The invariant used as an index has shown many advantages over the pose
dependent methods in model-based object recognition. Although perspec
tive, or even weak perspective invariants do not exist for general thr
ee-dimensional point sets from a single view, invariants do exist for
structured three-dimensional point sets. However, such invariants are
not easy to derive. A new interpretation of calculating invariants for
a special structure of three-dimensional objects is presented. The 3D
invariant structure proposed by Rothwell requires seven points that l
ie on the vertices of a six-sided polyhedral and is applicable to posi
tion free objects. In comparison, the proposed algorithm requires only
six points on adjacent (virtual) planes that provide two sets of four
coplanar points and does not require the position free condition. Hen
ce it is applicable to a wider class of objects. The algorithm is demo
nstrated on images from real scenes.