Camera Calibration and Bird's-Eye-View Transform for Lane and Parking Perception

The problem

Lane keeping, parking assistance and surround view need measurements in metres on the road plane, not pixels. A bird's-eye-view transform provides that, but only if intrinsics, mounting height and orientation are accurate and the road is flat. Errors in any of these distort the BEV and the downstream measurements built on it.

Objectives

• Calibrate intrinsics and lens distortion with a checkerboard.
• Estimate extrinsics (height, pitch, yaw, roll) from a ground-plane target.
• Build an inverse perspective mapping to a metric BEV image.
• Measure lane width, lateral offset and parking-slot geometry in the BEV.
• Quantify BEV error and its sensitivity to extrinsic errors.

What you need

Key concepts

Intrinsics and distortion

Focal lengths, principal point and radial and tangential distortion coefficients that describe the camera itself, independent of where it is mounted.

Extrinsics

The rotation and translation from the vehicle or ground frame to the camera: mounting height and pitch, yaw and roll angles.

Inverse perspective mapping

A homography that maps the road plane from the camera image to a top-down metric grid, valid only for points on that plane.

Flat-world assumption

IPM assumes all mapped points lie on one plane. Objects above the road, such as vehicles, appear stretched and slopes cause scale errors.

Step-by-step guide

1. 1

   Define requirements and the vehicle frame

   Define what the BEV must deliver: for example a top-down image covering 3 to 25 m ahead and ±5 m sideways at 2 cm per pixel, with position error below a stated value within 15 m. Define the vehicle coordinate frame (origin, axes) following the convention used by Automated Driving Toolbox. Choose a flat test area such as a lab floor or a closed car park with permission.

   Checkpoint: A requirements note with BEV range, resolution, accuracy targets and a sketch of the frames.

2. 2

   Calibrate intrinsics

   Capture 20 to 30 checkerboard images covering the whole field of view, including corners where distortion is strongest. Run the Camera Calibrator app in MATLAB with two radial coefficients (three for a wide lens) and tangential distortion, and remove images with high reprojection error. Repeat the calibration in OpenCV with cv2.calibrateCamera on the same images and compare focal lengths and distortion coefficients.

   Checkpoint: Mean reprojection error below about half a pixel and matching intrinsics from both tools.

3. 3

   Mount the camera and survey ground points

   Fix the camera rigidly at a measured height, roughly windscreen height, looking forward with slight downward pitch. Lay out a grid of tape marks or a large checkerboard on the floor and measure each point's position in the vehicle frame with a tape measure. Record these ground-truth coordinates in a table. Keep some marks for validation only, not for estimating extrinsics.

   Checkpoint: A survey table of ground-point coordinates, split into estimation and validation points.

4. 4

   Estimate extrinsics

   Detect the ground pattern in an undistorted image and use estimateExtrinsics in MATLAB (or cv2.solvePnP in OpenCV) with the estimation points to obtain camera rotation and translation. Convert to height, pitch, yaw and roll and compare height with the tape-measured value. Create a monoCamera object with the intrinsics, height and pitch, and check that imageToVehicle returns correct coordinates for the estimation points.

   Checkpoint: Estimated height within a few centimetres of measured and low reprojection error on ground points.

5. 5

   Build the bird's-eye view

   Create a birdsEyeView object with the output area and image size from the requirements and transform the camera image. In OpenCV, compute a homography from four or more ground correspondences with cv2.findHomography and warp with cv2.warpPerspective to the same metric grid. Overlay a metre grid on both BEV images and inspect straight lines and right angles on the floor pattern.

   Checkpoint: BEV images from MATLAB and OpenCV in which floor lines appear straight and parallel with the grid aligned.

6. 6

   Measure BEV accuracy

   Locate each validation mark in the BEV image, convert to metres and compute the position error against the survey. Plot error against distance from the camera. Repeat for three or four camera poses to check repeatability. Compare MATLAB and OpenCV pipelines on the same images to separate implementation differences from calibration error. Separate the error into longitudinal and lateral components, because lateral error matters most for lane keeping while longitudinal error matters more for parking depth. State whether errors grow linearly or faster with distance.

   Checkpoint: An error-versus-distance plot for validation points that meets or explains the accuracy target.

7. 7

   Quantify sensitivity to extrinsic errors

   Perturb pitch by ±0.5 and ±1 degree, height by ±2 and ±5 cm and roll by ±0.5 degree in the transform, and recompute validation point errors. Plot error growth against perturbation and distance. This shows why vehicle pitch from braking or loading matters. Optionally record the camera while pitching the mount slightly to see the effect in real images. Express each sensitivity as centimetres of error per degree or per centimetre of perturbation at fixed distances such as 5, 10 and 20 m.

   Checkpoint: Sensitivity plots showing how each extrinsic error grows with distance.

8. 8

   Apply BEV to lanes and parking slots

   Mark lane lines and a parking slot outline on the floor, or use recorded footage from a closed car park, and detect them in the BEV with thresholding and line fitting (Hough or RANSAC). Compute lane width, lateral offset of the camera from lane centre and slot width, depth and orientation in metres, then compare with tape measurements. Show how a vehicle in the image is stretched by the flat-world assumption.

   Checkpoint: Lane and slot measurements in metres compared with tape-measured values.

9. 9

   Analyse and recommend

   Combine the results into recommendations: which calibration errors dominate at which distances, how often extrinsics should be re-estimated, and when online pitch estimation from lane vanishing points would be required. Compare the effort and accuracy of the MATLAB and OpenCV workflows. Discuss the flat-world limit for ramps and kerbs and how multi-camera surround view extends the method. Turn the findings into a short calibration procedure that another student could follow with the same camera and mount.

   Checkpoint: A written recommendation backed by the error and sensitivity results.

10. 10

    Write the thesis chapter

    Present the camera model, calibration procedure, extrinsic estimation, BEV construction, accuracy and sensitivity results and the lane and parking applications. Include photographs of the setup, the survey table and all scripts. State the limitations: one camera, a flat test surface and static poses. Present a clear error budget that a reader could use to specify a calibration process. Add a short section comparing your measured error with the requirement set in the first step and explain any shortfall.

    Checkpoint: A chapter with an error budget and reproducible calibration scripts.

Testing & validation

• Intrinsic reprojection error from both tools.
• BEV position error against surveyed validation points by distance.
• Sensitivity of BEV error to pitch, height and roll perturbations.
• Lane width and parking slot dimensions against tape measurements.

Expected results

A calibrated monocular camera with a metric bird's-eye view, measured accuracy against surveyed points, an extrinsic error budget and working lane and parking measurements.

Take it further

• Estimate pitch online from lane vanishing points and compare accuracy.
• Stitch two or four cameras into a surround-view BEV.
• Use the BEV in a parking-slot detector on recorded car-park video.
• Calibrate a fisheye lens with the fisheye model and compare.

Viva and review questions

Learn it at DIYguru

These DIYguru courses and programmes teach what this project needs.