Direct simple computation of middle surface between 3D point clouds and/or discrete surfaces by tracking sources in distance function calculation algorithms

Abstract

In this paper, we introduce novel methods for computing middle
surfaces between various 3D data sets such as point clouds and/or discrete
surfaces. Traditionally the middle surface is obtained by detecting singularities
in computed distance function such as ridges, triple junctions, etc. It requires
to compute second order dierential characteristics and also some kinds of
heuristics must be applied. Opposite to that, we determine the middle surface
just from computing the distance function itself which is a fast and simple
approach. We present and compare the results of the fast sweeping method,
the vector distance transform algorithm, the fast marching method, and the
Dijkstra-Pythagoras method in nding the middle surface between 3D data
sets.