Signed Distance Transform Using Graphics Hardware

• Authors: Christian Sigg;Ronald Peikert;Markus Gross
• Venue: Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
• Year: 2003

This paper presents a signed distance transform algorithm using graphics hardware, which computes the scalar valued function of the Euclidean distance to a given manifold of co-dimension one. If this manifold is closed and orientable, the distance has a negative sign on one side of the manifold and a positive sign on the other. Triangle meshes are considered for the representation of a two-dimensional manifold and the distance function is sampled on a regular Cartesian grid. In order to achieve linear complexity in the number of grid points, to each primitive we assign a simple poly-hedron enclosing its Voronoi cell. Voronoi cells are known to contain exactly all points that lay closest to its corresponding primitive. Thus, the distance to the primitive only has to be computed for grid points inside its polyhedron. Although Voronoi cells partition space, the polyhedrons enclosing these cells do overlap. In regions where these overlaps occur, the minimum of all computed distances is assigned to a grid point. In order to speed up computations, points inside each polyhedron are determined by scan conversion of grid slices using graphics hardware. For this task, a fragment program is used to perform the nonlinear interpolation and minimization of distance values.