Information
- Publication Type: Journal Paper with Conference Talk
- Workgroup(s)/Project(s):
- Date: October 2022
- Journal: Computer Graphics Forum
- Volume: 41
- Open Access: yes
- Number: 7
- Location: Kyoto, Japan
- Lecturer: Diana Marin
- ISSN: 1467-8659
- Event: 30th Pacific Conference on Computer Graphics and Applications, Pacific Graphics 2022
- DOI: 10.1111/cgf.14654
- Call for Papers: Call for Paper
- Booktitle: Pacific Graphics 2022
- Pages: 12
- Publisher: The Eurographics Association and John Wiley & Sons Ltd.
- Conference date: 5. October 2022 – 8. October 2022
- Pages: 25 – 36
- Keywords: Curve reconstruction, Spheres-of-influence graph
Abstract
Determining connectivity between points and reconstructing their shape boundaries are long-standing problems in computer graphics. One possible approach to solve these problems is to use a proximity graph. We propose a new proximity graph computed by intersecting the to-date rarely used proximity-based graph called spheres-of-influence graph (SIG) with the Delaunay triangulation (DT). We prove that the resulting graph, which we name SIGDT, contains the piece-wise linear reconstruction for a set of unstructured points in the plane for a sampling condition superseding current bounds and capturing well practical point sets' properties. As an application, we apply a dual of boundary adjustment steps from the CONNECT2D algorithm to remove the redundant edges. We show that the resulting algorithm SIG-CONNECT2D yields the best reconstruction accuracy compared to state-of-the-art algorithms from a recent comprehensive benchmark, and the method offers the potential for further improvements, e.g., for surface reconstruction.Additional Files and Images
Weblinks
BibTeX
@article{marin-2022-sigdt, title = " SIGDT: 2D Curve Reconstruction", author = "Diana Marin and Stefan Ohrhallinger and Michael Wimmer", year = "2022", abstract = "Determining connectivity between points and reconstructing their shape boundaries are long-standing problems in computer graphics. One possible approach to solve these problems is to use a proximity graph. We propose a new proximity graph computed by intersecting the to-date rarely used proximity-based graph called spheres-of-influence graph (SIG) with the Delaunay triangulation (DT). We prove that the resulting graph, which we name SIGDT, contains the piece-wise linear reconstruction for a set of unstructured points in the plane for a sampling condition superseding current bounds and capturing well practical point sets' properties. As an application, we apply a dual of boundary adjustment steps from the CONNECT2D algorithm to remove the redundant edges. We show that the resulting algorithm SIG-CONNECT2D yields the best reconstruction accuracy compared to state-of-the-art algorithms from a recent comprehensive benchmark, and the method offers the potential for further improvements, e.g., for surface reconstruction.", month = oct, journal = "Computer Graphics Forum", volume = "41", number = "7", issn = "1467-8659", doi = "10.1111/cgf.14654", booktitle = "Pacific Graphics 2022", pages = "12", publisher = "The Eurographics Association and John Wiley & Sons Ltd.", pages = "25--36", keywords = "Curve reconstruction, Spheres-of-influence graph", URL = "https://www.cg.tuwien.ac.at/research/publications/2022/marin-2022-sigdt/", }