Polyhedrization of the Boundary of a Voxel Object

  • Jean Françon
  • Laurent Papier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)


A voxel object (finite set of voxels) is considered in the cuberille approach (more precisely, the 3D cell complex approach). Its boundary is a set of surfels (faces of voxels). We assume, without loss of generality, that this set of surfels is a polyhedron whose faces are surfels. These faces can be agglomerated in such a way that the boundary is a polyhedron whose faces are topological disks of standard arithmetic planes; this new kind of polyhedron is called a discrete standard polyhedron. Thus, these new faces are generally much bigger than one surfel, and a discrete standard polyhedron has generally a less smaller space complexity than the starting set of surfels. This process, called polyhedrization or facetization, is the 3D extension of the known polygonalization of 2D discrete curves. The other main properties of this polyhedrization are the non-uniqueness, and the reversibility, i.e. starting from the discrete standard polyhedron, the boundary can be exactly computed back again. A polyhedrization algorithm is presented in this paper. It uses a recent algorithm for recognizing standard arithmetic planes. Examples of polyhedrizations of synthetic and natural objects are given. Examples of application to the visualization of the boundary of a voxel object are also given.


Standard Plane Topological Disk Digital Plane Standard Face Current Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Jean Françon
    • 1
  • Laurent Papier
    • 1
  1. 1.d’Informatique et de TélédétectionLaboratoire des Sciences de l’ImageIllkirchFrance

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