Modeling the uncertainty of indirect calculations from 2D detected edges of projected 3D circular markers’ centers in photogrammetric systems

Abstract. Optical markers’ centres’ calculation, indirectly inferred from fitted ellipses’ borders, is subject to uncertainties which arise from both noise in data and systematic errors and whose nonlinear propagation has a strong impact on the attainable overall uncertainty of industrial close-range photogrammetric systems. Based on both exhaustive experimental measurements and a revisit of pinhole projection theory mapping the 2D detected ellipses’ borders onto 3D circular markers’ borders, the detection’s precision, shown to be independent of systematic errors and markers’ size in the range of sizes 40–160 px, is characterized as a function of markers’ gray intensity and orientation, both of which measurable during image processing. The proposed model has two or three experimental coefficients which need to be customized according to the used camera-lens system and edge-detection algorithm.