## Abstract

This paper describes a new 3-D object representation which can be used to
determine the pose of an object. In this representation (called the Complex
Extended Gaussian Image, or 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 while 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 two-fold: it not only allows the
pose of the object to be extracted, but it also distinguishes a convex
object from a non-convex 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.