Display Settings:

Format

Send to:

Choose Destination
See comment in PubMed Commons below
Discrete Comput Geom. 2008 Oct 1;40(3):325-356.

Reconstruction Using Witness Complexes.

Author information

  • 1Dept. Computer Science, Stanford University, Stanford, CA 94305, USA.

Abstract

We present a novel reconstruction algorithm that, given an input point set sampled from an object S, builds a one-parameter family of complexes that approximate S at different scales. At a high level, our method is very similar in spirit to Chew's surface meshing algorithm, with one notable difference though: the restricted Delaunay triangulation is replaced by the witness complex, which makes our algorithm applicable in any metric space. To prove its correctness on curves and surfaces, we highlight the relationship between the witness complex and the restricted Delaunay triangulation in 2d and in 3d. Specifically, we prove that both complexes are equal in 2d and closely related in 3d, under some mild sampling assumptions.

PMID:
21643440
[PubMed]
PMCID:
PMC3105630
Free PMC Article

Images from this publication.See all images (7)Free text

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for PubMed Central
    Loading ...
    Write to the Help Desk