<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Direct Simple Computation of Middle Surface Between 3D Point Clouds and/or Discrete Surfaces by Tracking Sources in Distance Function Calculation Algorithms

Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering

Slovak University of Technology in Bratislava

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces....

Direct Simple Computation of Middle Surface Between 3D Point Clouds and/or Discrete Surfaces by Tracking Sources in Distance Function Calculation Algorithms

Published Online: Dec 18, 2023

Page range: -

Received: Nov 13, 2022

Accepted: Oct 09, 2023

DOI: https://doi.org/10.2478/tmmp-2023-0033

Keywords
Middle surface, 3D point cloud, triangulated surface, fast sweeping method, fast marching method, vector distance transform, Dijkstra-Pythagoras method

© 2023 Balázs Kósa et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Direct Simple Computation of Middle Surface Between 3D Point Clouds and/or Discrete Surfaces by Tracking Sources in Distance Function Calculation Algorithms

Published Online: Dec 18, 2023

Page range: -

Received: Nov 13, 2022

Accepted: Oct 09, 2023

DOI: https://doi.org/10.2478/tmmp-2023-0033

KeywordsMiddle surface, 3D point cloud, triangulated surface, fast sweeping method, fast marching method, vector distance transform, Dijkstra-Pythagoras method

© 2023 Balázs Kósa et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Middle surface, 3D point cloud, triangulated surface, fast sweeping method, fast marching method, vector distance transform, Dijkstra-Pythagoras method