Topological Repairing of 3D Digital Images

  • Authors:

  • Marcelo Siqueira;Longin Jan Latecki;Nicholas Tustison;Jean Gallier;James Gee

  • Affiliations:

  • Departamento de Computação e Estatística, Universidade Federal de Mato Grosso do Sul, Campo Grande, Brazil 79070-900;Department of Computer and Information Sciences, Temple University, Philadelphia, USA 19122;Penn Image and Computing Sciences Laboratory, Department of Radiology, University of Pennsylvania, Philadelphia, USA 19104;Department of Computer and Information Science, University of Pennsylvania, Philadelphia, USA 19104;Penn Image and Computing Sciences Laboratory, Department of Radiology, University of Pennsylvania, Philadelphia, USA 19104

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2008

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Abstract

We present here a new randomized algorithm for repairing the topology of objects represented by 3D binary digital images. By "repairing the topology", we mean a systematic way of modifying a given binary image in order to produce a similar binary image which is guaranteed to be well-composed. A 3D binary digital image is said to be well-composed if, and only if, the square faces shared by background and foreground voxels form a 2D manifold. Well-composed images enjoy some special properties which can make such images very desirable in practical applications. For instance, well-known algorithms for extracting surfaces from and thinning binary images can be simplified and optimized for speed if the input image is assumed to be well-composed. Furthermore, some algorithms for computing surface curvature and extracting adaptive triangulated surfaces, directly from the binary data, can only be applied to well-composed images. Finally, we introduce an extension of the aforementioned algorithm to repairing 3D digital multivalued images. Such an algorithm finds application in repairing segmented images resulting from multi-object segmentations of other 3D digital multivalued images.