Topological reconstruction of a smooth manifold-solid from its occluding contour

  • Lance R. Williams
Geometry and Shape I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 800)


This paper describes a simple construction for building a combinatorial model of a smooth manifold-solid from a labeled figure representing its occluding contour. The motivation is twofold. First, deriving the combinatorial model is an essential intermediate step in the visual reconstruction of solid-shape from image contours. A description of solid-shape consists of a metric and a topological component. Both are necessary: the metric component specifies how the topological component is embedded in three-dimensional space. The paneling construction described in this paper is a procedure for generating the topological component from a labeled figure representing an occluding contour. Second, the existence of this construction establishes the sufficiency of a labeling scheme for line-drawings of smooth solid-objects originally proposed by Huffman[5]. By sufficiency, it is meant that every set of closed plane-curves satisfying this labeling scheme is shown to correspond to a generic view of a manifold-solid. Together with the Whitney theorem[12], this confirms that Huffman's labeling scheme correctly distinguishes possible from impossible solid-objects.


Label Scheme Combinatorial Model Kidney Bean Planar Partition Image Contour 
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 1994

Authors and Affiliations

  • Lance R. Williams
    • 1
  1. 1.NEC Research InstitutePrincetonUSA

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