Approximating Geodesics on Point Set Surfaces

Ruggeri, Mauro R.; Darom, Tal; Saupe, Dietmar; Kiryati, Nahum

Approximating Geodesics on Point Set Surfaces

Files

085-093.pdf (289 KB)

Date

2006

Authors

Ruggeri, Mauro R.
Darom, Tal
Saupe, Dietmar
Kiryati, Nahum

Publisher

The Eurographics Association

Abstract

We present a technique for computing piecewise linear approximations of geodesics on point set surfaces by minimizing an energy function defined for piecewise linear path. The function considers path length, closeness to the surface for the nodes of the piecewise linear path and for the intermediate line segments. Our method is robust with respect to noise and outliers. In order to avoid local minima, a good initial piecewise linear approximation of a geodesic is provided by Dijkstra s algorithm that is applied to a proximity graph constructed over the point set. As the proximity graph we use a sphere-of-influence weighted graph extended for surfel sets. The convergence of our method has been studied and compared to results of other methods by running experiments on surfaces whose geodesics can be computed analytically. Our method is presented and optimized for surfel-based representations but it has been implemented also for MLS surfaces. Moreover, it can also be applied to other surface representations, e.g., triangle meshes, radial-basis functions, etc.

        @inproceedings{10.2312:SPBG/SPBG06/085-093
,
booktitle = {Symposium on Point-Based Graphics
},
editor = {Mario Botsch and Baoquan Chen and Mark Pauly and Matthias Zwicker
},
title = {{Approximating Geodesics on Point Set Surfaces
}},
author = {Ruggeri, Mauro R. and 
Darom, Tal and 
Saupe, Dietmar and 
Kiryati, Nahum
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1811-7813
},
ISBN = {3-905673-32-0
},
DOI = {10.2312/SPBG/SPBG06/085-093
}
}