Camera calibration as machine learning problem using dense phase shifting pattern, checkerboards, and different cameras

Abstract

Non-contact measurements using digital cameras require a reliable camera calibration typically based on a pinhole camera model with a few lower-order distortions (in OpenCV typically up to 14 parameters). The assessment of the calibration quality is typically done with the re-projection error (RPE). We propose a different quality measure, the forward propagation error (FPE) that determines the deviation in real world coordinates using parameters from the camera calibration. In addition, we introduce a machine learning-inspired method for a more reliable camera calibration. We explore the quality of our camera calibration using RPE, FPE, and a machine learning method by a series of checkerboard (using spares points) or phase shifting patterns (dense points), different camera types, and different camera models by comparing results from simulations and experiments. The machine learning inspired method helps to identify outliers which can easily be removed from the calibration process ensuring a reliable camera calibration. Our investigation shows the better the camera the better the camera calibration. We found that the 5 parameter OpenCV model was sufficient for our camera calibration. In addition, the 5 parameter model and the dense phase shifting pattern were precise and accurate and only limited by our target 8k monitor with about 0.09 mm pixel pitch in terms of FPE. We found already a good calibration using about 20 different poses and a checkerboard pattern by a correct generation of poses. The checkerboard pattern shows good results, and can easily be interpreted with the FPE.