Tripod operators for recognizing objects in range images: rapid rejection of library objects

The tripod operator is a class of feature extraction operators for range images which facilitate the recognition and localization of objects. It consists of three points in 3-space fixed at the vertices of an equilateral triangle and a procedure for making several scalar measurements in the coordinate frame of the triangle. The triangle is then moved as a rigid body until the three vertices lie on the surface of some range image or modeled object. The resulting measurements are local shape features which are invariant under rigid motions. These features can be used to automatically find distinctive regions at which to begin recognition, to rapidly screen candidate objects for a match, and to speed pruning in the generation of interpretation trees. Tripod operators are applicable to all 3-D shapes, and reduce the need for specialized feature detectors. A key property is that they can be moved on the surface of an object in only three DOF (like a surveyor’s tripod on the ground). Consequently, only a 3-dimensional manifold of feature space points can be generated, for any dimensionality of feature vector. Thus, objects can be represented compactly, and in a form allowing fast matching. They are used here to characterize objects by generating a cloud of points in feature space for each object by random placement of the operator. Then new feature measurements are made by operator placements in a range image containing one of those objects. Using a simple nearest-neighbor approach, we determine which objects are rejected and which remain as recognition candidates. Experiments were performed using this approach, showing that tripod operators have excellent discriminating power.