2D Shape Similarity for Voronoi-Delone Algorithms in Surface Reconstruction.

build surfaces between 2D contours in consecutive cross sections. This
problem has been traditionally attacked by (i) direct reconstruction based
on local geometric proximity between the contours, and (ii) classification
of topological events between the cross sections. These approaches have
been separately applied with limited success. In case (i), the resulting
surfaces may have overstretched or unnatural branches. These arise from
local contour proximity which does not reflect global similarity between the
contours. In case (ii), the topological events are identified but are not
translated into the actual construction of a surface. This article presents
an integration of the approaches (i) and (ii). Similarity between the
composite 2D regions bounded by the contours in consecutive cross sections
is used to: (a) decide whether a surface should actually relate two
composite 2D regions, (b) identify the type and location of topological
transitions between cross sections and (c) drives the surface construction
for the regions found to be related in step (a). The implemented method
avoids overstretched or unnatural branches, rendering a surface which is
both geometrically intuitive and topologically faithful to the cross
sections of the original object. The presented method is a good alternative
in cases in which correct reproduction of the topology of the surface (e.g.
simulation of flow in conduits) is more important than its geometry (e.g.
assessment of tumor mass in radiation planning).