, 2)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corners.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": 7,
     "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1d5b76390c8>"
      ]
     },
     "execution_count": 8,
     "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": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "dots = cv2.imread('../DATA/dot_grid.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1d5b76bb908>"
      ]
     },
     "execution_count": 10,
     "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": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "found, corners = cv2.findCirclesGrid(dots, (10,10), cv2.CALIB_CB_SYMMETRIC_GRID)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": 13,
     "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": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1d5b793b308>"
      ]
     },
     "execution_count": 14,
     "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)"
   ]
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}