Camera Calibration with Weighted Direct Linear Transformation and Anisotropic Uncertainties of Image Control Points

Camera calibration is a crucial step for computer vision in many applications. For example, adequate calibration is required in infrared thermography inside gas turbines for blade temperature measurements, for associating each pixel with the corresponding point on the blade 3D model. The blade has to be used as the calibration frame, but it is always only partially visible, and thus, there are few control points. We propose and test a method that exploits the anisotropic uncertainty of the control points and improves the calibration in conditions where the number of control points is limited. Assuming a bivariate Gaussian 2D distribution of the position error of each control point, we set uncertainty areas of control points' position, which are ellipses (with specific axis lengths and rotations) within which the control points are supposed to be. We use these ellipses to set a weight matrix to be used in a weighted Direct Linear Transformation (wDLT). We present the mathematical formalism for this modified calibration algorithm, and we apply it to calibrate a camera from a picture of a well known object in different situations, comparing its performance to the standard DLT method, showing that the wDLT algorithm provides a more robust and precise solution. We finally discuss the quantitative improvements of the algorithm by varying the modules of random deviations in control points' positions and with partial occlusion of the object.