3-D object recognition using a new invariant relationship by single-view

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 oo-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 planet 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 el 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 ct 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. (C) 2000 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.