Level Set Method for Surface Reconstruction and Its Application in Surveying

Abstract

A novel approach to a three-dimensional (3D) model creation from data sets obtained by laser scanning or photogrammetry is presented, including a description of the method and efficient numerical algorithms for 3D model creation for surveying applications. The presented method solves the fundamental problem of surface reconstruction by constructing models using differential geometry and partial differential equations. The time-relaxed eikonal equation was used to obtain the distance function from the cloud of points, and the 3D model was then created by the evolution of an initial guess by the advection equation regularized by curvature, where the advective velocity is given by the gradient of the computed distance function. The partial differential equations were discretized by the finite-difference schemes, and the results of the 3D model creation are presented and discussed.