Systematic geometric image measurement errors of circular object targets: Mathematical formulation and correction

The use of circular object targets is very common in spatial photogrammetric object reconstruction. An object circle is projected on to the image plane as an ellipse if the object plane and the image plane are not parallel to each other. The image co-ordinates of the centre of the ellipse are usually determined automatically by means of digital image processing. These co-ordinates are then used as observations for a subsequent reconstruction of the three dimensional object point. The image co-ordinates of the centre of the ellipse and the true co-ordinates of the projected centre of the circular object target are not identical; thus eccentricity is caused, resulting in systematic geometric image measurement errors. This paper describes the functional context of this eccentricity for a typical target/camera set-up. The possible solutions for a correction of this systematic eccentricity error are derived. Guidelines for the correct combination of object target sizes and exposure distances, guaranteeing reliable image point measurements and accurate object point determination, are proposed.