Interpolating an unorganized 2D point cloud with a single closed shape

Stefan Ohrhallinger, Sudhir Mudur
Interpolating an unorganized 2D point cloud with a single closed shape
Computer-Aided Design, 43(1):1629-1638, January 2011. [paper]

Information

Abstract

Given an unorganized two-dimensional point cloud, we address the problem of efficiently constructing a single aesthetically pleasing closed interpolating shape, without requiring dense or uniform spacing. Using Gestalt’s laws of proximity, closure and good continuity as guidance for visual aesthetics, we require that our constructed shape be a minimal perimeter, non-self intersecting manifold. We find that this yields visually pleasing results. Our algorithm is distinct from earlier shape reconstruction approaches, in that it exploits the overlap between the desired shape and a related minimal graph, the Euclidean Minimum Spanning Tree (EMST). Our algorithm segments the EMST to retain as much of it as required and then locally partitions and solves the problem efficiently. Comparison with some of the best currently known solutions shows that our algorithm yields better results.

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paper: Reconstruction of 2D Point Cloud paper: Reconstruction of 2D Point Cloud

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BibTeX

@article{ohrhallinger_stefan-2011-001,
  title =      "Interpolating an unorganized 2D point cloud with a single
               closed shape",
  author =     "Stefan Ohrhallinger and Sudhir Mudur",
  year =       "2011",
  abstract =   "Given an unorganized two-dimensional point cloud, we address
               the problem of efficiently constructing a single
               aesthetically pleasing closed interpolating shape, without
               requiring dense or uniform spacing. Using Gestalt’s laws
               of proximity, closure and good continuity as guidance for
               visual aesthetics, we require that our constructed shape be
               a minimal perimeter, non-self intersecting manifold. We find
               that this yields visually pleasing results. Our algorithm is
               distinct from earlier shape reconstruction approaches, in
               that it exploits the overlap between the desired shape and a
               related minimal graph, the Euclidean Minimum Spanning Tree
               (EMST). Our algorithm segments the EMST to retain as much of
               it as required and then locally partitions and solves the
               problem efficiently. Comparison with some of the best
               currently known solutions shows that our algorithm yields
               better results. ",
  month =      jan,
  issn =       "0010-4485",
  journal =    "Computer-Aided Design",
  number =     "1",
  volume =     "43",
  pages =      "1629--1638",
  keywords =   "EMST, Curve, Point cloud, Reconstruction, Shape
               Construction, Boundary, Computational geometry, Point set",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2011/ohrhallinger_stefan-2011-001/",
}