3D Reconstruction of Complex Polyhedral Shapes from Contours using a Simplified Generalized Voronoi Diagram

Abstract

We are interested in modelling the suface of very irregular objects known through a few planar polygonal cross-sections. This problem is considered difficult when severe topology and morphology variations appear between neighbouring cross-sections (multi-branching, holes, disconnected areas). Only few methods deal with this problem in a systematic way.The paper describes an original method allowing to build, in a fully automatic and systematic way, an external surface with a valid topology in any case. It moreover allows to adjust details of the reconstructed surface in view of the morphologies and topologies of the various initial cross-sectional contours.At first, a global correspondence is operated between each couple of adjacent cross-sections by extracting polygonal areas of difference. Next steps are based on the computation in each area of difference of the bisector network, a well-defined simplified generalised Voronoi diagram. This structure is used both for connecting initial contour points and for interpolating new intermediate portions of contours. It depends on the complexity of initial 2D shapes. Interpolation stage is then recursively operated until a satisfactory surface has been obtained or until a maximum number of new intermediate cross-sectional contours have been built. The valid final suface is directly obtained by concatenating all the tiling areas of difference without need of any post processing step. The processing of several real data related to geological bodies or human organs has proved that the described method allows detailed modelling of irregular objects with very performing CPU times. The reconstruction appears insensitive to severe variations of the object shape, including apparitions of holes or disconnections.