Abstract
In this paper, we present a formalization of an algorithm to construct admissible discrete vector fields in the Coq theorem prover taking advantage of the SSReflect library. Discrete vector fields are a tool which has been welcomed in the homological analysis of digital images since it provides a procedure to reduce the amount of information but preserving the homological properties. In particular, thanks to discrete vector fields, we are able to compute, inside Coq, homological properties of biomedical images which otherwise are out of the reach of this system.
Partially supported by Ministerio de Educación y Ciencia, project MTM2009-13842-C02-01, and by the European Union’s 7th Framework Programme under grant agreement nr. 243847 (ForMath).
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Heras, J., Poza, M., Rubio, J. (2012). Verifying an Algorithm Computing Discrete Vector Fields for Digital Imaging. In: Jeuring, J., et al. Intelligent Computer Mathematics. CICM 2012. Lecture Notes in Computer Science(), vol 7362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31374-5_15
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