New algorithm for calculating an invariant of 3D point sets from a single view

The invariant used as an index has shown many advantages over the pose dependent methods in model-based object recognition. Although perspective, or even weak perspective invariants do not exist for general three-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 lie on the vertices of a six-sided polyhedral and is applicable to position 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. Hence it is applicable to a wider class of objects. The algorithm is demonstrated on images from real scenes.