The perspective projection of a sphere appears as an ellipse in the image where the ellipse center differs from the projection of the sphere's center. This eccentricity leads to systematic errors in photogrammetric measurements. For a sphere of 40 mm diameter on a plate with 33 cm distance from the camera's projection center, 15 cm distance to the nadir point and a principal distance of 12 mm, the eccentricity can reach more than 20 μm in the image. The publication at hand deals with eccentricity correction terms that can be applied either to the measured image coordinates or through a model adaption. An overview of existing correction terms in image space is provided and a new extension of the pinhole camera model for spheres is proposed which also can be used simultaneously for the sphere parameter determination. Furthermore, estimation procedures for the initial values of the sphere radius as well as the principal distance and the principal point from the ellipse measurements in a single image are presented. In experiments, the proposed methods reduced the reprojection error by a factor of three and achieved a relative scale accuracy of 0.2% to 0.3% when using known radii.