The Complex EGI: A New Representation for 3-D Pose Determination

Abstract

The complex extended Gaussian image (CEGI), a 3D object representation that can be used to determine the pose of an object, is described. In this representation, 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 are presented to illustrate the feasibility of this method.