Using the Single Camera Calibrator App

Camera Calibrator Overview

You can use the Camera Calibrator app to estimate camera intrinsic parameters. You can use these camera parameters for various computer vision applications. These applications, such as removing the effects of lens distortion from an image, measuring planar objects, or reconstructing 3-D scenes from multiple cameras.

Camera capturing checkerboard calibration patterns posed at various angles. All checkerboard calibration patterns are within the field of view of the camera. Additional workflow diagram; Prepare, Add Images, Calibrate, Evalute, Improve, and Export.

Use this workflow to calibrate your camera and to follow best practices to prepare and capture calibration images and to evaluate calibration accuracy.

The Camera Calibrator app incorporates a suite of functions to implement the camera calibration workflow. You can use these functions directly in the MATLAB^® workspace. For a list of these functions, see the Camera Calibration topic.

Choose a Calibration Pattern

The Camera Calibrator app supports checkerboard, circle grid, AprilTag, ChArUco, and custom detector patterns. For details on each of these patterns and PDF files containing printable patterns, see Calibration Patterns. The app can calibrate cameras with a field of view (FOV) of up to 195 degrees.

Capture Calibration Images

For best calibration results, use between 10 and 20 images of the calibration pattern. The calibrator requires at least three images. Use uncompressed images or lossless compression formats such as PNG. The calibration pattern and the camera setup must satisfy a set of requirements to work with the calibrator. For more details on camera setup and capturing images, see Prepare Camera and Capture Images For Camera Calibration.

Using the Camera Calibrator App

Open the App

MATLAB Toolstrip: On the Apps tab, in the Image Processing and Computer Vision section, click the Camera Calibrator icon.
MATLAB command prompt: Enter cameraCalibrator

Add Images and Select Camera Model

To begin calibration, you must add images. You can add saved images from a folder or add images directly from a camera. The calibrator analyzes the images to ensure they meet the calibrator requirements. The calibrator then detects the points of the selected pattern. For details on camera setup and capturing images, see Prepare Camera and Capture Images For Camera Calibration.

Add Images from File

Acquire Live Images

The Camera Calibrator app works with UVC compliant webcams. You can acquire live images from a webcam using MATLAB Webcam support. To use this feature, you must install the MATLAB Support Package for USB Webcams. See Webcam Acquisition Overview. To add live images, follow these steps.

On the Calibration tab, in the File section, click Add Images, then select From camera.
This opens the Camera tab. If only one webcam is connected to your system, the app selects it by default and a live preview pane opens. If you have multiple cameras connected and want to use one other than the default, select that camera in the Camera list.
(Optional) Set properties for the camera to control the image. Select the Camera Properties to open the Camera Properties dialog box for the selected camera. The available properties vary depending on your device.
Use the sliders and lists to change the available property settings. The preview pane updates dynamically when you change a setting. When you are done setting properties, click anywhere outside of the dialog box to dismiss it.
Enter a location to save the acquired image files in the Save Location box. You can type the path to a folder or use the Browse button. You must have permission to write to the folder you specify.
Set the capture parameters.
- To set the number of seconds between image captures, use the Capture Interval (sec) box or slider. The default is 5 seconds, the minimum is 1 second, and the maximum is 60 seconds.
- To set the number of image captures, use the Number of images to capture box or slider. The default is 20 images, the minimum is 2 images, and the maximum is 100 images.
The default configuration captures a total of 20 images, one every 5 seconds.
The preview pane shows the live images streamed as RGB data. After you adjust any device properties and capture settings, use the Preview window as a guide to line up the camera to acquire the pattern image you want to capture.
Select Capture. The app captures the specified number of images, and the thumbnails of the snapshots appear in the Data Browser pane. They are automatically named incrementally, and are captured as .png files.
You can stop the image capture before the designated number of images are captured by selecting Stop Capture.
When you are capturing images of a pattern, after the designated number of images are captured, the app displays the Image and Pattern Properties dialog box. Select the calibration pattern in the image and specify the pattern properties. Click OK.
The app then calculates and displays the detection results.
To dismiss the Detection Results dialog box, click OK.
When you have finished acquiring live images, select Close Image Capture to close the Camera tab.

After you add images, the Image and Pattern Properties dialog box to your session, appears. Before the calibrator can analyze the calibration patterns, you must select the calibration pattern to detect and set image properties for the pattern structure. For more details on this dialog, see Select Calibration Pattern and Set Properties.

Analyze Images

View Images and Detected Points

Calibrate

Once you are satisfied with the accepted images, on the Calibration tab, select Calibrate. The default calibration settings use a minimum set of camera parameters. Start by running the calibration with the default settings. After evaluating the results, you can try to improve calibration accuracy by adjusting the settings or adding or removing images, and then calibrating again. If you switch between the standard and fisheye camera models, you must recalibrate.

Select Camera Model

Standard Model Options

Fisheye Model Options

Calibration Algorithm

For fisheye camera model calibration, see Fisheye Calibration Basics.

The standard camera model calibration algorithm assumes a pinhole camera model:

$w [\begin{matrix} x & y & 1 \end{matrix}] = [\begin{matrix} X & Y & Z & 1 \end{matrix}] [\begin{matrix} R \\ t \end{matrix}] K$

(X,Y,Z) — World coordinates of a point.
(x,y) — Image coordinates of the corresponding image point in pixels.
w — Arbitrary homogeneous coordinates scale factor.
K — Camera intrinsic matrix, defined as:

$[\begin{matrix} f_{x} & 0 & 0 \\ s & f_{y} & 0 \\ c_{x} & c_{y} & 1 \end{matrix}]$
The coordinates (c_x, c_y) represent the optical center (the principal point), in pixels. When the x- and y-axes are exactly perpendicular, the skew parameter, s, equals 0. The matrix elements are defined as:
- f_x = F*s_x, expressed in pixels.
- f_y = F*s_y, expressed in pixels.
- F is the focal length in world units, typically expressed in millimeters.
- s_x and s_y are the number of pixels per world unit in the x- and y- respectively.
R — Matrix representing the 3-D rotation of the camera.
t — Translation of the camera relative to the world coordinate system.

The camera calibration algorithm estimates the values of the intrinsic parameters, the extrinsic parameters, and the distortion coefficients. Camera calibration involves these steps:

Solve for the intrinsics and extrinsics in closed form, assuming that lens distortion is zero. [1]
Estimate all parameters simultaneously, including the distortion coefficients, using nonlinear least-squares minimization (Levenberg–Marquardt algorithm). Use the closed-form solution from the preceding step as the initial estimate of the intrinsics and extrinsics. Set the initial estimate of the distortion coefficients to zero. [1][2]

Evaluate Calibration Results

You can evaluate calibration accuracy by examining the reprojection errors, examining the camera extrinsics, or viewing the undistorted image. For best calibration results, use all three methods of evaluation.

Camera calibration results, displaying undistorted image, reprojection errors chart, and camera extrinsics diagram

Examine Reprojection Errors

Examine Extrinsic Parameter Visualization

View Undistorted Image

Improve Calibration

To improve the calibration, you can remove high-error images, add more images, or modify the calibrator settings.

Consider adding more images if:

You have fewer than 10 images.
The calibration patterns do not cover enough of the image frame.
The calibration patterns do not have enough variation in orientation with respect to the camera.

Consider removing images if the images:

Have a high mean reprojection error.
Are blurry.
Contain a calibration pattern at an angle greater than 45 degrees relative to the camera plane.
Incorrectly detected calibration pattern points.

Standard Model: Change the Number of Radial Distortion Coefficients

You can specify two or three radial distortion coefficients. On the Calibrations tab, in the Camera Model section, with Standard selected, click Options. Specify the Radial Distortion as either two or three coefficients by selecting 2 Coefficients or 3 Coefficients, respectively.

Radial distortion is the displacement of image points along radial lines extending from the principal point.

As image points move away from the principal point (positive radial displacement), image magnification decreases and a pincushion-shaped distortion occurs on the image.
As image points move toward the principal point (negative radial displacement), image magnification increases and a barrel-shaped distortion occurs on the image.

Three grids that each represent a type of distortion. One with pincushion distortion (positive radial displacement), one with no distortion, and one with barrel distortion (negative radial displacement)

The radial distortion coefficients model this type of distortion. The distorted points are denoted as (x_distorted, y_distorted):

x_distorted = x(1 + k₁*r² + k₂*r⁴ + k₃*r⁶)

y_distorted= y(1 + k₁*r² + k₂*r⁴ + k₃*r⁶)

x, y — Undistorted pixel locations. x and y are in normalized image coordinates. Normalized image coordinates are calculated from pixel coordinates by translating to the optical center and dividing by the focal length in pixels. Thus, x and y are dimensionless.
k₁, k₂, and k₃ — Radial distortion coefficients of the lens.
r² = x² + y²

Typically, two coefficients are sufficient for calibration. For severe distortion, such as in wide-angle lenses, you can select three coefficients to include k₃.

The undistorted pixel locations are in normalized image coordinates, with the origin at the optical center. The coordinates are expressed in world units.

Standard Model: Compute Skew

Standard Model: Compute Tangential Distortion

Fisheye Model: Estimate Alignment

Export Camera Parameters

When you are satisfied with your calibration accuracy, select Export Camera Parameters for a standard camera model or Export Camera Parameters for a fisheye camera model. You can either export the camera parameters to an object in the MATLAB workspace or generate the camera parameters as a MATLAB script. If the default values work well, then you do not need to make any adjustments before exporting the parameters

Export Camera Parameters

Generate MATLAB Script

References

[1] Zhang, Z. “A Flexible New Technique for Camera Calibration.” IEEE Transactions on Pattern Analysis and Machine Intelligence. 22, no. 11 (November 2000): 1330–34. https://doi.org/10.1109/34.888718.

[2] Heikkila, J., and O. Silven. “A Four-step Camera Calibration Procedure with Implicit Image Correction.” In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition. 1106–12. San Juan, Puerto Rico: IEEE Comput. Soc, 1997. https://doi.org/10.1109/CVPR.1997.609468.

[3] Scaramuzza, Davide, Agostino Martinelli, and Roland Siegwart. "A Toolbox for Easily Calibrating Omnidirectional Cameras." In Proceedings of IEEE International Workshop on Intelligent Robots and Systems 2006 (IROS 2006), 5695–701. Beijing, China: IEEE, 2006. https://doi.org/10.1109/IROS.2006.282372

[4] Urban, Steffen, Jens Leitloff, and Stefan Hinz. “Improved Wide-Angle, Fisheye and Omnidirectional Camera Calibration.” ISPRS Journal of Photogrammetry and Remote Sensing 108 (October 2015): 72–79. https://doi.org/10.1016/j.isprsjprs.2015.06.005.