Representing the world in terms of visible surfaces and the freespacesexisting between these surfaces and the viewer is an important problemsin robotics. Recently, researchers have proposed using the 3DsDelaunay Tessellation for representing 3D stereo vision data and thesfreespace determined therefrom. We discuss problems with using thes3D Delaunay Tessellation as the basis of the representation andspropose an alternative representation that we are currentlysinvestigating. This new representation is appropriate for planningsmobile robot navigation and promises to be robust when using stereosdata that has errors and uncertainty.