  This paper presents an analytical study for the metric properties of the
paraboloidal double projection, i.e. central and orthogonal projections used in
the catadioptric camera system. Metric properties have not sufficiently studied
in previous treatments of such system. These properties incorporate the
determination of the true lengths of projected lines and areas bounded by
projected lines. The advantageous main gain of determining metric elements of
the paraboloidal double projection is studying distortion analysis and camera
calibration, which is considered an essential tool in testing camera accuracy.
Also, this may be considered as a significant utility in studying comparison
analysis between different cameras projection systems.
