Topological Reconstruction of a Smooth Manifold-Solid from Its OccludingContour

  • Authors:
  • Lance R. Williams

  • Affiliations:
  • NEC Research Institute, 4 Independence Way, Princeton, NJ 08540. E-mail: williams@research.nj.nec.com

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

This paper describes a simple construction for building a combinatorialmodel of a smooth manifold-solid from a labeled-figure representing itsoccluding contour. The motivation is twofold. First, deriving thecombinatorial model is an essential intermediate step in the visualreconstruction of solid-shape from image contours. A description ofsolid-shape consists of a metric and a topological component. Both arenecessary: the metric component specifies how the topological component isembedded in three-dimensional space. Thepaneling construction described in this paper is aprocedure for generating the topological component from a labeled-figurerepresenting the occluding contour. Second, the existence of thisconstruction establishes the sufficiency of a labeling scheme forline-drawings of smooth solid-objects originally proposed by Huffman (1971).By sufficiency, it is meant that every set of closed plane-curves satisfyingthis labeling scheme is shown to correspond to a generic view of amanifold-solid. Together with the Whitney theorem (Whitney, 1955), thisconfirms that Huffman‘s labeling scheme correctly distinguishes possible fromimpossible smooth solid-objects.