The Sampling-Reconstruction Dual

Information

• Publication Type: Invited Talk
• Workgroup(s)/Project(s): not specified
• Date: February 2025
• Event: Infinite-dimensional Geometry: Theory and Applications
• Conference date: 13. January 2025 – 14. February 2025
• Keywords: surface reconstruction, sampling

Abstract

Reconstructing surfaces of the real world from scans is an important and challenging problem. Its feasibility is limited by the number of the acquired points and their geometric configuration. The question of how many points exactly are required for the faithful reconstruction of the features leads to its inverse problem, sampling a known surface with the least possible number of points. This talk is about reconstruction algorithms and attempts to prove their theoretical bounds in the number of points required and its dual, sampling curves (as their simpler 2D equivalent) and surfaces with specified bounds from different representations such as meshes, smooth higher-order boundaries, subdivision limit surfaces, and signed distance functions, depending on the application, e.g., lossless reduction of scanned data size, measuring scan error, handling scan artifacts such as noise, outliers, and holes, or secondary goals such as accelerating simulations. The underlying assumption is that the smooth surface (reconstructed, or sampled) is richer than the sparse discrete set of geometric primitives (points + connectivity) it is represented with, leading to the goal of representing object boundaries, e.g., from the physical world, with the least amount of geometry.

Additional Files and Images

Weblinks

• Entry in reposiTUm (TU Wien Publication Database)

BibTeX

@talk{ohrhallinger-2025-tsd,
  title =      "The Sampling-Reconstruction Dual",
  author =     "Stefan Ohrhallinger",
  year =       "2025",
  abstract =   "Reconstructing surfaces of the real world from scans is an
               important and challenging problem. Its feasibility is
               limited by the number of the acquired points and their
               geometric configuration. The question of how many points
               exactly are required for the faithful reconstruction of the
               features leads to its inverse problem, sampling a known
               surface with the least possible number of points.   This
               talk is about reconstruction algorithms and attempts to
               prove their theoretical bounds in the number of points
               required and its dual, sampling curves (as their simpler 2D
               equivalent) and surfaces with specified bounds from
               different representations such as meshes, smooth
               higher-order boundaries, subdivision limit surfaces, and
               signed distance functions, depending on the application,
               e.g., lossless reduction of scanned data size, measuring
               scan error, handling scan artifacts such as noise, outliers,
               and holes, or secondary goals such as accelerating
               simulations.   The underlying assumption is that the smooth
               surface (reconstructed, or sampled) is richer than the
               sparse discrete set of geometric primitives (points +
               connectivity) it is represented with, leading to the goal of
               representing object boundaries, e.g., from the physical
               world, with the least amount of geometry.",
  month =      feb,
  event =      "Infinite-dimensional Geometry: Theory and Applications",
  keywords =   "surface reconstruction, sampling",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2025/ohrhallinger-2025-tsd/",
}