How are camera calibration extrinsic parameters' errors computed?

The standard errors (standard deviations) are given with matlab checkerboard camera calibration, but I am wondering how those errors are computed. In the available documentation, I can not find reference to an algorithm or method for this but only the algorithms/methods for the camera calibration itself.

I very much appreciate any help!

Answer 1

[Vidip Jain]

I understand that you want to know about how the standard errors for camera calibration are computed.

The standard errors (or standard deviations) provided by the MATLAB checkerboard camera calibration function give you an estimate of the uncertainty or precision of the calibration parameters computed during the camera calibration process, it relies on general statistical principles like-

1. Residual Analysis: During camera calibration, the calibration software minimizes the error between the observed image points (where checkerboard corners are detected) and the corresponding projected points on the calibration pattern's 3D model. The residuals are the differences between these observed and projected points.
2. Parameter Estimation: The camera calibration process involves estimating various intrinsic and extrinsic camera parameters, such as focal length, distortion coefficients, rotation, and translation. These parameters are adjusted to minimize the sum of the squared residuals.
3. Covariance Matrix: After parameter estimation, the calibration software computes the covariance matrix of the estimated parameters. This matrix quantifies how each parameter's uncertainty affects the others.

Refer to this documentation for more information: https://www.mathworks.com/help/vision/ref/cameracalibrationerrors.html