New efficient numerical method for 3D point cloud surface reconstruction by using level set methods

Kósa, Balázs, Haličková-Brehovská, Jana, and Mikula, Karol. "New efficient numerical method for 3D point cloud surface reconstruction by using level set methods." Proceedings of Equadiff 14. Bratislava: Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing, 2017. 387-396. <http://eudml.org/doc/294904>.

@inProceedings{Kósa2017,
abstract = {In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is a construction of initial condition by a simple tagging algorithm which allows us also to highly speed up the numerical scheme when solving PDEs. For the numerical discretization of the model we suggested an unconditionally stable method, in which the semi-implicit co-volume scheme is used in curvature part and implicit upwind scheme in advective part. The method was tested on representative examples and applied to real data representing the historical and cultural objects scanned by 3D laser scanners.},
author = {Kósa, Balázs, Haličková-Brehovská, Jana, Mikula, Karol},
booktitle = {Proceedings of Equadiff 14},
keywords = {Point cloud, level set methods, reconstruction},
location = {Bratislava},
pages = {387-396},
publisher = {Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing},
title = {New efficient numerical method for 3D point cloud surface reconstruction by using level set methods},
url = {http://eudml.org/doc/294904},
year = {2017},
}

TY - CLSWK
AU - Kósa, Balázs
AU - Haličková-Brehovská, Jana
AU - Mikula, Karol
TI - New efficient numerical method for 3D point cloud surface reconstruction by using level set methods
T2 - Proceedings of Equadiff 14
PY - 2017
CY - Bratislava
PB - Slovak University of Technology in Bratislava, SPEKTRUM STU Publishing
SP - 387
EP - 396
AB - In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is a construction of initial condition by a simple tagging algorithm which allows us also to highly speed up the numerical scheme when solving PDEs. For the numerical discretization of the model we suggested an unconditionally stable method, in which the semi-implicit co-volume scheme is used in curvature part and implicit upwind scheme in advective part. The method was tested on representative examples and applied to real data representing the historical and cultural objects scanned by 3D laser scanners.
KW - Point cloud, level set methods, reconstruction
UR - http://eudml.org/doc/294904
ER -