Vol. 33 (5), pp. 741-754

We propose a new method for recognizing three-dimensional objects using a three-dimensional invariant relationship
and geometric hashing by single-view. We develop a special structure consisting of four co-planar points and any two
non-planar points with respect to the plane. We derive an invariant relationship for the structure, which is represented by
a plane equation. For the recognition of three-dimensional objects using the geometric hashing, a set of points on the
plane, thereby satisfying the invariant relationship, are mapped into a set of points intersecting the plane and the unit
sphere. Since the structure is much more general than the previous structures proposed by Rothwell et al. (Oxford
University TR-OUEL 1927/92, 1992) and Zhu et al. (Proceedings of the 12th International Conference on Robotics and
Automation, Nagoya, Japan, 1995, pp. 1726}1731), it gives enough many voting to generate hypotheses. We also show
that from the proposed invariant relationship, an invariant for the structure by two-view and an invariant for a structure
proposed by Zhu et al. (Proceedings of the 12th International Conference on Robotics and Automation, Nagoya,
Japan, 1995, pp. 1726}1731) can also be derived. Experiments using three-dimensional polyhedral objects are carried out
to demonstrate the feasibility of our method for three-dimensional objects.