SIGDT: 2D Curve Reconstruction

Information

• Publication Type: Journal Paper with Conference Talk
• Workgroup(s)/Project(s):
  • Modeling the World at Scale
• 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

• Paper
• Entry in reposiTUm (TU Wien Publication Database)
• DOI: 10.1111/cgf.14654

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/",
}