front_camera_calibration.ipynb

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   "mimetype": "text/x-python",
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   "pygments_lexer": "ipython3",
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  "kernelspec": {
   "name": "python37764bitcarlaconda44b743731b2f46ec8e17b5d02d653591",
   "display_name": "Python 3.7.7 64-bit ('carla': conda)"
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 "cells": [
  {
   "source": [
    "## Camera Calibration Matrix for Front Facing Semantic Camera\n",
    "\n",
    "This notebook constructs the calibration matrix for front facing semantic camera. Since the camera in Carla is ideal and without installation errors, these matrices can be manually set."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import cv2\n",
    "import yaml\n",
    "\n",
    "import numpy as np\n",
    "from math import tan\n",
    "import cv2\n",
    "from scipy.spatial.transform import Rotation\n",
    "import matplotlib.pyplot as plt\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
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     },
     "metadata": {},
     "execution_count": 2
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# Prepare data\n",
    "config_path = r\"settings/carlasim.yaml\"\n",
    "with open(config_path, 'r') as config_file:\n",
    "    config_args = yaml.safe_load(config_file)\n",
    "# FOV in deg\n",
    "fov = float(config_args['sensor']['front_camera']['fov'])\n",
    "\n",
    "# Image resolution\n",
    "res_h = int(config_args['sensor']['front_camera']['res_h'])\n",
    "res_v = int(config_args['sensor']['front_camera']['res_v'])\n",
    "\n",
    "# Image for calibration\n",
    "calib_img = cv2.imread('calib_images/ss_image.png')\n",
    "plt.imshow(calib_img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Calibration matrix\n",
    "# Intrinsic calibration matrix of semantic camera\n",
    "# FOV (in rad)\n",
    "fov_rad = fov * np.pi / 180  # 60 degrees\n",
    "# Focal length of semantic camera (in pixel)\n",
    "f = res_h/2 / tan(fov_rad/2)\n",
    "\n",
    "# Intrinsic calibration matrix\n",
    "K = np.array([[f, 0, res_h/2],\n",
    "              [0, f, res_v/2],\n",
    "              [0, 0, 1]])\n",
    "\n",
    "# Extrinsic calibration matrix\n",
    "# Compute relative translation of camera wrt front bumper\n",
    "dist_cam_to_fbumper = (config_args['ego_veh']['raxle_to_fbumper'] \n",
    "    - config_args['sensor']['front_camera']['pos_x'] \n",
    "    - config_args['ego_veh']['raxle_to_cg'])\n",
    "\n",
    "camera_height = config_args['sensor']['front_camera']['pos_z']\n",
    "# Camera's origin (principal point) wrt the reference frame, which is the front bumper center in the x-y plane in this case\n",
    "x0 = np.array([[-dist_cam_to_fbumper, 0, camera_height]]).T\n",
    "\n",
    "# Rotation matrix describing the orientation of reference frame wrt the camera frame\n",
    "# This is trival enough to set it manually in this project. Some automation might be needed in the future.\n",
    "R = Rotation.from_euler('zyx', [90, 0, 90], degrees=True).as_matrix()\n",
    "\n",
    "P = K @ R @ np.concatenate((np.eye(3), -x0), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "<matplotlib.image.AxesImage at 0x7fbe2022bd50>"
     },
     "metadata": {},
     "execution_count": 4
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "# World to image projection\n",
    "calib_image_copy = calib_img.copy()\n",
    "for x in range(40):\n",
    "    for y in [-1.75, 0, 1.75]:\n",
    "        x_world = np.array([[x, y, 0, 1]]).T\n",
    "        x_img = P @ x_world\n",
    "        x_img /= x_img[-1]\n",
    "        calib_image_copy = cv2.circle(\n",
    "            calib_image_copy, tuple(x_img[0:2]), 10, color=[0, 0, 255], thickness=2)\n",
    "plt.imshow(calib_image_copy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This matrix is useful for projecting 2D pixels into the 3D world with z known\n",
    "# Pole detection will use it.\n",
    "K_inv = np.linalg.inv(K)\n",
    "H = R.T @ K_inv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "calib_data = {}\n",
    "calib_data['K'] = K\n",
    "calib_data['R'] = R\n",
    "calib_data['x0'] = x0\n",
    "\n",
    "with open('calib_data.pkl', 'wb') as f:\n",
    "    pickle.dump(calib_data, f)"
   ]
  }
 ]
}