The Visual Computer

, Volume 24, Issue 3, pp 155–172 | Cite as

Enhancing 3D mesh topological skeletons with discrete contour constrictions

  • Julien Tierny
  • Jean-Philippe Vandeborre
  • Mohamed Daoudi
Original Article
First Online:

Abstract

This paper describes a unified and fully automatic algorithm for Reeb graph construction and simplification as well as constriction approximation on triangulated surfaces.

The key idea of the algorithm is that discrete contours – curves carried by the edges of the mesh and approximating the continuous contours of a mapping function – encode both topological and geometrical shape characteristics. Therefore, a new concise shape representation, enhanced topological skeletons, is proposed, encoding the contours’ topological and geometrical evolution.

First, mesh feature points are computed. Then they are used as geodesic origins for the computation of an invariant mapping function that reveals the shape most significant features. Next, for each vertex in the mesh, its discrete contour is computed. As the set of discrete contours recovers the whole surface, each of them can be analyzed, both to detect topological changes and constrictions. Constriction approximations enable Reeb graphs refinement into more visually meaningful skeletons, which we refer to as enhanced topological skeletons.

Extensive experiments showed that, without any preprocessing stage, proposed algorithms are fast in practice, affine-invariant and robust to a variety of surface degradations (surface noise, mesh sampling and model pose variations). These properties make enhanced topological skeletons interesting shape abstractions for many computer graphics applications.

Keywords

Shape abstraction Topological skeletons Feature points Constrictions Topology driven segmentation 
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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Julien Tierny
    • 1
  • Jean-Philippe Vandeborre
    • 2
  • Mohamed Daoudi
    • 2
  1. 1.LIFL (UMR USTL/CNRS 8022)University of LilleLilleFrance
  2. 2.GET/TELECOM Lille 1, LIFL (UMR USTL/CNRS 8022)University of LilleLilleFrance

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