Efficient Representation and Extraction of 2-Manifold Isosurfaces Using kd-Trees (extended version)

In: Graphical Models (Nov. 2004), 66:6(370-397)
 

Abstract

In this paper, we propose the utilization of a kd-tree based hierarchy as an implicit object representation. Compared to an octree, the kd-tree based hierarchy is superior in terms of adaptation to the object surface. In consequence, we obtain considerably more compact implicit representations especially in case of thin object structures. We describe a new isosurface extraction algorithm for this kind of implicit representation. In contrast to related algorithms for octrees, it generates 2-manifold meshes even for kd-trees with cells containing multiple surface components. The algorithm retains all the good properties of the Dual Contouring approach by Ju et al. [ACM Trans. Graphics 21 (2002) 339-346] like feature preservation, computational efficiency, etc. In addition, we present a simplification framework for the surfaces represented by the kd-tree based on quadric error metrics. We adapt this framework to quantify the influence of topological changes, thereby allowing controlled topological simplification of the object. The advantages of the new algorithm are demonstrated by several examples.

Keywords: Hierarchical Structures, Isosurfaces, Mesh Generation, Topological Simplification

(See also the article's webpage from the Graphical Models journal for an online version of the paper.)

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Bibtex

@ARTICLE{gress-2004-efficient,
     author = {Gre{\ss}, Alexander and Klein, Reinhard},
      pages = {370--397},
      title = {Efficient Representation and Extraction of 2-Manifold Isosurfaces Using kd-Trees (extended version)},
    journal = {Graphical Models},
     volume = {66},
     number = {6},
       year = {2004},
      month = nov,
  publisher = {Elsevier},
   keywords = {Hierarchical Structures, Isosurfaces, Mesh Generation, Topological Simplification},
   abstract = {In this paper, we propose the utilization of a kd-tree based hierarchy as an implicit object
               representation. Compared to an octree, the kd-tree based hierarchy is superior in terms of
               adaptation to the object surface. In consequence, we obtain considerably more compact implicit
               representations especially in case of thin object structures. We describe a new isosurface
               extraction algorithm for this kind of implicit representation. In contrast to related algorithms for
               octrees, it generates 2-manifold meshes even for kd-trees with cells containing multiple surface
               components. The algorithm retains all the good properties of the Dual Contouring approach by Ju et
               al. [ACM Trans. Graphics 21 (2002) 339-346] like feature preservation, computational efficiency,
               etc. In addition, we present a simplification framework for the surfaces represented by the kd-tree
               based on quadric error metrics. We adapt this framework to quantify the influence of topological
               changes, thereby allowing controlled topological simplification of the object. The advantages of the
               new algorithm are demonstrated by several examples.}
}