Part 4 - Geometric Camera Calibration.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c4eade51",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib widget\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from utils import *\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c76d4b0d",
   "metadata": {},
   "source": [
    "### Create Groundtruth matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f616f3a2",
   "metadata": {},
   "source": [
    "#### Define Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "83e2714b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# define extrinsic parameters\n",
    "# -------------------------------\n",
    "\n",
    "# rotate an angle of pi/4 along the standard Y axis\n",
    "angles = [np.pi/4]\n",
    "order = 'y'\n",
    "\n",
    "# transalte by the given offset\n",
    "offset = np.array([0, -8, 0])\n",
    "\n",
    "# define intrinsic parameters\n",
    "# -------------------------------\n",
    "\n",
    "f = 2\n",
    "s = 0\n",
    "a = 1\n",
    "cx = 0\n",
    "cy = 0\n",
    "img_size = (10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aafbafb3",
   "metadata": {},
   "source": [
    "#### Create Extrinsic and Intrinsic Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5525f473",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create extrinsic matrix\n",
    "# --------------------------\n",
    "\n",
    "# create rotation transformation matrix\n",
    "R = create_rotation_transformation_matrix(angles, order)\n",
    "R_ = np.identity(4)\n",
    "R_[:3, :3] = R\n",
    "\n",
    "# create translation transformation matrix\n",
    "T_ = create_translation_matrix(offset)\n",
    "\n",
    "E = np.linalg.inv(T_ @ R_)\n",
    "E = E[:-1, :]\n",
    "\n",
    "# create intrinsic matrix\n",
    "# ---------------------------\n",
    "K = compute_intrinsic_parameter_matrix(f, s, a, cx, cy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac593c66",
   "metadata": {},
   "source": [
    "#### generate random points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1d76cd46",
   "metadata": {},
   "outputs": [],
   "source": [
    "# choose the lower limit of the points such they're always beyond the image plane\n",
    "\n",
    "n_points = 12\n",
    "rand_points = generate_random_points(n_points, (-10, 0), (-10, 10), (f, 10))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18f800cb",
   "metadata": {},
   "source": [
    "#### Plot the setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "29d349ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create an image grid\n",
    "xx, yy, Z = create_image_grid(f, img_size)\n",
    "# convert the image grid to homogeneous coordinates\n",
    "pt_h = convert_grid_to_homogeneous(xx, yy, Z, img_size)\n",
    "# transform the homogeneous coordinates\n",
    "pt_h_transformed = T_ @ R_ @ pt_h\n",
    "# convert the transformed homogeneous coordinates back to the image grid\n",
    "xxt, yyt, Zt = convert_homogeneous_to_grid(pt_h_transformed, img_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c7450e85",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Z-axis')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "model_id": "173fae7205e54d5884057173006ad717",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define axis and figure\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.add_subplot(111,projection='3d')\n",
    "\n",
    "# set limits\n",
    "ax.set(xlim=(-10, 5), ylim=(-15, 5), zlim=(0, 10))\n",
    "\n",
    "# plot the camera in the world\n",
    "ax = pr.plot_basis(ax, R, offset)\n",
    "ax.plot_surface(xxt, yyt, Zt, alpha=0.75)\n",
    "\n",
    "# plot the generated random points\n",
    "c = 0\n",
    "for i in range(n_points):\n",
    "    point = rand_points[:, c]\n",
    "    ax.scatter(*point, color=\"orange\")\n",
    "    ax.plot(*make_line(offset, point), color=\"purple\", alpha=0.25)\n",
    "    c += 1\n",
    "\n",
    "ax.set_title(\"The Setup\")\n",
    "ax.set_xlabel(\"X-axis\")\n",
    "ax.set_ylabel(\"Y-axis\")\n",
    "ax.set_zlabel(\"Z-axis\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b892aa",
   "metadata": {},
   "source": [
    "#### Compute Projection of these points and form image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a336133a",
   "metadata": {},
   "outputs": [],
   "source": [
    "rand_points_camera = compute_coordniates_wrt_camera(rand_points, E, is_homogeneous=False)\n",
    "projections = compute_image_projection(rand_points_camera, K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "81479c57",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'projection of points in the image')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0ee01c332211466aa23923cce94120de",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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FBCipO++8s+jxPffcEzt37tynm6ZNnTq1+YvQH7vjjjuiqqqqza13q6qq4uSTT47Vq1fHhAkT4v3vf3+Ln6YvTtOmTYvf/OY3zacUtaY9fwmfNGlS9O3bN7773e8Wtb/88svNp5SVwimnnBIR0eI4TzzxRPz6179+18fZ/ff2ve99LyLeuQ9K0/vvfvz77rsv3nzzzZJ9zn0Z+8rKyjjppJPimmuuiYiI1atXl+TY+6oUKyWnn356/OpXv4rDDjus1fmaO4A0/UFg93vG3HTTTUWPx48fH4ccckjcc889Re1r166NFStWFLWdfvrpsXHjxmhoaGj1M44fP74DPgnQFVgBAUpq4cKF0bNnz/joRz8azzzzTHzlK1+JY445psU546258sorm8+N/4d/+IcYNGhQ3HnnnfHQQw/F1772taiurm7ztddff32ceOKJMXny5LjgggtizJgxsWXLlnjhhRfiRz/6UXPgmDt3btx9990xY8aMuOyyy+K4446Lbdu2xbJly+L000+Pk08+OQYMGBCjR4+OH/7whzF16tQYNGhQDB48uMUWoxER73nPe+IrX/lKXHHFFfGZz3wmPv3pT8fGjRtj/vz50adPn7jyyiv3eyz/2Pjx4+Nv/uZv4l/+5V+ioqIipk2bFmvWrImvfOUrUVtbG1/4whf2+7179+4d//zP/xxvvPFGfOADH4gVK1bEVVddFdOmTYsTTzwxIiI++tGPxsc+9rH40pe+FPX19fGhD30onn766bjyyivj2GOPjVmzZpXkcx599NEREXHNNdfEtGnTokePHjFhwoS46qqr4uWXX46pU6fGyJEjY9OmTXH99dcXXaeQS1ON119/fcyePTt69eoV48ePb9df9L/61a/G4sWL44QTTojPf/7zMX78+Ni+fXusWbMmHn744bjxxhtLeqrg3pxwwglx0EEHxec+97m48soro1evXnHnnXfGL37xi6J+FRUVMX/+/Dj//PPjrLPOivPOOy82bdoU8+fPj2HDhhVdf3L22WfHnXfeGdOnT49LLrkkjjvuuOjVq1e8/PLLsWTJkpgxY0aceeaZ2T4j0ImU+yp44MDQtPPSqlWr0hlnnJH69++fBgwYkD796U+nV199tajv6NGj02mnndbq+/zyl79MZ5xxRqqurk69e/dOxxxzTNFuVym9s+PP7bff3qL9vPPOSyNGjEi9evVKNTU16YQTTkhXXXVVUb/XX389XXLJJWnUqFGpV69eaciQIem0005Lzz33XHOfn/70p+nYY49NlZWVKSKad1FqbRvelFK65ZZb0oQJE1Lv3r1TdXV1mjFjRoudjGbPnp369evX5tjtTUNDQ7rmmmvSuHHjUq9evdLgwYPTX/7lX7bYZre9u2D169cvPf3002nKlCmpb9++adCgQemCCy5Ib7zxRlHfbdu2pS996Utp9OjRqVevXmnYsGHpggsuSK+//npRv7Z2aPr617/e4vix225jO3bsSH/913+dampqUqFQaB7rBx98ME2bNi2NGDEi9e7dOw0ZMiRNnz49LV++fK+fsa1dsH7wgx8U9Wttd7W2XH755Wn48OGpoqIiRURasmRJ87Fam9u7j0lKjbutff7zn09jx45NvXr1SoMGDUoTJ05MX/7yl1uM/d7er60xbuuzNs3jJ554orltxYoVadKkSamqqirV1NSkv/7rv07/9V//1eqY3HzzzelP/uRPUu/evdO4cePSrbfemmbMmJGOPfbYon5/+MMf0rXXXpuOOeaY1KdPn9S/f/90+OGHp/PPPz/99re/3eNnBA5chZRSyh97gAPNvHnzYv78+bFhw4aSXffQll/84hfx3ve+N370ox/F6aef3qHHOtDNmTMn7r333njjjTfKXQpd2KZNm2LcuHHxyU9+Mm6++eZylwN0ck7BArqUJUuWxC233BK9e/eO973vfeUuB7qd9evXx9VXXx0nn3xyHHzwwfHSSy/FN7/5zdiyZUtccskl5S4P6AIEEKBL+ehHPxpjx46N2267LfuFukDjhepr1qyJv/3bv43/+Z//ad4g4sYbb2zeRhhgT5yCBQAAZGMb3g6yYMGCKBQKMXfu3HKXAgAAnYYA0gGeeOKJuPnmm2PChAnlLgUAADoVAaTE3njjjTj33HPj3/7t3+Kggw4qdzkAANCpuAi9xC688MI47bTT4iMf+UhcddVV7Xrtrl274ne/+10MGDCg+a60AAB0Himl2LJlSwwfPrzo5pvsOwGkhL7//e/HqlWr4sknn9yn/jt27IgdO3Y0P37llVfiyCOP7KjyAAAokbq6uhg5cmS5y+iSBJASqauri0suuSQeeeSR6NOnzz69ZsGCBTF//vxW32vgwIGlLhEAgHepvr4+amtrY8CAAeUupcuyDW+JPPDAA3HmmWdGjx49mtsaGhqiUChERUVF7Nixo+i5iJYrIE0TevPmzQIIAEAnVF9fH9XV1b6vvQtWQEpk6tSp8ctf/rKo7a/+6q/i8MMPjy996UstwkdE482cKisrc5UIAABlJ4CUyIABA+Koo44qauvXr18cfPDBLdoBAKC7cuk+AACQjRWQDrR06dJylwAAAJ2KFRAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgG3dCBwCga9rVELFhecS2dRF9h0XUTI6o6FHuqtgLAQQAgK6nbmHEqksitr78TlvVyIiJ10fUzixfXeyVU7AAAOha6hZGLD+rOHxERGx9pbG9bmF56mKfCCAAAHQduxoaVz4itfLk222r5jb2o1MSQAAA6Do2LG+58lEkRWyta+xHpySAAADQdWxbV9p+ZCeAAADQdfQdVtp+ZCeAAADQddRMbtztKgptdChEVNU29qNTEkAAAOg6Kno0brUbES1DyNuPJ17nfiCdmAACAEDXUjszYvK9EVUjiturRja2uw9Ip+ZGhAAAdD21MyNGzHAn9C5IAAEAoGuq6BExdEq5q6CdnIIFAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AUiLf/va3Y8KECTFw4MAYOHBgTJo0KX784x+XuywAAOhUBJASGTlyZPzTP/1TPPnkk/Hkk0/GKaecEjNmzIhnnnmm3KUBAECnUUgppXIXcaAaNGhQfP3rX4/Pfvaz+9S/vr4+qqurY/PmzTFw4MAOrg4AgPbyfe3d61nuAg5EDQ0N8YMf/CDefPPNmDRpUrnLAQCATkMAKaFf/vKXMWnSpNi+fXv0798/7r///jjyyCPb7L9jx47YsWNH8+P6+vocZQIAQNm4BqSExo8fH0899VQ8/vjjccEFF8Ts2bPj2WefbbP/ggULorq6uvmntrY2Y7UAAJCfa0A60Ec+8pE47LDD4qabbmr1+dZWQGpra51TCADQSbkG5N1zClYHSikVBYzdVVZWRmVlZcaKAACgvASQErniiiti2rRpUVtbG1u2bInvf//7sXTp0li0aFG5SwMAgE5DACmRV199NWbNmhXr1q2L6urqmDBhQixatCg++tGPlrs0AADoNASQEvnOd75T7hIAAKDTswsWAACQjQACAABkI4AAAADZCCAAAEA2LkIH4MCwqyFiw/KIbesi+g6LqJkcUdGj3FUBsBsBBICur25hxKpLIra+/E5b1ciIiddH1M4sX10AtOAULAC6trqFEcvPKg4fERFbX2lsr1tYnroAaJUAAkDXtauhceUjUitPvt22am5jPwA6BQEEgK5rw/KWKx9FUsTWusZ+AHQKAggAXde2daXtB0CHE0AA6Lr6DittPwA6nAACQNdVM7lxt6sotNGhEFFV29gPgE5BAAGg66ro0bjVbkS0DCFvP554nfuBAHQiAggAXVvtzIjJ90ZUjShurxrZ2O4+IACdihsRAtD11c6MGDHDndABugABBIADQ0WPiKFTyl0FAHvhFCwAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAsulZ7gIAAGCPdjVEbFgesW1dRN9hETWTIyp6lLsq9pMAAgBA51W3MGLVJRFbX36nrWpkxMTrI2pnlq8u9ptTsAAA6JzqFkYsP6s4fEREbH2lsb1uYXnq4l0RQAAA6Hx2NTSufERq5cm321bNbexHlyKAAADQ+WxY3nLlo0iK2FrX2I8uRQABAKDz2bautP3oNAQQAAA6n77DStuPTkMAAQCg86mZ3LjbVRTa6FCIqKpt7EeXIoAAAND5VPRo3Go3IlqGkLcfT7zO/UC6IAEEAIDOqXZmxOR7I6pGFLdXjWxsdx+QLsmNCAEA6LxqZ0aMmOFO6AcQAQQAgM6tokfE0CnlroIScQoWAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgJTIggUL4gMf+EAMGDAghgwZEp/85Cfj+eefL3dZAADQqQggJbJs2bK48MIL4/HHH4/FixfHzp0749RTT40333yz3KUBAECnUUgppXIXcSDasGFDDBkyJJYtWxYf/vCH9+k19fX1UV1dHZs3b46BAwd2cIUAALSX72vvnhWQDrJ58+aIiBg0aFCZKwEAgM6jZ7kLOBCllOLSSy+NE088MY466qg2++3YsSN27NjR/Li+vj5HeQAAUDZWQDrARRddFE8//XTcdddde+y3YMGCqK6ubv6pra3NVCEAAJSHa0BK7OKLL44HHnggHnvssRg7duwe+7a2AlJbW+ucQgCATso1IO+eU7BKJKUUF198cdx///2xdOnSvYaPiIjKysqorKzMUB0AAHQOAkiJXHjhhfG9730vfvjDH8aAAQNi/fr1ERFRXV0dffv2LXN1AADQOTgFq0QKhUKr7bfddlvMmTNnn97Dkh4AQOfm+9q7ZwWkROQ4AADYO7tgAQAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZNOz3AVAl7OrIWLD8oht6yL6DouomRxR0aPcVQEAdAkCCLRH3cKIVZdEbH35nbaqkRETr4+onVm+ugAAuginYMG+qlsYsfys4vAREbH1lcb2uoXlqQsAoAsRQGBf7GpoXPmI1MqTb7etmtvYDwCANgkgsC82LG+58lEkRWyta+wHAECbBBDYF9vWlbYfAEA3JYDAvug7rLT9AAC6KQEE9kXN5MbdrqLQRodCRFVtYz8AANokgMC+qOjRuNVuRLQMIW8/nnid+4EAAOyFAAL7qnZmxOR7I6pGFLdXjWxsdx8QAIC9ciNCaI/amREjZrgTOgDAfhJAoL0qekQMnVLuKgAAuiSnYAEAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggJfTYY4/FGWecEcOHD49CoRAPPPBAuUsCAIBORQApoTfffDOOOeaY+Nd//ddylwIAAJ1Sz3IXcCCZNm1aTJs2rdxlAABAp2UFBAAAyMYKSBnt2LEjduzY0fy4vr6+jNUAAEDHswJSRgsWLIjq6urmn9ra2nKXBAAAHUoAKaPLL788Nm/e3PxTV1dX7pIAAKBDOQWrjCorK6OysrLcZQAAQDYCSAm98cYb8cILLzQ/fvHFF+Opp56KQYMGxahRo8pYGQAAdA4CSAk9+eSTcfLJJzc/vvTSSyMiYvbs2XH77beXqSoAAOg8BJASmjJlSqSUyl0GAAB0Wi5CBwAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsepa7AMpkV0PEhuUR29ZF9B0WUTM5oqJHuasCAOAAJ4B0R3ULI1ZdErH15XfaqkZGTLw+onZm+eoCAOCA5xSs7qZuYcTys4rDR0TE1lca2+sWlqcuAA58uxoiXl0aseauxv/uaih3RUAZWAHpTnY1NK58RGrlyRQRhYhVcyNGzHA6FgClZfUdeJsVkO5kw/KWKx9FUsTWusZ+AFAqVt+BPyKAdCfb1pW2HwDszV5X36Nx9d3pWNBtCCDdSd9hpe0HAHtj9R3YjQDSndRMbjzfNgptdChEVNU29gOAUrD6DuxGAOlOKno0XuwXES1DyNuPJ17nAnQASsfqO7AbAaS7qZ0ZMfneiKoRxe1VIxvb7UQCQClZfQd2Yxve7qh2ZuNWu+6EDkBHa1p9X35WNIaQP74Y3eo7dEcCSHdV0SNi6JRyVwFAd9C0+t7qfUCus/oO3YwAAgB0PKvvwNsEEAAgD6vvQLgIHQAAyEgAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyKZnuQuALmdXQ8SG5RHb1kX0HRZRMzmioke5qwIA6BIEEGiPuoURqy6J2PryO21VIyMmXh9RO7N8dQEAdBFOwYJ9VbcwYvlZxeEjImLrK43tdQvLUxcAQBcigMC+2NXQuPIRqZUn325bNbexHwAAbRJAYF9sWN5y5aNIitha19gPAIA2CSCwL7atK20/AIBuykXosC/6DittPw4cdkUDgHYRQGBf1Exu3O1q6yvR+nUghcbnaybnroxysisaALSbU7BgX1T0aPxSGRERhd2efPvxxOv85bs7sSsaAOwXAQT2Ve3MiMn3RlSNKG6vGtnY7i/e3Ydd0QBgvzkFC9qjdmbEiBnO+e/u2rMr2tApuaoCgC5BAIH2qujhS2V3Z1c0ANhvTsECaC+7ogHAfhNAANqraVe0FhsSNClEVNXaFQ0AWiGAALSXXdEAYL8JIAD7w65oALBfXIQOsL/sigYA7SaAALwbdkUDgHZxChYAAJCNAAIAAGQjgJTYDTfcEGPHjo0+ffrExIkTY/ny5eUuCTqPXQ0Rry6NWHNX4393NZS7IgAgM9eAlNDdd98dc+fOjRtuuCE+9KEPxU033RTTpk2LZ599NkaNGlXu8qC86hZGrLokYuvL77RVjWzcztaOUQDQbRRSSqncRRwoPvjBD8b73ve++Pa3v93cdsQRR8QnP/nJWLBgwV5fX19fH9XV1bF58+YYOHBgR5YKedUtjFh+VkTs/s/N2/fMsG0tAF2E72vvnlOwSuStt96KVatWxamnnlrUfuqpp8aKFSvKVBV0ArsaGlc+WoSPeKdt1VynYwFAN+EUrBL5/e9/Hw0NDTF06NCi9qFDh8b69etbfc2OHTtix44dzY/r6+s7tEYoiw3Li0+7aiFFbK1r7Gc7WwA44FkBKbFCoVD0OKXUoq3JggULorq6uvmntrY2R4mQ17Z1pe0HAHRpAkiJDB48OHr06NFiteO1115rsSrS5PLLL4/Nmzc3/9TV1eUoFfLqO6y0/QCALk0AKZHevXvHxIkTY/HixUXtixcvjhNOOKHV11RWVsbAgQOLfuCAUzO5cberaH0lMKIQUVXb2A8AOOAJICV06aWXxi233BK33npr/PrXv44vfOELsXbt2vjc5z5X7tKgfCp6NG61GxEtQ8jbjyde19gPADjguQi9hP7iL/4iNm7cGF/96ldj3bp1cdRRR8XDDz8co0ePLndpUF61Mxu32m31PiDX2YIXALoR9wHpROwrzQFvV0Pjblfb1jVe81Ez2coHAF2K72vvnhUQIJ+KHrbaBYBuzjUgAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNbXihvdzLAgBgvwkg0B51C9u4m/f17uYNALAPnIIF+6puYcTys4rDR0TE1lca2+sWlqcuAIAuRACBfbGroXHlI1IrT77dtmpuYz8AANokgMC+2LC85cpHkRSxta6xHwAAbRJAYF9sW1fafgAA3ZQAAvui77DS9gMA6KYEENgXNZMbd7uKQhsdChFVtY39AABokwAC+6KiR+NWuxHRMoS8/Xjide4HAgCwFwII7KvamRGT742oGlHcXjWysd19QAAA9sqNCKE9amdGjJjhTugAAPtJAIH2qugRMXRKuasAAOiSnIIFAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGQjgAAAANkIIAAAQDYCCAAAkI0AAgAAZCOAAAAA2QggAABANgIIAACQjQACAABkI4AAAADZCCAAAEA2AggAAJCNAAIAAGTTs9wF0E3saojYsDxi27qIvsMiaiZHVPQod1UAAGQmgNDx6hZGrLokYuvL77RVjYyYeH1E7czy1QUAQHZOwaJj1S2MWH5WcfiIiNj6SmN73cLy1AUAQFkIIHScXQ2NKx+RWnny7bZVcxv7AQDQLQggdJwNy1uufBRJEVvrGvsBANAtCCAlcvXVV8cJJ5wQVVVV8Z73vKfc5XQO29aVth8cKHY1RLy6NGLNXY3/tQoIQDfiIvQSeeutt+JTn/pUTJo0Kb7zne+Uu5zOoe+w0vaDA4FNGQDo5gSQEpk/f35ERNx+++3lLaQzqZnc+MVq6yvR+nUghcbnaybnrgzKo2lTht3/99C0KcPke4UQAA54TsGi41T0aPyrbkREFHZ78u3HE69zPxC6B5syAEBECCBltWPHjqivry/6OeDUzmz8q27ViOL2qpH+2kv3YlMGAIgIAWSP5s2bF4VCYY8/Tz755H6//4IFC6K6urr5p7a2toTVdyK1MyM+sSZi6pKIE77X+N9PvCh80L3YlAEAIsI1IHt00UUXxdlnn73HPmPGjNnv97/88svj0ksvbX5cX19/4IaQih4RQ6eUuwooH5syAEBECCB7NHjw4Bg8eHCHvX9lZWVUVlZ22PsDnYhNGQAgIpyCVTJr166Np556KtauXRsNDQ3x1FNPxVNPPRVvvPFGuUsDOgObMgBAREQUUkqt/SmOdpozZ078+7//e4v2JUuWxJQpU/bpPerr66O6ujo2b94cAwcOLHGFQKfQ6n1AahvDh+uiADo939fePQGkEzGhoZvY1dC429W2dY3XfNRMtvIB0EX4vvbuuQYEIDebMgDQjbkGBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyKZnuQvgHSmliIior68vcyUAALSm6Xta0/c22k8A6US2bNkSERG1tbVlrgQAgD3ZsmVLVFdXl7uMLqmQxLdOY9euXfG73/0uBgwYEIVCoay11NfXR21tbdTV1cXAgQPLWktnZHz2zhjtmfHZO2O0Z8Zn74zRnhmfvWttjFJKsWXLlhg+fHhUVLiaYX9YAelEKioqYuTIkeUuo8jAgQP9o7QHxmfvjNGeGZ+9M0Z7Znz2zhjtmfHZu93HyMrHuyO2AQAA2QggAABANgIIraqsrIwrr7wyKisry11Kp2R89s4Y7Znx2TtjtGfGZ++M0Z4Zn70zRh3DRegAAEA2VkAAAIBsBBAAACAbAQQAAMhGAAEAALIRQIiIiNdffz1mzZoV1dXVUV1dHbNmzYpNmzbt8TVz5syJQqFQ9HP88cfnKTiDG264IcaOHRt9+vSJiRMnxvLly/fYf9myZTFx4sTo06dPHHrooXHjjTdmqrR82jNGS5cubTFfCoVCPPfccxkrzuexxx6LM844I4YPHx6FQiEeeOCBvb6mO82h9o5Pd5s/CxYsiA984AMxYMCAGDJkSHzyk5+M559/fq+v605zaH/GqDvNo29/+9sxYcKE5hvoTZo0KX784x/v8TXdaf5EtH+MutP86WgCCBERcc4558RTTz0VixYtikWLFsVTTz0Vs2bN2uvrPv7xj8e6deuafx5++OEM1Xa8u+++O+bOnRtf/vKXY/Xq1TF58uSYNm1arF27ttX+L774YkyfPj0mT54cq1evjiuuuCI+//nPx3333Ze58nzaO0ZNnn/++aI586d/+qeZKs7rzTffjGOOOSb+9V//dZ/6d7c51N7xadJd5s+yZcviwgsvjMcffzwWL14cO3fujFNPPTXefPPNNl/T3ebQ/oxRk+4wj0aOHBn/9E//FE8++WQ8+eSTccopp8SMGTPimWeeabV/d5s/Ee0foybdYf50uES39+yzz6aISI8//nhz28qVK1NEpOeee67N182ePTvNmDEjQ4X5HXfccelzn/tcUdvhhx+eLrvsslb7/5//83/S4YcfXtR2/vnnp+OPP77Daiy39o7RkiVLUkSk119/PUN1nUtEpPvvv3+PfbrjHGqyL+PTnedPSim99tprKSLSsmXL2uzTnedQSvs2Rt19Hh100EHplltuafW57j5/muxpjLr7/CklKyDEypUro7q6Oj74wQ82tx1//PFRXV0dK1as2ONrly5dGkOGDIlx48bF//7f/ztee+21ji63w7311luxatWqOPXUU4vaTz311DbHY+XKlS36f+xjH4snn3wy/vCHP3RYreWyP2PU5Nhjj41hw4bF1KlTY8mSJR1ZZpfS3ebQ/uqu82fz5s0RETFo0KA2+3T3ObQvY9Sku82jhoaG+P73vx9vvvlmTJo0qdU+3X3+7MsYNelu86cjCCDE+vXrY8iQIS3ahwwZEuvXr2/zddOmTYs777wzHn300fjnf/7neOKJJ+KUU06JHTt2dGS5He73v/99NDQ0xNChQ4vahw4d2uZ4rF+/vtX+O3fujN///vcdVmu57M8YDRs2LG6++ea47777YuHChTF+/PiYOnVqPPbYYzlK7vS62xxqr+48f1JKcemll8aJJ54YRx11VJv9uvMc2tcx6m7z6Je//GX0798/Kisr43Of+1zcf//9ceSRR7bat7vOn/aMUXebPx2pZ7kLoOPMmzcv5s+fv8c+TzzxREREFAqFFs+llFptb/IXf/EXzf/3UUcdFe9///tj9OjR8dBDD8XMmTP3s+rOY/fPvrfxaK1/a+0HkvaM0fjx42P8+PHNjydNmhR1dXVx7bXXxoc//OEOrbOr6I5zaF915/lz0UUXxdNPPx3/+Z//ude+3XUO7esYdbd5NH78+Hjqqadi06ZNcd9998Xs2bNj2bJlbX7B7o7zpz1j1N3mT0cSQA5gF110UZx99tl77DNmzJh4+umn49VXX23x3IYNG1r8NWRPhg0bFqNHj47f/va37a61Mxk8eHD06NGjxV/yX3vttTbH45BDDmm1f8+ePePggw/usFrLZX/GqDXHH398fPe73y11eV1Sd5tDpdAd5s/FF18c/+///b947LHHYuTIkXvs213nUHvGqDUH8jzq3bt3/Mmf/ElERLz//e+PJ554Iq6//vq46aabWvTtrvOnPWPUmgN5/nQkAeQANnjw4Bg8ePBe+02aNCk2b94cP//5z+O4446LiIif/exnsXnz5jjhhBP2+XgbN26Murq6GDZs2H7X3Bn07t07Jk6cGIsXL44zzzyzuX3x4sUxY8aMVl8zadKk+NGPflTU9sgjj8T73//+6NWrV4fWWw77M0atWb16dZefL6XS3eZQKRzI8yelFBdffHHcf//9sXTp0hg7duxeX9Pd5tD+jFFrDuR5tLuUUpunSXe3+dOWPY1Ra7rT/Cmpslz6Tqfz8Y9/PE2YMCGtXLkyrVy5Mh199NHp9NNPL+ozfvz4tHDhwpRSSlu2bElf/OIX04oVK9KLL76YlixZkiZNmpRGjBiR6uvry/ERSur73/9+6tWrV/rOd76Tnn322TR37tzUr1+/tGbNmpRSSpdddlmaNWtWc////u//TlVVVekLX/hCevbZZ9N3vvOd1KtXr3TvvfeW6yN0uPaO0Te/+c10//33p9/85jfpV7/6VbrssstSRKT77ruvXB+hQ23ZsiWtXr06rV69OkVE+sY3vpFWr16dXnrppZSSOdTe8elu8+eCCy5I1dXVaenSpWndunXNP1u3bm3u093n0P6MUXeaR5dffnl67LHH0osvvpiefvrpdMUVV6SKior0yCOPpJTMn5TaP0bdaf50NAGElFJKGzduTOeee24aMGBAGjBgQDr33HNbbDMXEem2225LKaW0devWdOqpp6aamprUq1evNGrUqDR79uy0du3a/MV3kG9961tp9OjRqXfv3ul973tf0daOs2fPTieddFJR/6VLl6Zjjz029e7dO40ZMyZ9+9vfzlxxfu0Zo2uuuSYddthhqU+fPumggw5KJ554YnrooYfKUHUeTds17v4ze/bslJI51N7x6W7zp7Wx+eN/g1Myh/ZnjLrTPDrvvPOa/32uqalJU6dObf5inZL5k1L7x6g7zZ+OVkjp7SuMAAAAOphteAEAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACyEUAAAIBsBBAAACAbAQQAAMhGAAEAALIRQAAAgGwEEAAAIBsBBAAAyEYAAQAAshFAAACAbAQQAAAgGwEEAADIRgABAACy+f8a16OXiuLkWwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "for i in range(n_points):\n",
    "    ax.scatter(*projections.reshape(-1, 2)[i], color=\"orange\")\n",
    "    \n",
    "ax.set_title(\"projection of points in the image\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c26bb65",
   "metadata": {},
   "source": [
    "### Perform Direct Linear Calibration"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "340636ef",
   "metadata": {},
   "source": [
    "#### Create the algebraic matrix A and find m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "76275893",
   "metadata": {},
   "outputs": [],
   "source": [
    "# compute the algebraic matrix A\n",
    "A = create_algebraic_matrix(rand_points, projections)\n",
    "\n",
    "# compute At x A\n",
    "A_ = np.matmul(A.T, A)\n",
    "# compute its eigenvectors and eigenvalues\n",
    "eigenvalues, eigenvectors = np.linalg.eig(A_)\n",
    "# find the eigenvector with the minimum eigenvalue\n",
    "# (numpy already returns sorted eigenvectors wrt their eigenvalues)\n",
    "m = eigenvectors[:, 11]\n",
    "\n",
    "# reshape m back to a matrix\n",
    "M = m.reshape(3, 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc3f0351",
   "metadata": {},
   "source": [
    "#### Compute predictions from the calibrated matrix M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "faa87bc3",
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = compute_world2img_projection(rand_points, M, is_homogeneous=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a78ae31c",
   "metadata": {},
   "source": [
    "#### plot predictions and the groundtruth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "534b7044",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e0c128c7f0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6f85c4bddabe4749ad661aa33223098d",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "for i in range(n_points):\n",
    "    if i == 0:\n",
    "        o_label = \"groundtruth\"\n",
    "        g_label = \"predictions\"\n",
    "    else:\n",
    "        o_label = \"\"\n",
    "        g_label = \"\"\n",
    "        \n",
    "    ax.scatter(*projections.reshape(-1, 2)[i], color=\"orange\", alpha=0.75, label=o_label)\n",
    "    ax.scatter(*predictions.reshape(-1, 2)[i], color=\"green\", alpha=0.75, label=g_label)\n",
    "    \n",
    "ax.set_title(\"groundtruth vs predictions - direct linear calibration\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6daf9a58",
   "metadata": {},
   "source": [
    "### Optimizing wrt Geometric Error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "af77330e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5c66c682",
   "metadata": {},
   "outputs": [],
   "source": [
    "result = minimize(geometric_error, m, args=(rand_points, projections))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c2a039aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "M_ = result.x.reshape(3, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3b4689bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions_v2 = compute_world2img_projection(rand_points, M_, is_homogeneous=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "39d4146e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1e0c22c16a0>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a79721c97ea3458aba8c86113f1a5b76",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "for i in range(n_points):\n",
    "    if i == 0:\n",
    "        o_label = \"groundtruth\"\n",
    "        g_label = \"predictions\"\n",
    "    else:\n",
    "        o_label = \"\"\n",
    "        g_label = \"\"\n",
    "        \n",
    "    ax.scatter(*projections.reshape(-1, 2)[i], color=\"orange\", alpha=0.5, label=o_label)\n",
    "    ax.scatter(*predictions_v2.reshape(-1, 2)[i], color=\"green\", alpha=0.5, label=g_label)\n",
    "    \n",
    "ax.set_title(\"groundtruth vs predictions - optimization wrt geometric error\")\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6aec69c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "67f75f3f3d364befabb0de91f75480ad",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(8, 6))\n",
    "\n",
    "for i in range(n_points):\n",
    "        \n",
    "    axes[0].scatter(*projections.reshape(-1, 2)[i], color=\"orange\", label=o_label)\n",
    "    axes[1].scatter(*predictions_v2.reshape(-1, 2)[i], color=\"green\", label=g_label)\n",
    "    \n",
    "axes[0].set_title(\"groundtruth\")\n",
    "axes[1].set_title(\"predictions\")\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff028366",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}