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Enhanced Parallel Generation of Tree Structures for the Recognition of 3D Images

  • P. RealEmail author
  • H. Molina-Abril
  • F. Díaz-del-Río
  • S. Blanco-Trejo
  • D. Onchis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11524)

Abstract

Segmentations of a digital object based on a connectivity criterion at n-xel or sub-n-xel level are useful tools in image topological analysis and recognition. Working with cell complex analogous of digital objects, an example of this kind of segmentation is that obtained from the combinatorial representation so called Homological Spanning Forest (HSF, for short) which, informally, classifies the cells of the complex as belonging to regions containing the maximal number of cells sharing the same homological (algebraic homology with coefficient in a field) information. We design here a parallel method for computing a HSF (using homology with coefficients in \(\mathbb {Z}/2\mathbb {Z}\)) of a 3D digital object. If this object is included in a 3D image of \(m_1\times m_2 \times m_3\) voxels, its theoretical time complexity order is near \(O(log(m_1+m_2+m_3))\), under the assumption that a processing element is available for each voxel. A prototype implementation validating our results has been written and several synthetic, random and medical tridimensional images have been used for testing. The experiments allow us to assert that the number of iterations in which the homological information is found varies only to a small extent from the theoretical computational time.

Keywords

3D digital images Parallel computing Abstract cell complex Homological Spanning Forest Crack transport 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • P. Real
    • 1
    Email author
  • H. Molina-Abril
    • 1
  • F. Díaz-del-Río
    • 1
  • S. Blanco-Trejo
    • 2
  • D. Onchis
    • 3
  1. 1.H.T.S. Informatics’ EngineeringUniversity of SevilleSevilleSpain
  2. 2.Dpto. Ingeniería Aeroespacial y Mecánica de FluidosUniversity of SevilleSevilleSpain
  3. 3.Faculty of MathematicsUniversity of ViennaViennaAustria

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