Abstract: A surface reconstruction system generates a “crust” to re-construct d dimensional surfaces from a set of sample points. A Voronoi diagram, which comprises a plurality of Voronoi cells and Voronoi vertices, is generated from the sample points to define the geometric shape of the Voronoi cells. The surface features of the original surface are re-constructed from the geometric shape of the Voronoi cell through selection of a subset of Voronoi vertices of the Voronoi diagram so as to approximate the medial axis of the original surface. In one embodiment, a subset of Voronoi vertices of the Voronoi diagram are selected by designating at least one pole for a corresponding Voronoi cell. The surface reconstruction technique also computes a Deluanay triangulation from the sample points and the poles, and then filters triangles from the Deluanay triangulation in which all three vertices are not sample points.

Abstract: The invention provides a simple method and apparatus for tracking image recording device motion using a light field. The invention locates the image recording device's position and orientation in each frame very precisely by checking the radiance seen along lines captured in previous frames. The invention provides an interactive system that provides the operator with feedback, to capture a sequence of frames that sufficiently cover the light field, to provide sufficient data for reconstruction of three-dimensional structures.