A certified reduction strategy for homological image processing

  1. Poza, M. 1
  2. Dominguez, C. 1
  3. Heras, J. 2
  4. Rubio, J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 University of Dundee
    info

    University of Dundee

    Dundee, Reino Unido

    GRID grid.8241.f

Journal:
ACM Transactions on Computational Logic

ISSN: 1529-3785

Year of publication: 2014

Volume: 15

Issue: 3

Pages: 23

Type: Article

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Summary

The analysis of digital images using homological procedures is an outstanding topic in the area of Computational Algebraic Topology. In this paper, we describe a certified reduction strategy to deal with digital images, but preserving their homological properties. We stress both the advantages of our approach (mainly, the formalisation of the mathematics allowing us to verify the correctness of algorithms) and some limitations (related to the performance of the running systems inside proof assistants). The drawbacks are overcome using techniques that provide an integration of computation and deduction. Our driving application is a problem in bioinformatics, where the accuracy and reliability of computations are specially requested