Representing stereo data with the Delaunay triangulation

A coherent way of interpolating 3-D data obtained by stereo, for example, with a simplicial polyhedral surface is discussed. The method is based on constrained Delaunay triangulation; the polyhedral surface is obtained by using a simple visibility property to mark tetrahedra likely to be empty. The method is intrinsically discontinuity-preserving and yields both a surface representation of objects and a volume representation of free space which may be useful in robotics. Algorithms to implement the method are described and their complexity analyzed in the worst case and average case situations where tools of probabilistic geometry are used