Extracting projective invariant of 3D line set from a single view

Although projective invariants do not exist for general 3D objects in a single view, they do exist for some special 3D constrained structures. So far, several kinds of structure and their invariants have been proposed, such as six points on two adjacent planes, six lines on three planes and so on. But the sorts of them are still limited, which constrains their wide use to 3D object recognition. In this paper, a novel non-coplanar line structure and its projective invariant were derived. This kind of structure can be easily found in the objects formed by intersected polyhedrons. The experimental results showed that the values of the proposed invariant remain stable in the perspective projection between 3D rigid object and its perspective images, and are slightly different over a range of viewpoints.