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

TL;DR

This paper presents a simple, fast method for computing middle surfaces between 3D point clouds and discrete surfaces by directly tracking sources in distance function calculations, avoiding complex differential analysis.

Contribution

It introduces a novel approach that computes middle surfaces directly from distance functions, simplifying and speeding up the process compared to traditional methods.

Findings

The proposed method is faster and simpler than traditional singularity-based approaches.

Comparison of algorithms shows the effectiveness of fast sweeping, fast marching, and Dijkstra-Pythagoras methods.

Results demonstrate accurate middle surface computation across various 3D data sets.

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 differential 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 finding the middle surface between 3D data sets.