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This paper discusses a feature of projective geometry which causes eccentricity in the image measurement of circular and spherical\udtargets. While it is commonly known that flat circular targets can have a significant displacement of the elliptical image centre with\udrespect to the true imaged circle centre, it can also be shown that the a similar effect exists for spherical targets. Both types of targets\udare imaged with an elliptical contour. As a result, if measurement methods based on ellipses are used to detect the target (e.g. best-fit\udellipses), the calculated ellipse centre does not correspond to the desired target centre in 3D space. This paper firstly discusses the\uduse and measurement of circular and spherical targets. It then describes the geometrical projection model in order to demonstrate the\udeccentricity in image space. Based on numerical simulations, the eccentricity in the image is further quantified and investigated.\udFinally, the resulting effect in 3D space is estimated for stereo and multi-image intersections. It can be stated that the eccentricity is\udlarger than usually assumed, and must be compensated for high-accuracy applications. Spherical targets do not show better results\udthan circular targets. The paper is an updated version of Luhmann (2014) new experimental investigations on the effect of length\udmeasurement errors

the international archives of the photogrammetry, remote sensing and spatial information sciences/international archives of the photogrammetry, remote sensing and spatial information sciences

Eccentricity in Images of Circular and Spherical Targets and its Impact to 3D Object Reconstruction