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Eccentricity in images of circular and spherical targets and its impact on spatial intersection
Author(s) -
Luhmann Thomas
Publication year - 2014
Publication title -
the photogrammetric record
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 51
eISSN - 1477-9730
pISSN - 0031-868X
DOI - 10.1111/phor.12084
Subject(s) - ellipse , eccentricity (behavior) , intersection (aeronautics) , projection (relational algebra) , geometry , image (mathematics) , mathematics , perspective (graphical) , space (punctuation) , optics , computer vision , physics , computer science , algorithm , engineering , aerospace engineering , operating system , law , political science
A behaviour of perspective projection which causes eccentricity in the image measurement of circular and spherical targets is discussed. While it is commonly known that flat circular targets can have a significant displacement of the elliptical image centre with respect to the true circle centre, it can also be shown that a similar effect also exists for spherical targets. Both types of target images exhibit elliptical characteristics. If measurement methods such as best‐fitting ellipses are used to detect the target, the calculated ellipse centre does not correspond to the desired target centre in 3D space. This paper firstly discusses the use and measurement of circular and spherical targets. It then describes the geometrical projection model in order to demonstrate the eccentricity in image space which, based on numerical simulations, is further quantified and investigated. Finally, the resulting effect in 3D space is estimated for stereo‐ and multi‐image intersections. It is shown that the eccentricity is larger than usually assumed, and must be compensated for in high‐accuracy applications. Furthermore, spherical targets do not display better results than circular targets.