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A parallel Homological Spanning Forest framework for 2D topological image analysis.

Fernando Diaz-Del-Rio1, Pedro Real2, Darian M Onchis3,4

  • 1Computer Architecture and Technology Department, University of Seville, Avda. Reina Mercedes s/n, Seville 41012, Spain.

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Summary
This summary is machine-generated.

This study introduces an efficient parallel algorithm for topological analysis of 2D digital objects using primal-dual abstract cell complexes. The framework maximizes parallelization for faster image processing on modern architectures.

Keywords:
2D digital imageComputational algebraic topologyHomological Spanning ForestParallel algorithmPrimal–dual abstract cell complexTopological analysis

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Area of Science:

  • Computer Vision
  • Digital Image Processing
  • Computational Topology

Background:

  • Topological analysis of 2D digital objects is crucial for image understanding.
  • Existing frameworks may not fully leverage parallel processing capabilities.
  • Efficient algorithms are needed for real-time applications.

Purpose of the Study:

  • To develop efficient algorithmic solutions for topological interrogation of 2D digital objects.
  • To maximize parallelization in topological analysis using pixel-level processing.
  • To adapt topological tools for efficient parallel implementation on various architectures.

Main Methods:

  • Utilized a primal-dual abstract cell complex (pACC) as the mathematical model.
  • Extended the concept of abstract cell complexes for parallel processing.
  • Employed combinatorial operations to transform symmetric pACC to asymmetric ones.
  • Focused on 4-adjacency for pixel connectivity in 2D objects.

Main Results:

  • Developed a framework for parallel topological analysis and recognition of 2D digital objects.
  • Maximized degree of parallelization by using pixel-level processing units.
  • Transformed fundamental topological tools for efficient parallel implementation.
  • Built a software prototype to model the parallel framework.

Conclusions:

  • The proposed framework enables efficient parallel topological interrogation of 2D digital images.
  • The pACC data structure supports Homological Spanning Forests for topological analysis.
  • The methods are suitable for implementation on GPUs, multi-threaded computers, and SIMD kernels.