Direct simple computation of middle surface between 3D point clouds and/or discrete surfaces by tracking sources in distance function calculation algorithms
This work addresses a computational geometry problem for researchers and practitioners in fields like computer graphics and medical imaging, offering an incremental improvement over existing methods by simplifying the process.
The paper tackled the problem of computing middle surfaces between 3D point clouds or discrete surfaces by introducing a fast and simple method that determines the middle surface directly from the distance function, avoiding traditional reliance on second-order differential characteristics and heuristics. It compared results from algorithms like fast sweeping, vector distance transform, fast marching, and Dijkstra-Pythagoras, showing improved efficiency in 3D data processing.
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.