THE COMPLEX EGI - A NEW REPRESENTATION FOR 3-D POSE DETERMINATION

This paper describes a new 3-D object representation that can be used to determine the pose of an object. In this representation (called the complex extended Gaussian image (CEGI)), the weight associated with each outward surface normal is a complex weight. The normal distance of the surface from the predefined origin is encoded as the phase of the weight, whereas the magnitude of the weight is the visible area of the surface. This approach decouples the orientation and translation determination into two distinct least-squares problems. The justification for using such a scheme is twofold: It not only allows the pose of the object to be extracted, but it also distinguishes a convex object from a nonconvex object having the same EGI representation. The CEGI scheme has the advantage of not requiring explicit spatial object-model surface correspondence in determining object orientation and translation. Experiments involving synthetic data of two polyhedral and two smooth objects indicate the feasibility of this method. The best results are 4.7 and 1.5% (total distance error) for the polyhedral and smooth objects, respectively. The figures are quoted in terms of percentages of the maximum allowable displacement. Experiments using real range data for the two smooth objects yielded reasonably good results.