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Topological Repairing of 3D Digital Images

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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.

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Authors and Affiliations

  1. Departamento de Computação e Estatística, Universidade Federal de Mato Grosso do Sul, Av. Costa e Silva, S/N, Campus Universitário, Campo Grande, MS, 79070-900, Brazil

    Marcelo Siqueira

  2. Department of Computer and Information Sciences, Temple University, Philadelphia, PA, 19122, USA

    Longin Jan Latecki

  3. Penn Image and Computing Sciences Laboratory, Department of Radiology, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Nicholas Tustison & James Gee

  4. Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Jean Gallier

Authors
  1. Marcelo Siqueira
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  2. Longin Jan Latecki
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  3. Nicholas Tustison
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  4. Jean Gallier
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  5. James Gee
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Correspondence to Marcelo Siqueira.

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Siqueira, M., Latecki, L.J., Tustison, N. et al. Topological Repairing of 3D Digital Images. J Math Imaging Vis 30, 249–274 (2008). https://doi.org/10.1007/s10851-007-0054-1

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  • DOI: https://doi.org/10.1007/s10851-007-0054-1

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