2D Shape similarity as a complement for Voronoi-Delone methods in shape reconstruction (2005)
In surface reconstruction from planar slices it is necessary to build surfaces between corresponding 2D regions in consecutive levels -- The problem has been traditionally attacked with (i) direct reconstruction based on local geometric proximity between the regions, and (ii) classification of topological events between the slices, which control the evolution of the cross cuts -- These approaches have been separately applied with mixed success -- In the case (i), the results may be surfaces with over-stretched or unnatural branches, resulting from a local contour proximity which does not correspond to global similarity between regions -- In (ii), the consequences from topological events upon the actual surface realization have not been drawn -- In this paper an integration of (i) and (ii) is presented, which uses a criteria of similarity between composed 2D regions in consecutive slices to: (a) decide if a surface should actually relate those regions, (b) identify the topological transitions between levels and (c) construct the local surface for the related regions -- The method implemented hinders over-stretched and unnatural branches, therefore rendering a surface which adjusts to geometrically-sound topological events -- This is a good alternative when the surface reconstructed needs to be topologically faithful (for example in flow simulation) in addition to represent the a rough geometrical space (for example in radiation planning)