Determining Object Attitude from Extended Gaussian Images

The Extended Gaussian Image (EGI) of an object records the variation of surface area with surface orientation, uniquely representing convex objects. The inversion problem for polyhedra (from an EGI to a description in terms of vertices and faces) has been solved, by an iterative algorithm [Little, 1983]. The algorithm depends upon the mixed volume, a geometric construction linking the areas and positions of the faces of an object. A robust method for determining object attitude from the EGI is developed here, using this construction. Experiments show the method's insensitivity to small attitude differences. 1 I n t r o d u c t i o n Orientation maps can be generated by binocular stereo [Baker and Binford, 1981] [Grimson, 1981], photometric stereo [Woodham, 1980], shape from shading [Horn, 1975], or by differentiation of laser range images[Brou, 1984]. By translating the surface normals of an object to a common point, a representation of the distribution of surface orientation is formed, called the Extended Gaussian Image (EGI) [Horn, 1984]. Figure 1 shows the Extended Gaussian Image of a polyhedron and the corresponding object. Horn and Ikeuchi[1984] demonstrated the feasibility of using EGIs for attitude determination, comparing the EGI of a prototype with a sensed EGI. The reconstruction method using the mixed volume suggests a new method for attitude determination. This method is practical and more robust than direct comparison of EGIs. A detailed discussion of this method is presented in [Little, 1985]. * This research was supported in part by a UBC University Graduate Fellowship and by the Natural Science and Engineering Research Council of Canada grant A3390.